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The 666 symbol is actually referring to today's neo-con Christianity and Zionism!

1-  What does the Bible say, and what does the modern-day Greek say that makes it equal to 666?
2-  Images and Proofs.

(a)-  Christianity's Sacred Symbols.

-  The following X I C is the original writing of the Chi Xi and Stigma from Revelation 13:18.  The following image-document is called Papyrus 115.  It doesn't even resemble the Xi and Stigma in Χ ξ ς .  These latter ones Χ ξ ς  came more than 1000 years later, even much later than Islam.  See the rebuttal by a Christian in the article, below.

 X I C These letters in Greek are: chi, iota, stigma.

-  The 666 lie that was invented 1,000 years after Jesus.

3-  The evil Zionist machine will rule the entire earth! (Islamic Prophecy)

(a)-  Albert Pike's letters [1] prove that the Zionists were behind World Wars I, II and the upcoming III.

 "The First World War must be brought about in order to permit the Illuminati to overthrow the power of the Czars in Russia and of making that country a fortress of atheistic Communism. The divergences caused by the "agentur" (agents) of the Illuminati between the British and Germanic Empires will be used to foment this war. At the end of the war, Communism will be built and used in order to destroy the other governments and in order to weaken the religions."   "The Second World War must be fomented by taking advantage of the differences between the Fascists and the political Zionists. This war must be brought about so that Nazism is destroyed and that the political Zionism be strong enough to institute a sovereign state of Israel in Palestine. During the Second World War, International Communism must become strong enough in order to balance Christendom, which would be then restrained and held in check until the time when we would need it for the final social cataclysm."   "The Third World War must be fomented by taking advantage of the differences caused by the "agentur" of the "Illuminati" between the political Zionists and the leaders of Islamic World. The war must be conducted in such a way that Islam (the Moslem Arabic World) and political Zionism (the State of Israel) mutually destroy each other.

 Israel vs. Daniel, Jesus and Palestine:    Jesus in Matthew 24 referenced Daniel 11.  The headquarters of the evil shepherd will be from Jerusalem to the Mediterranean sea.  That is precisely Israel today:    Daniel 11:45: "(the evil one) will establish his settlement between Mount Zion (Jerusalem) and the Mediterranean sea.  Then he will be destroyed, and no one will be able to save him."      www.answering-christianity.com/911_is_the_biggest_lie.htm  (9/11 was 100% an Israeli mossad and CIA job) Thermite melted the pillars:     Thermite causes the metal to burn wildly, and if you pour water on it, it will be enraged even more.  Airplanes do not carry thermite!  Thermite was used to bring down the Twin Towers on 9/11/2001 by the Israeli Mossad and CIA. Daniel 11:45: "(the evil one) will establish his settlement between Mount Zion (Jerusalem) and the Mediterranean sea.  Then he will be destroyed, and no one will be able to save him."    Dust blower: Also, the Paris attack Israeli Mossad and CIA lie.  The machine gun was a dust blower.  The terrorist shot flour or white-dust at the Israeli agent.  Notice how the shot-agent's right arm and hand is reaching inside to the collar.  This is all after he got his brain blown out at point blank range by the terrorist's lethal children's nerf gun.  No instant paralysis, no instant death, no blood, bones and flesh splashed mess, no pain:         Also, the following images are from the Boston bombing Israeli Mossad and CIA Photoshop-patch lie [1] [2]:     Videos: [1] [2] 911 | Boston | Woolwich | Canada  | ISIS | Paris | 666 | Racism | Blog    More details and verses on this here....

(b)-  Zionist symbols in
Saudi Arabia and the United States Seal.
(c)-  The Islamic Prophecy about the
Horn of Satan will come from Saudi Arabia.

4-  Islam is the Original Faith to all of mankind.
5-  Conclusion.

Detailed rebuttals to Walid Shoebat's lies:

The ones that Walid Shoebat used are in the C19 Italian facsimile of the Codex, which came 1000 years after.  Read below in this table.

Also, please click on the links for the detailed and thorough rebuttals to the charlatan and fraud [2] [3] [4] [5], Walid Shoebat.  Many rebuttals to this charlatan and fraud are also included in the link.  CNN thoroughly exposed this fraud, and also proved that he WAS NOT a former terrorist as he claims.  Also visit:

•
Also in the following rebuttal, you'll clearly see the proofs that Revelation 13:18's ORIGINAL GREEK TEXT was the following:

X I C

Again, these letters in Greek are: chi, iota, stigma.

The following one that is widely used by the anti-Islamics is a MODIFIED GREEK TEXT that came more than 1000 years later, even much later after Islam:

These letters in the more than 1000-years-later Greek are: chi, xi, stigma.  There is a massive difference between the iota and the xi.  And there is a big difference between the two stigmas.

The following rebuttal by Richard Bartholomew thoroughly demonstrates this.

Richard Bartholomew thoroughly refutes Walid Shoebat on 666 being Islam:

Richard Bartholomew demonstrates that Walid Shoebat lied about the 666 [2] in his drawings:

"Apparently Shoebat has been promoting this “theory” for a few years, and it appears in an obscure book by a certain Simon Altaf, entitled Islam: Peace? or Beast? (Altaf and Shoebat collaborated on an equally obscure book, entitled This is our Eden, This is our End.) Some details are here (and more at sites such as this one), including the supposed evidence, from the Codex Vaticanus

One website adds the unpromising caption:

Very Old Text (Rev. 13:18) in glass display at Bob Jones University Library – Greenville, S.C.

One small problem however, is that the Codex Vaticanus does not include the Book of Revelation. The above is from a much later supplement, and the Greek is in a ”miniscule” script which came in only centuries later. Irenaeus in the Second Century discusses the text as consisting of the number “666″, and there are no fragments of Revelation which predate this source: therefore any ancient copies we have must have been written by scribes who certainly intended to write Greek characters."  (Source)

Mr.  further referenced the following article:

# The Other Number of the Beast: 616

## P.Oxy. LVI 4499

The newest volume of Oxyrhynchus Papyri contains a fragmentary papyrus of Revelation which is the earliest known witness to some sections (late third / early fourth century). A detailed discussion of its place in the MS tradition is given in the printed volume. You will find images at 150dpi and 300dpi in the papyri section of this site, accessible from the main menu.

One feature of particular interest is the number that this papyrus assigns to the Beast: 616, rather than the usual 666. (665 is also found.) We knew that this variant existed: Irenaeus cites (and refutes) it. But this is the earliest instance that has so far been found. The number — chi, iota, stigma (hexakosiai deka hex) — is in the third line of the fragment shown below. But why does it matter what the number is? For that, we have to turn to ancient Greek ideas about numerology.

And in another quote in one of his replies on his blog, Mr. Richard Bartholomew also said:

"Eh? We don’t have anything that was written in the author’s own hand. The earliest Greek fragment gives Greek symbols – although they don’t look like Shoebat’s nonsensical presentation – while others (such as the Codex Sinaiticus) spell it out as a word. And the section added to the Codex Vaticanus more than a thousand years after it was created is neither here nor there. There is no need for John to “guess” future Greek symbols, as the context shows that he was obviously talking about a number, and that was how early Christians understood it.

It’s bizarre that conservative Evangelicals, who generally insist that Scripture should not be deconstructed in any way, are prepared to re-write part of the Bible just to fit anti-Muslim sentiments."
(Source)

And in a reply to a poster, Mr. Richard Bartholomew also said regarding the new modified Greek that we have today:

"…by about more than a 1000 years!

You and Shoebat appear to have confused the ancient manuscript with a
C19 Italian facsimile of the Codex which has an (obviously) typeset copy of Revelation tacked on the end. I’ve now dicussed this here."  (Source)

Conjecture:

"Jesus Messiah and his Israelite disciples would have rejected the nonsense of a beast mark 666, 656 or 616 to be written in greek alphabets.

However it seems that Holy Spirit disagrees, and so He introduced arabic typeset to the Greek letters in the 19th century. And waits for another few hundreds year to finally enter the bodies of Shoebat and pals giving them guidance and knowledge about the mark of the beast."

Well put, dear brother Submit.  This is the type of garbage one gets from the yapping quacks of the religions of conjecture.  This is precisely what Allah Almighty summed up Christianity:

[004:157]  And for their saying, `We did slay the Messiah, Jesus, son of Mary, the Messenger of ALLAH;' whereas they slew him not, nor did they bring about his death upon the cross, but he was made to appear to them like one crucified; and those who differ therein are certainly in a state of doubt about it; they have no certain knowledge thereof, but only pursue a conjecture; and they did not arrive at a certainty concerning it.

Take care,
Osama Abdallah

 Walid Shoebat's frauds thoroughly exposed by CNN: Walid Shoebat the Fraud exposed by CNN's Anderson Cooper & Andrew Griffin [1] [2] [3] [4] [5].  CNN did a thorough investigation on this fraud's taxes and questionable charities, and they demonstrated his lies and fraudulent activities. They also did a thorough investigation, in Israel, about the place he claims to have bombed, and that he spent two weeks in jail, in Israel. It turns out, these claims are all false, and Israel confirmed to CNN that this fraud was never arrested by them, nor was the place ever bombed! And besides, how could you only spend 2 weeks in jail, and be released without any charge or court appearance, according to him, for bombing a place anyway?! Also, Walid Shoebat is a hateful charlatan [2] [3] [4] [5] [6].  CNN thoroughly exposed this fraud, and also proved that he WAS NOT a former terrorist as he claims.

Israel vs. Daniel, Jesus and Palestine:

1-  What does the Bible say, and what does the Greek say that makes it equal to 666?

Let us look at what the Bible says:

Revelation 13
The Beast out of the Sea
1 The dragon [a] stood on the shore of the sea. And I saw a beast coming out of the sea. It had ten horns and seven heads, with ten crowns on its horns, and on each head a blasphemous name.
2 The beast I saw resembled a leopard, but had feet like those of a bear and a mouth like that of a lion. The dragon gave the beast his power and his throne and great authority.
3 One of the heads of the beast seemed to have had a fatal wound, but the fatal wound had been healed. The whole world was filled with wonder and followed the beast.

4 People worshiped the dragon because he had given authority to the beast, and they also worshiped the beast and asked, “Who is like the beast? Who can wage war against it?”

5 The beast was given a mouth to utter proud words and blasphemies and to exercise its authority for forty-two months.
6 It opened its mouth to blaspheme God, and to slander his name and his dwelling place and those who live in heaven.
7 It was given power to wage war against God’s holy people and to conquer them.
And it was given authority over every tribe, people, language and nation.
8 All inhabitants of the earth will worship the beast—all whose names have not been written in the Lamb’s book of life, the Lamb who was slain from the creation of the world. [b]
9 Whoever has ears, let them hear.
10
“If anyone is to go into captivity,
into captivity they will go.
If anyone is to be killed [c] with the sword,
with the sword they will be killed.” [d]

This calls for patient endurance and faithfulness on the part of God’s people.

The Beast out of the Earth
11 Then I saw a second beast, coming out of the earth. It had two horns like a lamb, but it spoke like a dragon.
12 It exercised all the authority of the first beast on its behalf, and made the earth and its inhabitants worship the first beast, whose fatal wound had been healed.
13 And it performed great signs, even causing fire to come down from heaven to the earth in full view of the people.
14 Because of the signs it was given power to perform on behalf of the first beast, it deceived the inhabitants of the earth. It ordered them to set up an image in honor of the beast who was wounded by the sword and yet lived.
15 The second beast was given power to give breath to the image of the first beast, so that the image could speak and cause all who refused to worship the image to be killed.

16 It also forced all people, great and small, rich and poor, free and slave, to receive a mark on their right hands or on their foreheads,
17
so that they could not buy or sell unless they had the mark, which is the name of the beast or the number of its name.

18 This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. [e] That number is 666.

Footnotes:
a. Revelation 13:1 Some manuscripts And I
b. Revelation 13:8 Or written from the creation of the world in the book of life belonging to the Lamb who was slain
c. Revelation 13:10 Some manuscripts anyone kills
d. Revelation 13:10 Jer. 15:2
e. Revelation 13:18 Or is humanity’s number

There are a few points to notice here:

1-  In verse 2 above, the dragon is the ruler of the beast.  This means satan is the ruler of the evil system that will rule the earth.

2-  In verse 7 above, the whole world will be eventually ruled by the evil and blasphemous beast.

3-  In verse 11 above, the beast had two horns like a lamb, but it spoke like a dragon.  This means that he will look like Christ, but he will be evil.  Christ is referred to as the lamb in the Bible, and here we see satan is referred to as the dragon.

4-  In verses 16-18 above, the people of the earth will receive the mark of the beast, to be part of his system, in order for them to be able to buy and sell.  Otherwise, they won't be allowed to buy and sell.  They won't be part of the system.  And his mark's value is equal to 666.  These are the modern-day Greek characters: Χ ξ ς, but let us analyze them in details.  Here is their image in case your fonts don't display them properly:

Image:

Text:

Χ  is the Greek letter "chi" (pronounced as kai), and it has the numerical value 600.

ξ  is the Greek letter "xi" (pronounced as zee), and it has the numerical value 60.

ς  is the Greek letter "stigma", and it has the numerical value 6.

Let us now take a look at some of Christianity's sacred symbols in the next section.

2-  Images and Proofs:

(a)-  Christianity's Sacred Symbols:

The original symbols are the XIC ones.  The ones that Walid Shoebat used are in the C19 Italian facsimile of the Codex, which came 1000 years after.

The original Chi, Xi and Stigma don't look like the modern-day ones.  The following document is called Papyrus 115, and it is the original writing of the 666 in Revelation 13:18.  It is not chi, xi, stigma.  These came more than 1000 years after, even many centuries after Islam.  The original letters are chi, iota, stigma.  The original doesn't even resemble the modern-day Xi and Stigma in: Χ ξ ς :

"Papyrus 115 (P. Oxy. 4499, designated by $\mathfrak{P}$115 in the Gregory-Aland numbering) is a fragmented manuscript of the New Testament written in Greek on papyrus. It consists of 12 fragments of a codex containing parts of the Book of Revelation. It dates to the 3rd century, ca. 225-275 AD.[1] Grenfell and Hunt discovered the papyrus at Oxyrhynchus, Egypt.
.......
An interesting textual variant of P115 is that it gives the
number of the beast as 616 (chi, iota, stigma (ΧΙϚ)), rather than the majority reading of 666 (chi, xi, stigma (ΧΞϚ)), as does Codex Ephraemi Rescriptus."  (Source)

And for Codex Ephraemi Rescriptus, we read:

""The number of the beast" it reads hexakosiai deka hex (lit. six hundred sixteen);[28] it is one of the most famous readings of the codex, it is also attested by Papyrus 115.[29](Source)

28. ^ Herman C. Hoskier, Concerning the Text of the Apocalypse, vol. 2, p. 364.
29.
^ Metzger, Bruce M.; Ehrman, Bart D. (2005). The Text of the New Testament: Its Transmission, Corruption and Restoration. New York – Oxford: Oxford University Press. p. 61. ISBN 978-0-19-516122-9.

X I C

Let us look at some of Christianity's sacred symbols.  Notice the Chi, and Xi wrapped around it:

This image is one of Christianity's earliest symbols, and it is called the Chi-Rho Symbol.  The symbol is also known as the Labarum Symbol.  The following is Constantine's coin.  Notice the Chi-Rho symbol in it, and also the snake:

Notice in this images the Chi, Xi and Stigma Greek letters Χ ξ ς from the Vatican and the United Nations:

Also visit:

•

(b)-  The Israeli 666 Symbol:

The 666 hand gesture or sign [2] [3] is particularly popular among Western Jews (the Zionists among them), and its' one of the NWO (New World Order) Symbols:

Never forget that 9/11 was 100% an Israeli Mossad Operation.

Also the Israeli Satanic ONE-EYE, the New World Order's (NWO) hand gesture:

Click on the following image to enlarge:

The evil zionist machine will reach "Mighty Heights" علوا كبيرا  of evil power and might on earth [1].  See Noble Verses 17:4-8 from the Glorious Quran:

Also visit:

Why is Saudi Arabia zionising Mecca and itself?
See how they're directly violating Islam!

The United States Seal has 666 clearly written in it!

Matthew 24:25-27: Jesus will from Syria.  Mentioned in the Bible and Islam.

The Israeli 666 symbol

Also, George Washington's hand gestures and being shirtless and resembling one of the Israeli Masonic gods,
Baphomet Grove, is also covered in the link.  See Main Section #2, below.

| 1john 2:22-23 | | | 666| Dividing Israel

Also, of non-Muslims and Muslims according to the Glorious Quran's Prophecy.

Zionist Israel will rule the earth with Mighty Evil!  (Islamic Prophecy)

The Jews will come from many lands to Palestine Prophecy.

See also Daniel Prophecies about Israel and its map.  Prophet Daniel said: "(the anti-Christ) will settle between Mont Zion (Jerusalem) and the Mediterranean sea".  That is precisely Israel today!

Furthermore, the modern-day symbol of the Trilateral Commission, which is a Zionist Entity of the New World Order, is the 666:

George Washington's hand gestures and being shirtless and resembling one of the Israeli Masonic gods, Baphomet Grove:

The following images and text about George Washington being shirtless are found at:

• http://www.oldnavalhospital.org/bowen_01.html
• http://www.oldnavalhospital.org/bowen_20.html
•

Click on any of the two images to enlarge:

### Title Page & Page 14 in Image and Text:

Title Page:

U.S. NAVAL HOSPITAL, WASHINGTON, D.C.

Ninth St. and Pennsylvania Avenue, S.E.

[Commissioned October 1, 1866]

E. Caylor Bowen, Editor

Transplantation Research Program Center

Naval Medical Research Institute

Naval Medical Command, National Capital Region

Bethesda, Maryland

Page 14: (underline emphasis below in the image is mine)

It was at the wharves of the Washington Navy Yard, in about 1841, that Horatio Greenough’s twelve-ton marble statue of George Washington arrived aboard a man-of-war from Florence, Italy. Commissioned by Congress as a tribute to President Washington, Congressmen and dignitaries were horrified to see that the nation’s great hero had been carved, sitting in a chair, nude to the waist. The pose is from the ancient Greek sculptor Phidias’ Zeus (c. 500-432 B.C.), chief god of the Greeks, and ruler of the heavens. General Henry Wise, a Virginia statesman, remarked at the time, “The man does not live, and never did live, who saw Washington without his shirt.” The statue was placed in the rotunda of the Capitol until 1843, when it was moved to the Capitol grounds; in 1908, it was placed in the Smithsonian Institution, where it is now on exhibit on the second floor of the National Museum of American History.

### U.S. Naval Hospital – Square 948

From the early records of 1802, we learn that Dr. John Bullus, a naval surgeon, and under orders form the Secretary of the Navy, prepared chests of medicines and surgical instruments for naval ships at the yard and for shore stations. He also examined applicants for service in the medical corps and was in charge of a small apothecary shop at the corner of Pennsylvania Avenue and 9th Street, southeast, built for the convenience of the public. Across form the shop, on the southwest corner, was Tunnicliff’s tavern, built in 1795. Later, known as the Eastern Branch Hotel, it was closed in 1821 and became continued on page 17)

3-  The evil Zionist machine will rule the entire earth! (Islamic Prophecy)

There are so many End of Times Prophecies that Islam made.  Here is the most important one of them, and the most unique one to Prophet Muhammad, peace be upon him:

• These links contain ample points and Noble Verses and other links that demonstrate the Islamic Prophecy in great details.

(a)-  Albert Pike's letters prove that the Zionists were behind World Wars I, II and the upcoming III:

This is discussed on this website's blog at:

• DISCLAIMER:  This is not generalizing all Jews.  See the Righteous Jews in the Glorious Quran [1] [2].  Besides, there are also many Jews who are 100% against the evil zionist Israel, which is the evil star of Lucifer (satan) and the Synagogue of Satan.  The latter two descriptions come straight from the Bible.  See verses below.  This article clearly proves, with ample eye witnesses and evidence, that 9/11 was 100% an Israeli Mossad Operation!

Albert Pike 100+ years ago architected WWI, WWII, and WWIII wars, where the latter will be between the "West" and the "Islamic World".  See his letters [1]:

 "The First World War must be brought about in order to permit the Illuminati to overthrow the power of the Czars in Russia and of making that country a fortress of atheistic Communism. The divergences caused by the "agentur" (agents) of the Illuminati between the British and Germanic Empires will be used to foment this war. At the end of the war, Communism will be built and used in order to destroy the other governments and in order to weaken the religions."   "The Second World War must be fomented by taking advantage of the differences between the Fascists and the political Zionists. This war must be brought about so that Nazism is destroyed and that the political Zionism be strong enough to institute a sovereign state of Israel in Palestine. During the Second World War, International Communism must become strong enough in order to balance Christendom, which would be then restrained and held in check until the time when we would need it for the final social cataclysm."   "The Third World War must be fomented by taking advantage of the differences caused by the "agentur" of the "Illuminati" between the political Zionists and the leaders of Islamic World. The war must be conducted in such a way that Islam (the Moslem Arabic World) and political Zionism (the State of Israel) mutually destroy each other.

(b)-  Zionist symbols in Saudi Arabia and the United States Seal:

In this video, the following two points are exposed:

• Why is Saudi Arabia zionising Mecca and itself?  See how they're directly violating Islam!

• The United States Seal has 666 clearly written in it!

• The video was taken from: http://www.youtube.com/DaveAbdellah, and it will shed the light on some of the serious issues with Saudi Arabia and the United States Government.  And here are some snapshots from the video:

1-  The United States Seal and the 666 Symbol:

2-  Some of Saudi Arabia's Government Zionist Logos:

3-  The zionising of the Holy City of Mecca.  The Saudi government has removed the obelisk pillar, which was a representation of satan that the Muslims would stone each with 7 stones, and replaced it with a mere wall.  Is it because the obelisk pillar is one of the zionist machine's symbols of today? [1]

Again, please see the video that I linked above for a good demonstration of the the following two points:

• Why is Saudi Arabia zionising Mecca and itself?  See how they're directly violating Islam!

• The United States Seal has 666 clearly written in it!

• And again, the video was taken from: http://www.youtube.com/DaveAbdellah, and it will shed the light on some of the serious issues with Saudi Arabia and the United States Government.  The above are nothing short of satanic symbols in many of Saudi Arabia's government and Islamic places.

(c)-  The Islamic Prophecy about the Horn of Satan will come from Saudi Arabia:

This Prophecy is covered in great details at: www.answering-christianity.com/ac11.htm#links (Islamic cults section).

4-  Islam is the Original Faith to all of mankind:

This is thoroughly demonstrated and prove at: https://www.answering-christianity.com/ac.htm#capsule:

 The original believers were called Muslims: [1] 1- The believers' title was always Muslims.  Salamays, Mushlams, Mushlemanies, etc...  This is also where we get Shalom from.  It is SALAM.  The Jews' deficient tongue pronouces the S as SH and the soft A as O.  This is similar to those who pronounce the W as V in India, and the TH as Z in Europe and elsewhere. 2- Moses' in-laws from Jethro and others were Salamays and Muslimays (video).  Believers also during Adam, Noah and Abraham's times were also called Muslims.  You can think of them as Arabia's Muwahiddeen (monotheists) before Prophet Muhammad became a Prophet. 3- Allah Almighty called Islam SELM or SILM [1] in the Glorious Quran. Because indeed, the religion before Allah Almighty is Islam, as He said, and before Prophet Muhammad it was called also Selm or silm. 4- Jesus also in the Bible called the believer's title Mushlem.  The English translators falsely translate it as "perfect". Peace be upon all of the Prophets of Allah Almighty.  Please visit: www.answering-christianity.com/ac.htm#capsule

5-  Conclusion:

The hateful and desperate bigots of the neo-cons have nothing on Islam.  They are no more than evil servants to the evil Zionist machine, which is responsible for much of the world's bloodsheds and corruption.  What bothers me from many of these modern-day neo-cons is that they are so desperate to become servants to the evil Israel that they are more than willing to:

1. Lie on their own scriptures to cover up to and support the evil zionist machine that is ruling them.

2. Make bold lies about Islam and Muslims just to please the Synagogue of Satan as the Bible calls them.

3. Not only not care about the innocents who died from the evil WARS & LIES of the zionists, but the neo-cons are more than willing to flush the blood of their very own brethrens away just to appease their masters and lords, the Zionists.  An example of this is their continuous cover ups and lies about the 9/11 attacks by blaming it on the Muslims.  9/11 was 100% an Israeli Mossad Operation!  The Muslims had nothing to do with 9/11.  Al-Qaeda is 100% a Zionist CIA agency, and its members are Yemeni and other Middle Eastern Jews.  This is why you've never seen Osama bin Laden's body after he was supposedly "killed".  Read Albert Pike's (one of the zionist leaders) letters in the early 1900's and see the grand Zionist conspiracy against the entire world to push the world into massacring each others.  This is who they will bring the rule of Lucifer's "religion" to dominate the entire world under their New World Order.

Another insult to their own brethrens are the pictures of the so-called holocaust.  Now while many innocent Jews have died in the holocaust, but not all of the tortured and maimed and baked and starved people were Jews.  Far too many of them were ordinary Christians from neighboring countries to Germany.  Not to mention also that many Muslims in Russia also were killed from the Nazis.

Islam is the Divine Truth.  Islam is GOD Almighty's Original Faith to mankind.  And all anti-Islamics are on their way to the Eternal Doom of Hell.  Again, please visit: The Israeli 666 symbol above.

Indeed, all Praise and Glory are due to Allah Almighty alone for making the Noble Quran be the Perfect and Everlasting Miracle, for us humans, out of all of His Divine Miracles!  And may Allah Almighty send His Peace, Mercy and Blessings upon our Beloved and Blessed Prophet, Teacher and Role Model, Muhammad.  Ameen.

DISCLAIMER:  This is not generalizing all Jews.  See the Righteous Jews in the Glorious Quran [1] [2].  Besides, there are also many Jews who are 100% against the evil zionist Israel, which is the evil star of Lucifer (satan) and the Synagogue of Satan.  The latter two descriptions come straight from the Bible.  See verses below.  This article clearly proves, with ample eye witnesses and evidence, that 9/11 was 100% an Israeli Mossad Operation!

Albert Pike 100+ years ago architected WWI, WWII, and WWIII wars, where the latter will be between the "West" and the "Islamic World".  See his letters [1]:

 "The First World War must be brought about in order to permit the Illuminati to overthrow the power of the Czars in Russia and of making that country a fortress of atheistic Communism. The divergences caused by the "agentur" (agents) of the Illuminati between the British and Germanic Empires will be used to foment this war. At the end of the war, Communism will be built and used in order to destroy the other governments and in order to weaken the religions."   "The Second World War must be fomented by taking advantage of the differences between the Fascists and the political Zionists. This war must be brought about so that Nazism is destroyed and that the political Zionism be strong enough to institute a sovereign state of Israel in Palestine. During the Second World War, International Communism must become strong enough in order to balance Christendom, which would be then restrained and held in check until the time when we would need it for the final social cataclysm."   "The Third World War must be fomented by taking advantage of the differences caused by the "agentur" of the "Illuminati" between the political Zionists and the leaders of Islamic World. The war must be conducted in such a way that Islam (the Moslem Arabic World) and political Zionism (the State of Israel) mutually destroy each other.

See also Daniel Prophecies about Israel and its map.  Prophet Daniel said: "Satan will settle between Mont Zion (Jerusalem) and the Mediterranean sea".  That is precisely Israel today!

Also, of non-Muslims and Muslims according to the Glorious Quran's Prophecy.

Zionist Israel will rule the earth with Mighty Evil!  (Islamic Prophecy)

Islamic Prophecy:  The dajjal (anti-Christ) will command the sky to rain, and it will rain.  And he will command the sky to cause drought, and it will cause drought.

The Islamic Prophecy about the Horn of Satan will come from Saudi Arabia.  (Islamic cults section).

Dhul Qarnayn's story.  Sunrise and sunset.  Also Why حمئة and not حاميةٍ.  Dhil Qarnayn's journey is detailed with scientific and geographical maps that are more 1000 years old.

• The sunsetless North Pole Miracle in the Glorious Quran [1].
• Sunrise and sunset in the Hadiths.
• The iron gates of Dhul Qarnayn were found.
• The overwhelming Scientific and Numerical Miracles in the Glorious Quran.
• The North and South Poles, and Prayer and Fasting Times.
•

What is the best way to convert a non-Muslim to Islam?

What is the place of Jews, Christians and non-Muslims in Islam.

Rebuttals to Walid Shoebat section.

Does the Bible predict the dividing of Israel?  Who are the nations that divided Israel?  And what will be their punishment?

Prophet Muhammad said that Jesus will return from Damascus, and the Bible in Matthew 24:25-27 fully supports it.

The ONE-EYED Dajjal's Signs and Powers according to Islam:

• Also, Man spoiling the land and sea and him will suffer on earth from it are prophesied in the Glorious Quran.

• Corruptions and Catastrophes on land and sea, done by men, is Prophesied in the Glorious Quran and confirmed by Science!

• I added new sections, and many new Hadiths and Noble Verses and proofs about the Dajjal, and proved that it is today's Zionist Machine, according to Islam.
•

Contradictions and proofs of Historical Corruptions in the Bible.

Why did Allah Almighty allow for the Bible to get corrupted?

Is the substitution of name "Ishmael" with "Isaac" within the Biblical text a matter of great consequential significance for the followers of Jesus?

Missing 2.3 Trillion Dollars is one of the main causes for 9/11
Donald Rumsfeld admitted \$2.3 Trillion missing on 9/10/2001;
one day before 9/11!!

 Walid Shoebat's frauds thoroughly exposed by CNN: Walid Shoebat the Fraud exposed by CNN's Anderson Cooper & Andrew Griffin [1] [2] [3] [4] [5].  CNN did a thorough investigation on this fraud's taxes and questionable charities, and they demonstrated his lies and fraudulent activities. They also did a thorough investigation, in Israel, about the place he claims to have bombed, and that he spent two weeks in jail, in Israel. It turns out, these claims are all false, and Israel confirmed to CNN that this fraud was never arrested by them, nor was the place ever bombed! And besides, how could you only spend 2 weeks in jail, and be released without any charge or court appearance, according to him, for bombing a place anyway?! Also, Walid Shoebat is a hateful charlatan [2] [3] [4] [5] [6].  CNN thoroughly exposed this fraud, and also proved that he WAS NOT a former terrorist as he claims.

Also Visit:

Matthew 24:25-27: Jesus will from Syria.  Mentioned in the Bible and Islam.

Israel vs. Daniel, Jesus and Palestine:


text:
## CryptoDB

### Brent Waters

#### Publications

Year
Venue
Title
2023
PKC
In this work, we present the first construction of a fully non-interactive publicly-verifiable delegation scheme for committed programs. More specifically, we consider a setting where Alice is a trusted author who delegates to an untrusted worker the task of hosting a program $P$, represented as a Boolean circuit. Alice also commits to a succinct value based on $P$. Any arbitrary user/verifier without knowledge of $P$ should be convinced that they are receiving from the worker an actual computation of Alice's program on a given input $x$. Before our work, the only object known to imply this challenging form of delegation was a SNARG/SNARK for $\mathcal{NP}$. This is because from the point of view of the user/verifier, the program $P$ is an unknown witness to the computation. However, constructing a SNARG for $\mathcal{NP}$ from standard assumptions remains a major open problem. In our work, we show how to achieve delegation in this challenging context assuming only the hardness of the Learning With Errors (LWE) assumption, bypassing the apparent need for a SNARG for $\mathcal{NP}$.
2023
EUROCRYPT
Attribute-based encryption (ABE) generalizes public-key encryption and enables fine-grained control to encrypted data. However, ABE upends the traditional trust model of public-key encryption by requiring a single trusted authority to issue decryption keys. If an adversary compromises the central authority and exfiltrates its secret key, then the adversary can decrypt every ciphertext in the system. This work introduces registered ABE, a primitive that allows users to generate secret keys on their own and then register the associated public key with a "key curator" along with their attributes. The key curator aggregates the public keys from the different users into a single compact master public key. To decrypt, users occasionally need to obtain helper decryption keys from the key curator which they combine with their own secret keys. We require that the size of the aggregated public key, the helper decryption keys, the ciphertexts, as well as the encryption/decryption times to be polylogarithmic in the number of registered users. Moreover, the key curator is entirely transparent and maintains no secrets. Registered ABE generalizes the notion of registration-based encryption (RBE) introduced by Garg et al. (TCC 2018), who focused on the simpler setting of identity-based encryption. We construct a registered ABE scheme that supports an a priori bounded number of users and policies that can be described by a linear secret sharing scheme (e.g., monotone Boolean formulas) from assumptions on composite-order pairing groups. Our approach deviates sharply from previous techniques for constructing RBE and only makes black-box use of cryptography. All existing RBE constructions (a weaker notion than registered ABE) rely on heavy non-black-box techniques. The encryption and decryption costs of our construction are comparable to those of vanilla pairing-based ABE. Two limitations of our scheme are that it requires a structured reference string whose size scales quadratically with the number of users (and linearly with the size of the attribute universe) and the running time of registration scales linearly with the number of users. Finally, as a feasibility result, we construct a registered ABE scheme that supports general policies and an arbitrary number of users from indistinguishability obfuscation and somewhere statistically binding hash functions.
2023
EUROCRYPT
Decentralized multi-authority attribute-based encryption (MA-ABE) is a distributed generalization of standard (ciphertext-policy) attribute-based encryption where there is no trusted central authority: any party can become an authority and issue private keys, and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. We present the first multi-authority attribute-based encryption schemes that are provably fully-adaptively secure. Namely, our construction is secure against an attacker that may corrupt some of the authorities as well as perform key queries adaptively throughout the life-time of the system. Our main construction relies on a prime order bilinear group where the k-linear assumption holds as well as on a random oracle. Along the way, we present a conceptually simpler construction relying on a composite order bilinear group with standard subgroup decision assumptions as well as on a random oracle. Prior to this work, there was no construction that could resist adaptive corruptions of authorities, no matter the assumptions used. In fact, we point out that even standard complexity leveraging style arguments do not work in the multi-authority setting.
2023
EUROCRYPT
We obtain a black-box construction of non-interactive CCA commitments against non-uniform adversaries. This makes black-box use of an appropriate base commitment scheme for small tag spaces, variants of sub-exponential hinting PRG (Koppula and Waters, Crypto 2019) and variants of keyless sub-exponentially collision-resistant hash function with security against non-uniform adversaries (Bitansky, Kalai and Paneth, STOC 2018 and Bitansky and Lin, TCC 2018). All prior works on non-interactive non-malleable or CCA commitments without setup first construct a base'' scheme for a relatively small identity/tag space, and then build a tag amplification compiler to obtain commitments for an exponential-sized space of identities. Prior black-box constructions either add multiple rounds of interaction (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) or only achieve security against uniform adversaries (Garg, Khurana, Lu and Waters, Eurocrypt 2021). Our key technical contribution is a novel tag amplification compiler for CCA commitments that replaces the non-interactive proof of consistency required in prior work. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA2 (chosen commitment attack) security. In addition to only making black-box use of the base scheme, our construction replaces sub-exponential NIWIs with sub-exponential hinting PRGs, which can be obtained based on assumptions such as (sub-exponential) CDH or LWE.
2022
TCC
We construct adaptively secure multiparty non-interactive key exchange (NIKE) from polynomially-hard indistinguishability obfuscation and other standard assumptions. This improves on all prior such protocols, which required sub-exponential hardness. Along the way, we establish several compilers which simplify the task of constructing new multiparty NIKE protocols, and also establish a close connection with a particular type of constrained PRF.
2022
EUROCRYPT
2022
CRYPTO
Non-interactive batch arguments for NP provide a way to amortize the cost of NP verification across multiple instances. They enable a prover to convince a verifier of multiple NP statements with communication much smaller than the total witness length and verification time much smaller than individually checking each instance. In this work, we give the first construction of a non-interactive batch argument for NP from standard assumptions on groups with bilinear maps (specifically, from either the subgroup decision assumption in composite-order groups or from the k-Lin assumption in prime-order groups for any k >= 1). Previously, batch arguments for NP were only known from LWE, or a combination of multiple assumptions, or from non-standard/non-falsifiable assumptions. Moreover, our work introduces a new direct approach for batch verification and avoids heavy tools like correlation-intractable hash functions or probabilistically-checkable proofs common to previous approaches. As corollaries to our main construction, we obtain the first publicly-verifiable non-interactive delegation scheme for RAM programs (i.e., a succinct non-interactive argument (SNARG) for P) with a CRS of sublinear size (in the running time of the RAM program), as well as the first aggregate signature scheme (supporting bounded aggregation) from standard assumptions on bilinear maps.
2022
TCC
Attribute-based encryption (ABE) extends public-key encryption to enable fine-grained control to encrypted data. However, this comes at the cost of needing a central trusted authority to issue decryption keys. A multi-authority ABE (MA-ABE) scheme decentralizes ABE and allows anyone to serve as an authority. Existing constructions of MA-ABE only achieve security in the random oracle model. In this work, we develop new techniques for constructing MA-ABE for the class of subset policies (which captures policies such as conjunctions and DNF formulas) whose security can be based in the plain model without random oracles. We achieve this by relying on the recently-proposed "evasive" learning with errors (LWE) assumption by Wee (EUROCRYPT 2022) and Tsabury (CRYPTO 2022). Along the way, we also provide a modular view of the MA-ABE scheme for DNF formulas by Datta et al. (EUROCRYPT 2021) in the random oracle model. We formalize this via a general version of a related-trapdoor LWE assumption by Brakerski and Vaikuntanathan (ITCS 2022), which can in turn be reduced to the plain LWE assumption. As a corollary, we also obtain an MA-ABE scheme for subset policies from plain LWE with a polynomial modulus-to-noise ratio in the random oracle model. This improves upon the Datta et al. construction which relied on LWE with a sub-exponential modulus-to-noise ratio. Moreover, we are optimistic that the generalized related-trapdoor LWE assumption will also be useful for analyzing the security of other lattice-based constructions.
2022
TCC
The random oracle methodology is central to the design of many practical cryptosystems. A common challenge faced in several systems is the need to have a random oracle that outputs from a structured distribution D, even though most heuristic implementations such as SHA-3 are best suited for outputting bitstrings. Our work explores the problem of sampling from discrete Gaussian (and related) distributions in a manner that they can be programmed into random oracles. We make the following contributions: - We provide a definitional framework for our results. We say that a sampling algorithm Sample() for a distribution is explainable if there exists an algorithm Explain(), where, for a x in the domain, we have that Explain(x) -> r \in {0,1}^n such that Sample(r)=x. Moreover, if x is sampled from D the explained distribution is statistically close to choosing r uniformly at random. We consider a variant of this definition that allows the statistical closeness to be a "precision parameter" given to the Explain() algorithm. We show that sampling algorithms which satisfy our explainability' property can be programmed as a random oracle. - We provide a simple algorithm for explaining any sampling algorithm that works over distributions with polynomial sized ranges. This includes discrete Gaussians with small standard deviations. - We show how to transform a (not necessarily explainable) sampling algorithm Sample() for a distribution into a new Sample'() that is explainable. The requirements for doing this is that (1) the probability density function is efficiently computable (2) it is possible to efficiently uniformly sample from all elements that have a probability density above a given threshold p, showing the equivalence of random oracles to these distributions and random oracles to uniform bitstrings. This includes a large class of distributions, including all discrete Gaussians. - A potential drawback of the previous approach is that the transformation requires an additional computation of the density function. We provide a more customized approach that shows the Miccancio-Walter discrete Gaussian sampler is explainable as is. This suggests that other discrete Gaussian samplers in a similar vein might also be explainable as is.
2022
TCC
Non-interactive batch arguments for $\mathsf{NP}$ provide a way to amortize the cost of $\mathsf{NP}$ verification across multiple instances. In particular, they allow a prover to convince a verifier of multiple $\mathsf{NP}$ statements with communication that scales sublinearly in the number of instances. In this work, we study fully succinct batch arguments for $\mathsf{NP}$ in the common reference string (CRS) model where the length of the proof scales not only sublinearly in the number of instances $T$, but also sublinearly with the size of the $\mathsf{NP}$ relation. Batch arguments with these properties are special cases of succinct non-interactive arguments (SNARGs); however, existing constructions of SNARGs either rely on idealized models or strong non-falsifiable assumptions. The one exception is the Sahai-Waters SNARG based on indistinguishability obfuscation. However, when applied to the setting of batch arguments, we must impose an a priori bound on the number of instances. Moreover, the size of the common reference string scales linearly with the number of instances. In this work, we give a direct construction of a fully succinct batch argument for $\mathsf{NP}$ that supports an unbounded number of statements from indistinguishability obfuscation and one-way functions. Then, by additionally relying on a somewhere statistically-binding (SSB) hash function, we show how to extend our construction to obtain a fully succinct and updatable batch argument. In the updatable setting, a prover can take a proof $\pi$ on $T$ statements $(x_1, \ldots, x_T)$ and "update" it to obtain a proof $\pi'$ on $(x_1, \ldots, x_T, x_{T + 1})$. Notably, the update procedure only requires knowledge of a (short) proof for $(x_1, \ldots, x_T)$ along with a single witness $w_{T + 1}$ for the new instance $x_{T + 1}$. Importantly, the update does not require knowledge of witnesses for $x_1, \ldots, x_T$.
2021
EUROCRYPT
We construct the first decentralized multi-authority attribute-based encryption (????????-????????????) scheme for a non-trivial class of access policies whose security is based (in the random oracle model) solely on the Learning With Errors (LWE) assumption. The supported access policies are ones described by ???????????? formulas. All previous constructions of ????????-???????????? schemes supporting any non-trivial class of access policies were proven secure (in the random oracle model) assuming various assumptions on bilinear maps. In our system, any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. A party can simply act as a standard ABE authority by creating a public key and issuing private keys to different users that reflect their attributes. A user can encrypt data in terms of any ???????????? formulas over attributes issued from any chosen set of authorities. Finally, our system does not require any central authority. In terms of efficiency, when instantiating the scheme with a global bound ???? on the size of access policies, the sizes of public keys, secret keys, and ciphertexts, all grow with ????. Technically, we develop new tools for building ciphertext-policy ABE (????????-????????????) schemes using LWE. Along the way, we construct the first provably secure ????????-???????????? scheme supporting access policies in ????????^1 under the LWE assumption that avoids the generic universal-circuit-based key-policy to ciphertext-policy transformation. In particular, our construction relies on linear secret sharing schemes with new properties and in some sense is more similar to ????????-???????????? schemes that rely on bilinear maps. While our ????????-???????????? construction is not more efficient than existing ones, it is conceptually intriguing and further we show how to extend it to get the ????????-???????????? scheme described above.
2021
EUROCRYPT
There has been recent exciting progress in building non-interactive non-malleable commitments from judicious assumptions. All proposed approaches proceed in two steps. First, obtain simple “base” commitment schemes for very small tag/identity spaces based on a various sub-exponential hardness assumptions. Next, assuming sub-exponential non-interactive witness indistinguishable proofs (NIWIs), and variants of keyless collision-resistant hash functions, construct non-interactive compilers that convert tag-based non-malleable commitments for a small tag space into tag-based non-malleable commitments for a larger tag space. We propose the first black-box construction of non-interactive non-malleable commitments. Our key technical contribution is a novel implementation of the non-interactive proof of consistency required for tag amplification. Prior to our work, the only known approach to tag amplification without setup and with black-box use of the base scheme (Goyal, Lee, Ostrovsky, and Visconti, FOCS 2012) added multiple rounds of interaction. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA (chosen commitment attack) security. In addition to being black-box, our approach dispenses with the need for sub-exponential NIWIs, that was common to all prior work. Instead of NIWIs, we rely on sub-exponential hinting PRGs which can be obtained based on a broad set of assumptions such as sub-exponential CDH or LWE.
2021
PKC
In this work, we put forth the notion of compatibility of any key generation or setup algorithm. We focus on the specific case of encryption, and say that a key generation algorithm KeyGen is X-compatible (for X \in {CPA, CCA1, CCA2}) if there exist encryption and decryption algorithms that together with KeyGen, result in an X-secure public-key encryption scheme. We study the following question: Is every CPA-compatible key generation algorithm also CCA-compatible? We obtain the following answers: - Every sub-exponentially CPA-compatible KeyGen algorithm is CCA1-compatible, assuming the existence of hinting PRGs and sub-exponentially secure keyless collision resistant hash functions. - Every sub-exponentially CPA-compatible KeyGen algorithm is also CCA2-compatible, assuming the existence of non-interactive CCA2 secure commitments, in addition to sub-exponential security of the assumptions listed in the previous bullet. Here, sub-exponentially CPA-compatible KeyGen refers to any key generation algorithm for which there exist encryption and decryption algorithms that result in a CPA-secure public-key encryption scheme {\em against sub-exponential adversaries}. This gives a way to perform CCA secure encryption given any public key infrastructure that has been established with only (sub-exponential) CPA security in mind. The resulting CCA encryption makes black-box use of the CPA scheme and all other underlying primitives.
2021
CRYPTO
Lossy trapdoor functions, introduced by Peikert and Waters (STOC '08), can be initialized in one of two indistinguishable modes: in injective mode, the function preserves all information about its input, and can be efficiently inverted given a trapdoor, while in lossy mode, the function loses some information about its input. Such functions have found countless applications in cryptography, and can be constructed from a variety of Cryptomania assumptions. In this work, we introduce \emph{targeted lossy functions (TLFs)}, which relax lossy trapdoor functions along two orthogonal dimensions. Firstly, they do not require an inversion trapdoor in injective mode. Secondly, the lossy mode of the function is initialized with some target input, and the function is only required to lose information about this particular target. The injective and lossy modes should be indistinguishable even given the target. We construct TLFs from Minicrypt assumptions, namely, injective pseudorandom generators, or even one-way functions under a natural relaxation of injectivity. We then generalize TLFs to incorporate \emph{branches}, and construct \emph{all-injective-but-one} and \emph{all-lossy-but-one} variants. We show a wide variety of applications of targeted lossy functions. In several cases, we get the first Minicrypt constructions of primitives that were previously only known under Cryptomania assumptions. Our applications include: \begin{itemize} \item \emph{Pseudo-entropy functions} from one-way functions. \item Deterministic leakage-resilient message-authentication codes and improved leakage-resilient symmetric-key encryption from one-way functions. \item Extractors for \emph{extractor-dependent sources} from one-way functions. \item Selective-opening secure symmetric-key encryption from one-way functions. \item A new construction of CCA PKE from (exponentially secure) trapdoor functions and injective pseudorandom generators. \end{itemize} We also discuss a fascinating connection to distributed point functions.
2021
ASIACRYPT
We give an attribute-based encryption system for Turing Machines that is provably secure assuming only the existence of identity- based encryption (IBE) for large identity spaces. Currently, IBE is known to be realizable from most mainstream number theoretic assumptions that imply public key cryptography including factoring, the search Diffie-Hellman assumption, and the Learning with Errors assumption. Our core construction provides security against an attacker that makes a single key query for a machine T before declaring a challenge string w∗ that is associated with the challenge ciphertext. We build our construction by leveraging a Garbled RAM construction of Gentry, Halevi, Raykova and Wichs; however, to prove security we need to introduce a new notion of security called iterated simulation security. We then show how to transform our core construction into one that is secure for an a-priori bounded number q = q(\lambda) of key queries that can occur either before or after the challenge ciphertext. We do this by first showing how one can use a special type of non-committing encryption to transform a system that is secure only if a single key is chosen before the challenge ciphertext is declared into one where the single key can be requested either before or after the challenge ciphertext. We give a simple construction of this non-committing encryption from public key encryption in the Random Oracle Model. Next, one can apply standard combinatorial techniques to lift from single-key adaptive security to q-key adaptive security.
2021
ASIACRYPT
One of the primary research challenges in Attribute-Based Encryption (ABE) is constructing and proving cryptosystems that are adaptively secure. To date the main paradigm for achieving adaptive security in ABE is dual system encryption. However, almost all such solutions in bilinear groups rely on (variants of) either the subgroup decision problem over composite order groups or the decision linear assumption. Both of these assumptions are decisional rather than search assumptions and the target of the assumption is a source or bilinear group element. This is in contrast to earlier selectively secure ABE systems which can be proven secure from either the decisional or search Bilinear Diffie-Hellman assumption. In this work we make progress on closing this gap by giving a new ABE construction for the subset functionality and prove security under the Search Bilinear Diffie-Hellman assumption. We first provide a framework for proving adaptive security in Attribute-Based Encryption systems. We introduce a concept of ABE with deletable attributes where any party can take a ciphertext encrypted under the attribute string x in {0, 1}^n and modify it into a ciphertext encrypted under any string x' in {0, 1, bot}^n where x' is derived by replacing any bits of x with bot symbols (i.e. deleting" attributes of x). The semantics of the system are that any private key for a circuit C can be used to decrypt a ciphertext associated with x' if none of the input bits read by circuit C are bot symbols and C(x') = 1. We show a pathway for combining ABE with deletable attributes with constrained pseudorandom functions to obtain adaptively secure ABE building upon the recent work of [Tsabary19]. Our new ABE system will be adaptively secure and be a ciphertext-policy ABE that supports the same functionality as the underlying constrained PRF as long as the PRF is deletion conforming". Here we also provide a simple constrained PRF construction that gives subset functionality. Our approach enables us to access a broader array of Attribute-Based Encryption schemes support deletion of attributes. For example, we show that both the [GPSW06] and [Boyen13] ABE schemes can trivially handle a deletion operation. And, by using a hardcore bit variant of GPSW scheme we obtain an adaptively secure ABE scheme under the Search Bilinear Diffie-Hellman assumption in addition to pseudo random functions in NC1. This gives the first adaptively secure ABE from a search assumption as all prior work relied on decision assumptions over source group elements.
2021
ASIACRYPT
Software watermarking schemes allow a user to embed an identifier into a piece of code such that the resulting program is nearly functionally-equivalent to the original program, and yet, it is difficult to remove the identifier without destroying the functionality of the program. Such schemes are often considered for proving software ownership or for digital rights management. Existing constructions of watermarking have focused primarily on watermarking pseudorandom functions (PRFs). In this work, we revisit the definitional foundations of watermarking, and begin by highlighting a major flaw in existing security notions. Existing security notions for watermarking only require that the identifier be successfully extracted from programs that preserve the exact input/output behavior of the original program. In the context of PRFs, this means that an adversary that constructs a program which computes a quarter of the output bits of the PRF or that is able to distinguish the outputs of the PRF from random are considered to be outside the threat model. However, in any application (e.g., watermarking a decryption device or an authentication token) that relies on PRF security, an adversary that manages to predict a quarter of the bits or distinguishes the PRF outputs from random would be considered to have defeated the scheme. Thus, existing watermarking schemes provide very little security guarantee against realistic adversaries. None of the existing constructions of watermarkable PRFs would be able to extract the identifier from a program that only outputs a quarter of the bits of the PRF or one that perfectly distinguishes. To address the shortcomings in existing watermarkable PRF definitions, we introduce a new primitive called a traceable PRF. Our definitions are inspired by similar definitions from public-key traitor tracing, and aim to capture a very robust set of adversaries: namely, any adversary that produces a useful distinguisher (i.e., a program that can break PRF security), can be traced to a specific identifier. We provide a general framework for constructing traceable PRFs via an intermediate primitive called private linear constrained PRFs. Finally, we show how to construct traceable PRFs from a similar set of assumptions previously used to realize software watermarking. Namely, we obtain a single-key traceable PRF from standard lattice assumptions and a fully collusion-resistant traceable PRF from indistinguishability obfuscation (together with injective one-way functions).
2020
CRYPTO
We provide a construction of chosen ciphertext secure public-key encryption from (injective) trapdoor functions. Our construction is black box and assumes no special properties (e.g. lossy'', correlated product secure'') of the trapdoor function.
2020
CRYPTO
2020
TCC
In a lockable obfuscation scheme a party takes as input a program P, a lock value alpha, a message msg, and produces an obfuscated program P'. The obfuscated program can be evaluated on an input x to learn the message msg if P(x)= alpha. The security of such schemes states that if alpha is randomly chosen (independent of P and msg), then one cannot distinguish an obfuscation of $P$ from a dummy obfuscation. Existing constructions of lockable obfuscation achieve provable security under the Learning with Errors assumption. One limitation of these constructions is that they achieve only statistical correctness and allow for a possible one-sided error where the obfuscated program could output the msg on some value x where P(x) \neq alpha. In this work we motivate the problem of studying perfect correctness in lockable obfuscation for the case where the party performing the obfuscation might wish to inject a backdoor or hole in the correctness. We begin by studying the existing constructions and identify two components that are susceptible to imperfect correctness. The first is in the LWE-based pseudo-random generators (PRGs) that are non-injective, while the second is in the last level testing procedure of the core constructions. We address each in turn. First, we build upon previous work to design injective PRGs that are provably secure from the LWE assumption. Next, we design an alternative last level testing procedure that has an additional structure to prevent correctness errors. We then provide surgical proof of security (to avoid redundancy) that connects our construction to the construction by Goyal, Koppula, and Waters (GKW). Specifically, we show how for a random value alpha an obfuscation under our new construction is indistinguishable from an obfuscation under the existing GKW construction.
2020
TCC
A proof of replication system is a cryptographic primitive that allows a server (or group of servers) to prove to a client that it is dedicated to storing multiple copies or replicas of a file. Until recently, all such protocols required fined-grained timing assumptions on the amount of time it takes for a server to produce such replicas. Damgard, Ganesh, and Orlandi [DGO19] proposed a novel notion that we will call proof of replication with client setup. Here, a client first operates with secret coins to generate the replicas for a file. Such systems do not inherently have to require fine-grained timing assumptions. At the core of their solution to building proofs of replication with client setup is an abstraction called replica encodings. Briefly, these comprise a private coin scheme where a client algorithm given a file m can produce an encoding \sigma. The encodings have the property that, given any encoding \sigma, one can decode and retrieve the original file m. Secondly, if a server has significantly less than n·|m| bit of storage, it cannot reproduce n encodings. The authors give a construction of encodings from ideal permutations and trapdoor functions. In this work, we make three central contributions: 1) Our first contribution is that we discover and demonstrate that the security argument put forth by [DGO19] is fundamentally flawed. Briefly, the security argument makes assumptions on the attacker's storage behavior that does not capture general attacker strategies. We demonstrate this issue by constructing a trapdoor permutation which is secure assuming indistinguishability obfuscation, serves as a counterexample to their claim (for the parameterization stated). 2) In our second contribution we show that the DGO construction is actually secure in the ideal permutation model from any trapdoor permutation when parameterized correctly. In particular, when the number of rounds in the construction is equal to \lambda·n·b where \lambda is the security parameter, n is the number of replicas and b is the number of blocks. To do so we build up a proof approach from the ground up that accounts for general attacker storage behavior where we create an analysis technique that we call "sequence-then-switch". 3) Finally, we show a new construction that is provably secure in the random oracle (or random function) model. Thus requiring less structure on the ideal function.
2019
CRYPTO
We present the first attribute-based encryption (ABE) scheme for deterministic finite automaton (DFA) based on static assumptions in bilinear groups; this resolves an open problem posed by Waters (CRYPTO 2012). Our main construction achieves selective security against unbounded collusions under the standard k-linear assumption in prime-order bilinear groups, whereas previous constructions all rely on q-type assumptions.
2019
PKC
An emerging trend is for researchers to identify cryptography primitives for which feasibility was first established under obfuscation and then move the realization to a different setting. In this work we explore a new such avenue—to move obfuscation-based cryptography to the assumption of (positional) witness encryption. Our goal is to develop techniques and tools, which we will dub “witness encryption friendly” primitives and use these to develop a methodology for building advanced cryptography from positional witness encryption.We take a bottom up approach and pursue our general agenda by attacking the specific problem of building collusion-resistant broadcast systems with tracing from positional witness encryption. We achieve a system where the size of ciphertexts, public key and private key are polynomial in the security parameter $\lambda$ and independent of the number of users N in the broadcast system. Currently, systems with such parameters are only known from indistinguishability obfuscation.
2019
CRYPTO
We provide generic and black box transformations from any chosen plaintext secure Attribute-Based Encryption (ABE) or One-sided Predicate Encryption system into a chosen ciphertext secure system. Our transformation requires only the IND-CPA security of the original ABE scheme coupled with a pseudorandom generator (PRG) with a special security property.In particular, we consider a PRG with an n bit input $s \in \{0,1\}^n$ and $n \cdot \ell$ bit output $y_1, \ldots , y_n$ where each $y_i$ is an $\ell$ bit string. Then for a randomly chosen s the following two distributions should be computationally indistinguishable. In the first distribution $r_{s_i, i} = y_i$ and $r_{\bar{s}_i, i}$ is chosen randomly for $i \in [n]$. In the second distribution all $r_{b, i}$ are chosen randomly for $i \in [n], b \in \{0,1\}$.We show that such PRGs can be built from either the computational Diffie-Hellman assumption (in non-bilinear groups) or the Learning with Errors (LWE) assumption (and potentially other assumptions). Thus, one can transform any IND-CPA secure system into a chosen ciphertext secure one by adding either assumption. (Or by simply assuming an existing PRG is hinting secure.) In addition, our work provides a new approach and perspective for obtaining chosen ciphertext security in the basic case of public key encryption.
2019
CRYPTO
A software watermarking scheme enables users to embed a message or mark within a program while preserving its functionality. Moreover, it is difficult for an adversary to remove a watermark from a marked program without corrupting its behavior. Existing constructions of software watermarking from standard assumptions have focused exclusively on watermarking pseudorandom functions (PRFs).In this work, we study watermarking public-key primitives such as the signing key of a digital signature scheme or the decryption key of a public-key (predicate) encryption scheme. While watermarking public-key primitives might intuitively seem more challenging than watermarking PRFs, our constructions only rely on simple assumptions. Our watermarkable signature scheme can be built from the minimal assumption of one-way functions while our watermarkable public-key encryption scheme can be built from most standard algebraic assumptions that imply public-key encryption (e.g., factoring, discrete log, or lattice assumptions). Our schemes also satisfy a number of appealing properties: public marking, public mark-extraction, and collusion resistance. Our schemes are the first to simultaneously achieve all of these properties.The key enabler of our new constructions is a relaxed notion of functionality-preserving. While traditionally, we require that a marked program (approximately) preserve the input/output behavior of the original program, in the public-key setting, preserving the “functionality” does not necessarily require preserving the exact input/output behavior. For instance, if we want to mark a signing algorithm, it suffices that the marked algorithm still output valid signatures (even if those signatures might be different from the ones output by the unmarked algorithm). Similarly, if we want to mark a decryption algorithm, it suffices that the marked algorithm correctly decrypt all valid ciphertexts (but may behave differently from the unmarked algorithm on invalid or malformed ciphertexts). Our relaxed notion of functionality-preserving captures the essence of watermarking and still supports the traditional applications, but provides additional flexibility to enable new and simple realizations of this powerful cryptographic notion.
2019
CRYPTO
We construct a broadcast and trace scheme (also known as trace and revoke or broadcast, trace and revoke) with N users, where the ciphertext size can be made as low as $O(N^\varepsilon )$ , for any arbitrarily small constant $\varepsilon >0$ . This improves on the prior best construction of broadcast and trace under standard assumptions by Boneh and Waters (CCS ‘06), which had ciphertext size $O(N^{1/2})$ . While that construction relied on bilinear maps, ours uses a combination of the learning with errors (LWE) assumption and bilinear maps.Recall that, in both broadcast encryption and traitor-tracing schemes, there is a collection of N users, each of which gets a different secret key ${\mathsf {sk}}_i$ . In broadcast encryption, it is possible to create ciphertexts targeted to a subset $S \subseteq [N]$ of the users such that only those users can decrypt it correctly. In a traitor tracing scheme, if a subset of users gets together and creates a decoder box D that is capable of decrypting ciphertexts, then it is possible to trace at least one of the users responsible for creating D. A broadcast and trace scheme intertwines the two properties, in a way that results in more than just their union. In particular, it ensures that if a decoder D is able to decrypt ciphertexts targeted toward a set S of users, then it should be possible to trace one of the users in the set S responsible for creating D, even if other users outside of S also participated. As of recently, we have essentially optimal broadcast encryption (Boneh, Gentry, Waters CRYPTO ’05) under bilinear maps and traitor tracing (Goyal, Koppula, Waters STOC ’18) under LWE, where the ciphertext size is at most poly-logarithmic in N. The main contribution of our paper is to carefully combine LWE and bilinear-map based components, and get them to interact with each other, to achieve broadcast and trace.
2019
TCC
In a traitor tracing (TT) system for n users, every user has his/her own secret key. Content providers can encrypt messages using a public key, and each user can decrypt the ciphertext using his/her secret key. Suppose some of the n users collude to construct a pirate decoding box. Then the tracing scheme has a special algorithm, called $\mathsf {Trace}$, which can identify at least one of the secret keys used to construct the pirate decoding box.Traditionally, the trace algorithm output only the ‘index’ associated with the traitors. As a result, to use such systems, either a central master authority must map the indices to actual identities, or there should be a public mapping of indices to identities. Both these options are problematic, especially if we need public tracing with anonymity of users. Nishimaki, Wichs, and Zhandry (NWZ) [Eurocrypt 2016] addressed this problem by constructing a traitor tracing scheme where the identities of users are embedded in the secret keys, and the trace algorithm, given a decoding box D, can recover the entire identities of the traitors. We call such schemes ‘Embedded Identity Traitor Tracing’ schemes. NWZ constructed such schemes based on adaptively secure functional encryption (FE). Currently, the only known constructions of FE schemes are based on nonstandard assumptions such as multilinear maps and iO.In this work, we study the problem of embedded identities TT based on standard assumptions. We provide a range of constructions based on different assumptions such as public key encryption (PKE), bilinear maps and the Learning with Errors (LWE) assumption. The different constructions have different efficiency trade offs. In our PKE based construction, the ciphertext size grows linearly with the number of users; the bilinear maps based construction has sub-linear ($\sqrt{n}$) sized ciphertexts. Both these schemes have public tracing. The LWE based scheme is a private tracing scheme with optimal ciphertexts (i.e., $\log (n)$). Finally, we also present other notions of traitor tracing, and discuss how they can be build in a generic manner from our base embedded identity TT scheme.
2019
ASIACRYPT
In this work, we study the fascinating notion of output-compressing randomized encodings for Turing Machines, in a shared randomness model. In this model, the encoder and decoder have access to a shared random string, and the efficiency requirement is, the size of the encoding must be independent of the running time and output length of the Turing Machine on the given input, while the length of the shared random string is allowed to grow with the length of the output. We show how to construct output-compressing randomized encodings for Turing machines in the shared randomness model, assuming iO for circuits and any assumption in the set $\{$ LWE, DDH, N $^{th}$ Residuosity $\}$ .We then show interesting implications of the above result to basic feasibility questions in the areas of secure multiparty computation (MPC) and indistinguishability obfuscation (iO): 1.Compact MPC for Turing Machines in the Random Oracle Model. In the context of MPC, we consider the following basic feasibility question: does there exist a malicious-secure MPC protocol for Turing Machines whose communication complexity is independent of the running time and output length of the Turing Machine when executed on the combined inputs of all parties? We call such a protocol as a compact MPC protocol. Hubácek and Wichs [HW15] showed via an incompressibility argument, that, even for the restricted setting of circuits, it is impossible to construct a malicious secure two party computation protocol in the plain model where the communication complexity is independent of the output length. In this work, we show how to evade this impossibility by compiling any (non-compact) MPC protocol in the plain model to a compact MPC protocol for Turing Machines in the Random Oracle Model, assuming output-compressing randomized encodings in the shared randomness model.2.Succinct iO for Turing Machines in the Shared Randomness Model. In all existing constructions of iO for Turing Machines, the size of the obfuscated program grows with a bound on the input length. In this work, we show how to construct an iO scheme for Turing Machines in the shared randomness model where the size of the obfuscated program is independent of a bound on the input length, assuming iO for circuits and any assumption in the set $\{$ LWE, DDH, N $^{th}$ Residuosity $\}$ .
2018
EUROCRYPT
2018
CRYPTO
In this work we seek to construct collusion-resistant traitor tracing systems with small ciphertexts from standard assumptions that also move toward practical efficiency. In our approach we will hold steadfast to the principle of collusion resistance, but relax the requirement on catching a traitor from a successful decoding algorithm. We define a f-risky traitor tracing system as one where the probability of identifying a traitor is $f(\lambda ,n)$f(λ,n) times the probability a successful box is produced. We then go on to show how to build such systems from prime order bilinear groups with assumptions close to those used in prior works. Our core system achieves, for any $k > 0$k>0, $f(\lambda ,n) \approx \frac{k}{n + k - 1}$f(λ,n)≈kn+k-1 where ciphertexts consists of $(k + 4)$(k+4) group elements and decryption requires $(k + 3)$(k+3) pairing operations.At first glance the utility of such a system might seem questionable since the f we achieve for short ciphertexts is relatively small. Indeed an attacker in such a system can more likely than not get away with producing a decoding box. However, we believe this approach to be viable for four reasons:1.A risky traitor tracing system will provide deterrence against risk averse attackers. In some settings the consequences of being caught might bear a high cost and an attacker will have to weigh his utility of producing a decryption D box against the expected cost of being caught.2.Consider a broadcast system where we want to support low overhead broadcast encrypted communications, but will periodically allow for a more expensive key refresh operation. We refer to an adversary produced algorithm that maintains the ability to decrypt across key refreshes as a persistent decoder. We show how if we employ a risky traitor tracing systems in this setting, even for a small f, we can amplify the chances of catching such a “persistent decoder” to be negligibly close to 1.3.In certain resource constrained settings risky traitor tracing provides a best tracing effort where there are no other collusion-resistant alternatives. For instance, suppose we had to support 100 K users over a radio link that had just 10 KB of additional resources for extra ciphertext overhead. None of the existing $\sqrt{N}$N bilinear map systems can fit in these constraints. On the other hand a risky traitor tracing system provides a spectrum of tracing probability versus overhead tradeoffs and can be configured to at least give some deterrence in this setting.4.Finally, we can capture impossibility results for differential privacy from $\frac{1}{n}$1n-risky traitor tracing. Since our ciphertexts are short ($O(\lambda )$O(λ)), we get the negative result which matches what one would get plugging in the obfuscation based tracing system Boneh-Zhandry [9] solution into the prior impossibility result of Dwork et al. [14].
2018
TCC
The notion of Functional Encryption (FE) has recently emerged as a strong primitive with several exciting applications. In this work, we initiate the study of the following question: Can existing public key encryption schemes be “upgraded” to Functional Encryption schemes without changing their public keys or the encryption algorithm? We call a public-key encryption scheme with this property to be FE-compatible. Indeed, assuming ideal obfuscation, it is easy to see that every CCA-secure public-key encryption scheme is FE-compatible. Despite the recent success in using indistinguishability obfuscation to replace ideal obfuscation for many applications, we show that this phenomenon most likely will not apply here. We show that assuming fully homomorphic encryption and the learning with errors (LWE) assumption, there exists a CCA-secure encryption scheme that is provably not FE-compatible. We also show that a large class of natural CCA-secure encryption schemes proven secure in the random oracle model are not FE-compatible in the random oracle model.Nevertheless, we identify a key structure that, if present, is sufficient to provide FE-compatibility. Specifically, we show that assuming sub-exponentially secure iO and sub-exponentially secure one way functions, there exists a class of public key encryption schemes which we call Special-CCA secure encryption schemes that are in fact, FE-compatible. In particular, each of the following popular CCA secure encryption schemes (some of which existed even before the notion of FE was introduced) fall into the class of Special-CCA secure encryption schemes and are thus FE-compatible:1.[CHK04] when instantiated with the IBE scheme of [BB04].2.[CHK04] when instantiated with any Hierarchical IBE scheme.3.[PW08] when instantiated with any Lossy Trapdoor Function.
2018
TCC
In this work we study the feasibility of achieving simulation security in functional encryption (FE) in the random oracle model. Our main result is negative in that we give a functionality for which it is impossible to achieve simulation security even with the aid of random oracles.We begin by giving a formal definition of simulation security that explicitly incorporates the random oracles. Next, we show a particular functionality for which it is impossible to achieve simulation security. Here messages are interpreted as seeds to a (weak) pseudorandom function family F and private keys are ascribed to points in the domain of the function. On a message s and private key x one can learn F(s, x). We show that there exists an attacker that makes a polynomial number of private key queries followed by a single ciphertext query for which there exists no simulator.Our functionality and attacker access pattern closely matches the standard model impossibility result of Agrawal, Gorbunov, Vaikuntanathan and Wee (CRYPTO 2013). The crux of their argument is that no simulator can succinctly program in the outputs of an unbounded number of evaluations of a pseudorandom function family into a fixed size ciphertext. However, their argument does not apply in the random oracle setting since the oracle acts as an additional conduit of information which the simulator can program. We overcome this barrier by proposing an attacker who decrypts the challenge ciphertext with the secret keys issued earlier without using the random oracle, even though the decryption algorithm may require it. This involves collecting most of the useful random oracle queries in advance, without giving the simulator too many opportunities to program.On the flip side, we demonstrate the utility of the random oracle in simulation security. Given only public key encryption and low-depth PRGs we show how to build an FE system that is simulation secure for any poly-time attacker that makes an unbounded number of message queries, but an a-priori bounded number of key queries. This bests what is possible in the standard model where it is only feasible to achieve security for an attacker that is bounded both in the number of key and message queries it makes. We achieve this by creating a system that leverages the random oracle to get one-key security and then adapt previously known techniques to boost the system to resist up to q queries.Finally, we ask whether it is possible to achieve simulation security for an unbounded number of messages and keys, but where all key queries are made after the message queries. We show this too is impossible to achieve using a different twist on our first impossibility result.
2018
TCC
A traitor tracing scheme is a public key encryption scheme for which there are many secret decryption keys. Any of these keys can decrypt a ciphertext; moreover, even if a coalition of users collude, put together their decryption keys and attempt to create a new decryption key, there is an efficient algorithm to trace the new key to at least one the colluders.Recently, Goyal, Koppula and Waters (GKW, STOC 18) provided the first traitor tracing scheme from LWE with ciphertext and secret key sizes that grow polynomially in $\log n$, where n is the number of users. The main technical building block in their construction is a strengthening of (bounded collusion secure) secret-key functional encryption which they refer to as mixed functional encryption (FE).In this work, we improve upon and extend the GKW traitor tracing scheme:We provide simpler constructions of mixed FE schemes based on the LWE assumption. Our constructions improve upon the GKW construction in terms of expressiveness, modularity, and security.We provide a construction of attribute-based traitor tracing for all circuits based on the LWE assumption.
2017
EUROCRYPT
2017
PKC
2017
PKC
2017
TCC
2016
EUROCRYPT
2016
EUROCRYPT
2016
CRYPTO
2016
ASIACRYPT
2016
TCC
2015
JOFC
2015
TCC
2015
EUROCRYPT
2015
CRYPTO
2015
ASIACRYPT
2015
ASIACRYPT
2015
ASIACRYPT
2014
CRYPTO
2014
CRYPTO
2014
EUROCRYPT
2014
EUROCRYPT
2014
PKC
2013
PKC
2013
PKC
2013
CRYPTO
2013
CRYPTO
2013
CRYPTO
2013
CRYPTO
2013
ASIACRYPT
2013
JOFC
In a proof-of-retrievability system, a data storage center must prove to a verifier that he is actually storing all of a client’s data. The central challenge is to build systems that are both efficient and provably secure—that is, it should be possible to extract the client’s data from any prover that passes a verification check. In this paper, we give the first proof-of-retrievability schemes with full proofs of security against arbitrary adversaries in the strongest model, that of Juels and Kaliski.Our first scheme, built from BLS signatures and secure in the random oracle model, features a proof-of-retrievability protocol in which the client’s query and server’s response are both extremely short. This scheme allows public verifiability: anyone can act as a verifier, not just the file owner. Our second scheme, which builds on pseudorandom functions (PRFs) and is secure in the standard model, allows only private verification. It features a proof-of-retrievability protocol with an even shorter server’s response than our first scheme, but the client’s query is long. Both schemes rely on homomorphic properties to aggregate a proof into one small authenticator value.
2012
TCC
2012
EUROCRYPT
2012
EUROCRYPT
2012
EUROCRYPT
2012
CRYPTO
2012
CRYPTO
2012
CRYPTO
2012
ASIACRYPT
2011
PKC
2011
TCC
2011
TCC
2011
TCC
2011
CRYPTO
2011
EUROCRYPT
2011
EUROCRYPT
2010
TCC
2010
EUROCRYPT
2010
EUROCRYPT
2009
TCC
2009
PKC
2009
EUROCRYPT
2009
EUROCRYPT
2009
CRYPTO
2009
CRYPTO
2008
EUROCRYPT
2008
ASIACRYPT
2008
CRYPTO
2007
PKC
2007
PKC
2007
TCC
2006
CRYPTO
2006
EUROCRYPT
2006
EUROCRYPT
2006
EUROCRYPT
2006
PKC
2005
CRYPTO
2005
EUROCRYPT
2005
EUROCRYPT

#### Program Committees

TCC 2021 (Program chair)
Eurocrypt 2019
Eurocrypt 2017
TCC 2016
Crypto 2014
Crypto 2010
PKC 2010
TCC 2009
Crypto 2008
Eurocrypt 2008
Eurocrypt 2007
Asiacrypt 2007

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# Relationship of area to circumference

### Math Forum - Ask Dr. Math

Label the diameter and radius of a circle and describe the relationship between them. Recall and apply the formula for the circumference and area of a circle to. Understanding the Area and Circumference of a Circle. Factoid: The Now think about the area of the circle in relationship to the area of the square. Obviously. My 6th grade daughter asked if there is a shortcut for converting from area to circumference and back without finding the radius.

Okay, let's do a formula. The line from one side of the circle to the other is called the diameter. It is usually abreviated as d.

## Relationship between the radius, diameter, circumference, and area of a circle.?

The length of the side of the square is also d 2. The area of the square is d squared d times dand 3. The area of the circle is.

Circumference of a Circle - pdl-inc.info - Math Help

The circumference of the circle is just a percentage of the circumference perimeter of the square, and it's the same percentage no matter what the size. Believe it or not, that percentage is A seemingly random number is the answer to two different problems. Mathematicians and Pi Maybe you would want to give this ratio, which is approximately I will call it cake. I used to call it pie. Then the formula for the area of a circle is exactly cake times d squared.

If we divide both sides by two pi, to solve for r, what are we left with? Well we have an r on the right hand side, we have r is equal to pi divided by pi, that's just one. Six divided by two is three. So we get that our radius, right over here, is equal to three units. And then we can use the fact that are is equal to pi, r squared, to figure out the area.

This is going to be equal to pi times three squared. Oh and you have to write parenthesis there. Pi, times three, squared, which is of course going to be equal to nine pi. So for this particular example, when the circumference is six pi units, we're able to figure out that the area, this is actually going to be nine pi square units, or I could write units squared.

Cause we're squaring the radius. The radius is three units, so you square that, you get the units squared.

Now let's see if we can come up with a general formula. So we know that circumference is equal to two pi r. And we know that area is equal to pi r squared.

## You need to have JavaScript enabled in order to access this site.

Can we come up with an expression or a formula that relates directly between circumference and area? And I'll give you a hint, solve for, you could solve for r right over here, and substitute back into this equation, or vice versa. Pause the video, see if you can do that.

• Understanding the Area and Circumference of a Circle
• Area and circumference of circles

However, my answer to the area question for this circle has to be 3. Still haven't figured out how this fits in.

### Circle: Area and Circumference

She's thinking like a mathematician. Why keep solving special cases of the same problem over and over, if you can just solve the general case one time and be done with it? In the long run, she'll probably learn more from your willingness to jump in and play around and look for the answer, than from actually finding the answer itself. It's that kind of playing around that kids are supposed to be learning in their math classes, but it hardly ever works out that way.

That's a good intuition. It might be more helpful than you think.

### Relationship between the radius, diameter, circumference, and area of a circle.? | Socratic

But let's set that aside for now. Again, it might be more helpful than you think. Let's go back to where your daughter started: