text:
1. ## Xanax

Fuck xanax, officially the stupidest recreational drug ever. Realised if I keep taking this shit then it's going to become a serious problem. started out as fun to take once in a while to chill and watch movies. Xanax, literally, does not chill you out unless it's one of your first couple times using it or if you have actual anxiety. After you get used to it, it is less likely to knock you out to sleep so you stay awake and do retarded shit. Also, the 'I need to take more factor' is 1000% worse than drinking. Imagine the amount of effort of taking 5 shots is as simple as swallowing a pill. Like at least when you're drinking you realize you're drunk, and you have to make an actual effort to drink more. With xanax you just want to feel even more chilled. More chilled = blackout. I wouldn't consider myself addicted to it, but for the few times I have taken it I sure have done some really dumb shit. Each time, it gets more and more stupid. Just to list off a couple things:

- Went to a movie. Fell asleep without knowing it until the movie ended. Proceeded to go to a park and smoke endless joints for 2-3 hours. Did not remember going to park until someone talked about it the next day and I was like 'what are you talking about we didn't do that'. Smoking weed in a park doesn't sound retarded to you? It was 1 am & the park was closed. Weed is illegal in my state. Having weed you might get lucky with a chill cop and he tells you to throw it away, or you could end up going to jail and then pretty much be ~$5,000-$10,000+ in the hole because you had to hire a lawyer, pay court fees, pay probation fees, pay fines & do community service and probably lose your job. You can argue that all that punishment sound unfair for a bit of weed. But it doesn't matter because I knew that's what would happen if I got caught. Maybe, but if you avoid smoking at a park it won't happen. It's also a felony to have any drug within < 1000 feet of a park. Being at a park when it's closed is a 100% guarantee for a cop to approach you if he sees anyone there. Oh yeah, I totally drove because 'derp took some xanax this joint isn't getting me high' >> 5 joints later "still not high".

- Smoked a joint in my room when I lived with my parents. Risking free rent to smoke weed in my room, nice.

- Woke up the next day & logged on to RS. Found myself wearing monks robes and a rune long in level 4 wild for some reason. Remembered I took xanax last night, went to look at how many I had left. Took every single one.

- took xanax for ~ 10 days straight at work. didn't do anything retarded but that whole time does not exist in my mind. I remember buying them, and then I remember running out.

- General holes in my memory anytime I took it more than a day in a row

- Decided taking 7 hits of LSD was a good idea because 'I want to trip tonight'. Took 3 more because my bartarded self wanted to say 'derp I took 1 mg of LSD'. I didn't even trip much because, turns out, I took more xanax and fell asleep.

- Gave someone at work 2 bars for their birthday. They took both of them. At work. They are no longer a co worker.

- Generally associating with other people who take xanax. Retardation by association.

- don't remember eating all the pills I had(again). this is the last time I took xanax.

Been a solid month since I have touched it. PSA to anyone wanting to try it: It's a fun chilltime the first couple times you take it, and then you fall asleep. Once you get used to it, it will make you want to take more to get that chilled out feeling again. The issue is you won't ever get chilled out since when you take more you will just black out. Your tolerance will become just high enough for you to stay awake, but just low enough for you to stay awake and do retarded shit. If you don't do anything stupid while you're xaned out your mind will tell you to take more until you do something stupid.

If you are prescribed any benzo, please for god sake take as recommended, and then less. You see that list of retarded shit above? That's from someone whos probably only taken less than ~100 in their lifetime. Imagine if I went full addict. That list would probably include a couple arrest stories, and maybe some stupid drama. Oh yeah, and benzo withdrawals can kill you. Seriously benzos are great for people who have anxiety disorders, but they hold little recreational value after you take them more than a couple times. Even then, it's best to deal with your anxiety issues with ways other than benzos.

TL;DR xanax bars are literal retard bombs, it's not even really a good recreational drug(basically benadryl that makes you retarded)

2. Don't ever do that shit. Xanax-like benzoes is what took my father's life last weekend.

3. Originally Posted by Joopi
Don't ever do that shit. Xanax-like benzoes is what took my father's life last weekend.
Sorry to hear that man. I myself did not become full on addicted to xanax so I can't speak for how hard the habit is to kick myself, but for what I've heard from other people it's pretty bad. I'm not sure what the case of your fathers is, but it's always a shame to hear when it starts with a prescription. I Know a guy at work who has been prescribed it for a couple years now and is trying to get off of it. He said he stopped refilling his script yet he still just bars it off other people & I told him look man if you have been taking it for the past couple years you can't just quit cold turkey. Go talk to your doctor so he can set you up to taper off of it. Benzos/alcohol you can't just quit cold turkey (but at least with benzos you can taper, with alcohol you can end up with reverse tolerance if you have liver damage)

Most common drugs people get addicted to:

Heroin/opiates, meth, crack/cocaine, benzos, alcohol, marijuana, caffeine, nicotine

of that list, the only ones who withdrawal can kill you:

benzos
alcohol

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I am pretty sure that herion/opiates can kill you aswell when you quit cold turkey.

What about adderal/ritalin etc. what do you think about that stuff?

5. My 2 rules for drugs:
1: not physically addicting
2: no (or very very low) potential for overdose

Even following these rules I've done some stupid shit that could have ended very badly if I hadn't been really lucky.
Drugs can be great if you're smart, but they will fucking destroy you if you're not.
When I had my wisdom teeth taken out I didn't take any of the painkillers they prescribed me.

@OP be smart and stay safe.

6. Originally Posted by Big Dennis
I am pretty sure that herion/opiates can kill you aswell when you quit cold turkey.

What about adderal/ritalin etc. what do you think about that stuff?
Nope, opiate withdrawals are shitty but won't kill you.

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Originally Posted by Citrus
My 2 rules for drugs:
1: not physically addicting
2: no (or very very low) potential for overdose
This. I've deviated a couple times, but generally always stick to it.

Benzos aren't even all that fun, just incredibly habit forming. Glad to hear you've moved on.

8. Originally Posted by rj
...

Most common drugs people get addicted to:

Heroin/opiates, meth, crack/cocaine, benzos, alcohol, marijuana, caffeine, nicotine

...
Those fucking three here...

9. Originally Posted by superuser
Those fucking three here...
Nicotine can be compared to heroin in terms of how addictive it is.
Alcohol addiction varies from none to a lot. (genetic I think)
Caffeine addiction isn't too serious. Easy to avoid and recover from.

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Originally Posted by Citrus
My 2 rules for drugs:
1: not physically addicting
2: no (or very very low) potential for overdose
Golden rules.

11. Good post, generally confirming my bewilderment as to why I was prescribed Klonopin in order to simply sleep better after Adderall, given all the horrible things I've heard about it. I've had some and not really noticed anything except feeling more chilled out but reading more about what it chemically does to you overtime is making me want to avoid the stuff completely.

Have heard that Klonopin is used as a middle tier drug to get people off a Xanax addiction so that all sounds like territory I want to steer clear from.

Best of luck man. Those golden rules are good @Citrus; and at first I only applied it to illegal substances e.g. Cocaine/heroine but it's funny how doctors can just expose you to something equally addictive under a "professional" setting.

12. I actually have an anxiety/panic disorder and was prescribed Xanax as a short term relief when it first started. At the beginning, it helped a lot, but damn that stuff was scary. I was on a low dose, but the effects you mentioned was as concerning as you've described above. I'm glad I'm off of that stuff.

13. Lol, found a 1/4 bar in my room that I hid from myself around a month ago

14. Originally Posted by Citrus
My 2 rules for drugs:
1: not physically addicting
2: no (or very very low) potential for overdose

Even following these rules I've done some stupid shit that could have ended very badly if I hadn't been really lucky.
Drugs can be great if you're smart, but they will fucking destroy you if you're not.
When I had my wisdom teeth taken out I didn't take any of the painkillers they prescribed me.

@OP be smart and stay safe.
Originally Posted by OSRS BOT
Golden rules.
3. Don't fuck with hallucinogens, especially if you're in a bad place mentally. It'll take you years, or maybe never to recover (speaking from experience).

15. Originally Posted by anth_
3. Don't fuck with hallucinogens, especially if you're in a bad place mentally. It'll take you years, or maybe never to recover (speaking from experience).
Yeah I've been there a few times, but it was my own fault for being an idiot.
I'd say they're worth the risk if you're smart about it. Do your research and respect the shit out of them. Don't fuck with sketchy RCs. Take it REALLY slow at first.

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Originally Posted by Citrus
Yeah I've been there a few times, but it was my own fault for being an idiot.
I'd say they're worth the risk if you're smart about it. Do your research and respect the shit out of them. Don't fuck with sketchy RCs. Take it REALLY slow at first.
Golden advice Anth; set and setting and mindset are the golden factors for a pleasant healthy trip.

Take them with people you trust in a place you trust after purchasing from a dealer you can trust

My friends that are stuck in the xanax bubble call the hulks "time travelers". They take them so they can miss a day and wake up for something they want to do. I'll never understand it, because they always look like shit after.

I'll elaborate. 10 hour road trip? OK, they will pop bars while I cruise shotgun. We get to the city, and the driver and I are good to go but my homies are walking with their feet dragging and have bags under their eyes and look ghastly, even the morning after. But hey, they missed the drive... worth?!!?!.................... zzz

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Originally Posted by anth_
3. Don't fuck with hallucinogens, especially if you're in a bad place mentally. It'll take you years, or maybe never to recover (speaking from experience).
Err, no, can't say I have any idea about that. I've always enjoyed them. Plus they fit my 2 rules.

18. Originally Posted by the bank
Err, no, can't say I have any idea about that. I've always enjoyed them. Plus they fit my 2 rules.
"Bad place mentally" being the most important point there

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Reading all this shit about pharmaceuticals just makes me glad i switched to Cannabis years ago.

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Last time i did bars was probably around a year ago its stupid asl i agree with you on that

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Originally Posted by rj
Fuck xanax, officially the stupidest recreational drug ever. Realised if I keep taking this shit then it's going to become a serious problem. started out as fun to take once in a while to chill and watch movies. Xanax, literally, does not chill you out unless it's one of your first couple times using it or if you have actual anxiety. After you get used to it, it is less likely to knock you out to sleep so you stay awake and do retarded shit. Also, the 'I need to take more factor' is 1000% worse than drinking. Imagine the amount of effort of taking 5 shots is as simple as swallowing a pill. Like at least when you're drinking you realize you're drunk, and you have to make an actual effort to drink more. With xanax you just want to feel even more chilled. More chilled = blackout. I wouldn't consider myself addicted to it, but for the few times I have taken it I sure have done some really dumb shit. Each time, it gets more and more stupid. Just to list off a couple things:

- Went to a movie. Fell asleep without knowing it until the movie ended. Proceeded to go to a park and smoke endless joints for 2-3 hours. Did not remember going to park until someone talked about it the next day and I was like 'what are you talking about we didn't do that'. Smoking weed in a park doesn't sound retarded to you? It was 1 am & the park was closed. Weed is illegal in my state. Having weed you might get lucky with a chill cop and he tells you to throw it away, or you could end up going to jail and then pretty much be ~$5,000-$10,000+ in the hole because you had to hire a lawyer, pay court fees, pay probation fees, pay fines & do community service and probably lose your job. You can argue that all that punishment sound unfair for a bit of weed. But it doesn't matter because I knew that's what would happen if I got caught. Maybe, but if you avoid smoking at a park it won't happen. It's also a felony to have any drug within < 1000 feet of a park. Being at a park when it's closed is a 100% guarantee for a cop to approach you if he sees anyone there. Oh yeah, I totally drove because 'derp took some xanax this joint isn't getting me high' >> 5 joints later "still not high".

- Smoked a joint in my room when I lived with my parents. Risking free rent to smoke weed in my room, nice.

- Woke up the next day & logged on to RS. Found myself wearing monks robes and a rune long in level 4 wild for some reason. Remembered I took xanax last night, went to look at how many I had left. Took every single one.

- took xanax for ~ 10 days straight at work. didn't do anything retarded but that whole time does not exist in my mind. I remember buying them, and then I remember running out.

- General holes in my memory anytime I took it more than a day in a row

- Decided taking 7 hits of LSD was a good idea because 'I want to trip tonight'. Took 3 more because my bartarded self wanted to say 'derp I took 1 mg of LSD'. I didn't even trip much because, turns out, I took more xanax and fell asleep.

- Gave someone at work 2 bars for their birthday. They took both of them. At work. They are no longer a co worker.

- Generally associating with other people who take xanax. Retardation by association.

- don't remember eating all the pills I had(again). this is the last time I took xanax.

Been a solid month since I have touched it. PSA to anyone wanting to try it: It's a fun chilltime the first couple times you take it, and then you fall asleep. Once you get used to it, it will make you want to take more to get that chilled out feeling again. The issue is you won't ever get chilled out since when you take more you will just black out. Your tolerance will become just high enough for you to stay awake, but just low enough for you to stay awake and do retarded shit. If you don't do anything stupid while you're xaned out your mind will tell you to take more until you do something stupid.

If you are prescribed any benzo, please for god sake take as recommended, and then less. You see that list of retarded shit above? That's from someone whos probably only taken less than ~100 in their lifetime. Imagine if I went full addict. That list would probably include a couple arrest stories, and maybe some stupid drama. Oh yeah, and benzo withdrawals can kill you. Seriously benzos are great for people who have anxiety disorders, but they hold little recreational value after you take them more than a couple times. Even then, it's best to deal with your anxiety issues with ways other than benzos.

TL;DR xanax bars are literal retard bombs, it's not even really a good recreational drug(basically benadryl that makes you retarded)
This made my day =D

The dark web sell chinese xanax dirt cheap... considering half a gram is 500 mg...

At the start of the night you are sensibly weighing out (most will fail) average scales 0.01 (10) mg the room for error is enormous.
By the end; well 500 mg later, 72 hours has passed and you realised that you just had your first encounter with Alzheimer's

10 mg of xanax for any newcomer will knock them out - considering the strongest dosage in AU is a 2 mg bar.

Well anyway if you think that's something to sneeze at; hell try some carfentanil

22. Sure, Alprazolam is not recreational drug, it's for medical use only. It works on GABAa receptors, what gives sedative effect on your brain. It removes anxiety and make you relaxed by calming down activeness of neurons - literally deactivating your brain. I wouldn't recommend shutting brain off for anyone.

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Originally Posted by bg5
Sure, Alprazolam is not recreational drug, it's for medical use only. It works on GABAa receptors, what gives sedative effect on your brain. It removes anxiety and make you relaxed by calming down activeness of neurons - literally deactivating your brain. I wouldn't recommend shutting brain off for anyone.
As a chronic pain sufferer; and as would most.. You seek out anything that would provide relief... even if only momentarily.

Hell i would even drink my own urine if i thought it would provide relief...

As the the doctors in my country will not prescribe actual pain medication anymore with fears that the effects of Australian prescription opiates is having a negative impact on society much like the US

The medication prescribe has caused me to have Epilepsy... So as you can guess i have lost all faith in the medical system and have had to look a little outside the box at times.

But i do agree long term Xanax will eventually lead to unintentional black outs; as the dosage increases... But the sedative effect of benzos provides great pain relief...

24. Originally Posted by AFools
As the the doctors in my country will not prescribe actual pain medication anymore with fears that the effects of Australian prescription opiates is having a negative impact on society much like the US

The medication prescribe has caused me to have Epilepsy... So as you can guess i have lost all faith in the medical system and have had to look a little outside the box at times.

But i do agree long term Xanax will eventually lead to unintentional black outs; as the dosage increases... But the sedative effect of benzos provides great pain relief...
I'm sorry to read that. But Xanax isn't created to be a pain killer. It can take away from you much more than pain. There still should be other drugs with less side effects.

25. Originally Posted by AFools
This made my day =D

The dark web sell chinese xanax dirt cheap... considering half a gram is 500 mg...

At the start of the night you are sensibly weighing out (most will fail) average scales 0.01 (10) mg the room for error is enormous.
By the end; well 500 mg later, 72 hours has passed and you realised that you just had your first encounter with Alzheimer's

10 mg of xanax for any newcomer will knock them out - considering the strongest dosage in AU is a 2 mg bar.

Well anyway if you think that's something to sneeze at; hell try some carfentanil
carfentil and aplrazolam and totally 2 different drugs lol..

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# X-shooter and ALMA spectroscopy of GRB 161023A - A study of metals and molecules in the line of sight towards a luminous GRB

A. de Ugarte Postigo, C. C. Thöne, J. Bolmer, S. Schulze, S. Martín, D. A. Kann, V. D'Elia, J. Selsing, A. Martin-Carrillo, D. A. Perley, S. Kim, L. Izzo, R. Sánchez-Ramírez, C. Guidorzi, A. Klotz, K. Wiersema, F. E. Bauer, K. Bensch, S. Campana, Z. CanoS. Covino, D. Coward, A. De Cia, I. de Gregorio-Monsalvo, M. De Pasquale, J. P. U. Fynbo, J. Greiner, A. Gomboc, L. Hanlon, M. Hansen, D. H. Hartmann, K. E. Heintz, P. Jakobsson, S. Kobayashi, D. B. Malesani, R. Martone, P. J. Meintjes, M. J. Michalowski, C. G. Mundell, D. Murphy, S. Oates, L. Resmi, L. Salmon, B. van Soelen, N. R. Tanvir, D. Turpin, D. Xu, T. Zafar

Research output: Contribution to journalArticlepeer-review

9 Citations (SciVal)

## Abstract

Long gamma-ray bursts are produced during the dramatic deaths of massive stars with very short lifetimes, meaning that they explode close to the birth place of their progenitors. During a short period they become the most luminous objects observable in the Universe, being perfect beacons to study high-redshift star-forming regions. To use the afterglow of GRB 161023A at a redshift $z=2.710$ as a background source to study the environment of the explosion and the intervening systems along its line-of-sight. r the first time, we complement UV/Optical/NIR spectroscopy with millimetre spectroscopy using ALMA, which allows us to probe the molecular content of the host galaxy. The X-shooter spectrum shows a plethora of absorption features including fine-structure and metastable transitions of Fe, Ni, Si, C and O. We present photometry ranging from 43 s to over 500 days after the burst. We infer a host-galaxy metallicity of [Zn/H] $=-1.11\pm0.07$, which corrected for dust depletion results in [X/H] $=-0.94\pm0.08$. We do not detect molecular features in the ALMA data, but we derive limits on the molecular content of \$log(N_{CO}/cm^{-2})
Original language English A119 23 Astronomy & Astrophysics 620 7 Dec 2018 https://doi.org/10.1051/0004-6361/201833094 Published - 7 Dec 2018

• astro-ph.HE

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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

CiteScore 2018: 1.01

SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541

ICV 2017: 162.45

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Volume 15, Issue 1

# A privacy-preserving parallel and homomorphic encryption scheme

Zhaoe Min
• Corresponding author
• School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China
• Email
• Other articles by this author:
/ Geng Yang
/ Jingqi Shi
Published Online: 2017-04-06 | DOI: https://doi.org/10.1515/phys-2017-0014

## Abstract

In order to protect data privacy whilst allowing efficient access to data in multi-nodes cloud environments, a parallel homomorphic encryption (PHE) scheme is proposed based on the additive homomorphism of the Paillier encryption algorithm. In this paper we propose a PHE algorithm, in which plaintext is divided into several blocks and blocks are encrypted with a parallel mode. Experiment results demonstrate that the encryption algorithm can reach a speed-up ratio at about 7.1 in the MapReduce environment with 16 cores and 4 nodes.

PACS: 9.70.-a; 89.70.EG

## 1 Introduction

Since 2009, cloud servers such as Microsoft, Amazon and Google have experienced security incidents and the security of cloud computing has become the paramount problem constraining its development. In 2011, Cloud Security Alliance (CSA) presented the cloud security model, emphasising the issue of privacy protection in cloud computing. The privacy problem in cloud computing results from the features of data outsourcing and service renting. Users lose their direct control of data while they store the data in the cloud, which can lead to the leakage and abuse of personal privacy data. Some privacy preserving methods are proposed in Papers [1, 2]. Furthermore, it is considered that data privacy can be protected from the two aspects of data encryption and user identity management. The homomorphic encryption (HE) technique supports the management of ciphertext data under the privacy protection, and can directly applied to ciphertexts for retrieval, computation and statistics in the clouds. Afterwards, the results are returned to the user in the form of ciphertexts, in contrast to the conventional encryption algorithm, which can eliminate the need for frequent operations of encryption and decryption between the clouds and the users, thus reducing the communication overhead and computation resources.

Cloud computing clusters possess large numbers of computational nodes, and they can be used for storing and processing mass data. It is easy to construct a cloud computing environment, therefore, many enterprises and research institutes have built private cloud computing platforms. We can conduct encryption on the data which need to be stored in the public clouds using the parallel features of the private cloud clusters and the computational capacities of the various nodes. Therefore, with pertinence to the problem of mass data and the frequent visits and clouds utilization, it is of great importance to speed up the processing capacities of mass data encryption, and then conduct parallel process of data encryption computations in combination with the features of cloud computing and the networks.

## 2 Related works

HE was first proposed by Rivest et al. in 1978 as a concept of “privacy homomorphism” [3], and is an encryption scheme which can directly conduct computations on the ciphertexts. Subsequently, RSA [4] and the ElGamal algorithm [5] with multiplicative homomorphism as well as Paillier [6] and the BNG algorithm [7] with additive homomorphism were successively proposed. Particularly, the above algorithms belong to the category of homomorphic encryption algorithms.

By 2009, Gentry proposed the first fully homomorphic scheme based on the ideal lattice [8], which can conduct any number of addition and multiplication operations on the ciphertext. Since then, more fully homomorphic scheme acts have been proposed, such as the fully homomorphic scheme DGHV [9] based on integers, BGV scheme [10] based on the RLWE, GSW13 scheme [11] based on the approximate eigenvectors, the multiple keys fully homomorphic ciphertext scheme [12] based on NTRU, and so on.

The low encryption efficiency is a problem which is mutually faced by the somewhat homomorphic encryption (SHE) algorithm and the fully homomorphic encryption( FHE) algorithm. In order to elevate the encryption efficiency, various kinds of schemes have been proposed.For example, papers [1316] introduce a scheme to elevate the efficiency of the RSA algorithm through different parallel methods, such as GPU, CPU or tree architecture. Wang et al. elaborated on the scheme of parallel technique on MapReduce so as to elevate the efficiency of Hill Cipher [17].

As for the fully homomorphic scheme, Gu proposed a kind of HE scheme which is based on the deal lattice together with SIMD technique [18]. Cheon improved the scheme of DGHV, and proposed an optimal method of batch processing plaintext [19]. Considering that the addition and multiplication calculations in the ciphertext homomorphism in the GSW scheme are only based on the addition and multiplication of the matrices, Hiromasa proposed a method to compress ciphertexts and optimize bootstrap [20].Moreover, the scheme was the first fully homomorphic method which can conduct encryptions of the matrices and support the homomorphic operations on the matrices.

Among all different kinds of the above mentioned HE algorithms, Hill Cipher has been proven to be lacking sufficient security. For the Paillier and RSA algorithms with the same length key, the Paillier algorithm has higher security. On the other hand, the Paillier algorithm is more suitable for parallel due to its property of additive homomorphism. More research has been done on the fully homomorphic encryption algorithm in recent years. However, due to the problem of encryption efficiency, most of them are still in the experimental stage and are not widely applied in practice.

With the goal of privacy protection, this paper realizes a kind of parallel encryption algorithm based on the MapReduce. Firstly, we use the additive homomorphism of the Paillier algorithm to divide the data that requires encryption into several approximately equal numbers according to the parity of each data packet. Then, using the parallelism in MapReduce, we realize the parallel encryption by grouping the plaintext. Experimental results show that the proposed scheme can achieve the speedup of 7.1 while maintaining security, thus solving the problem of low computational efficiency for a somewhat homomorphic encryption algorithm.

## 3.1 Paillier algorithm

In 1999, Paillier proposed a kind of probabilistic public key crypto system based on a high order residual class, i.e. the Paillier algorithm [6]. The concrete encryption scheme is defined as follows.

Generating key: Set n = p × q and λ = lcm(p − 1)(q − 1), where p and q are large primes, and then we randomly select a base $g\in {Z}_{{n}^{2}}^{\ast }$, this can be done efficiently by checking whether $gcd(L(gλmodn2),n)=1$(1) where the function L is defined as: $L\left(u\right)=\frac{u-1}{n}$, Now, (n, g) is regarded as public keys while the pair (p, q) (or equivalently λ) remains private.

Encryption: Plaintext mZn, a random number of $r\in {Z}_{n}^{\ast }$ is selected, then the ciphertext is defined as follows: $c=E(m)=gmrnmodn2$(2)

Decryption: Ciphertext $c\in {Z}_{{n}^{2}}^{\ast }$, Plaintext m is defined as follows: $m=D(c)=L(cλmodn2)L(gλmodn2)modn$(3)

It can be observed that Paillier's public key encryption algorithm has additive homomorphism, and the proving process is listed as follows: $E(m1)×E(m2)=(gm1r1nmodn2)(gm2r2nmodn2)=gm1+m2(r1r2)nmodn2E(m1+m2)=gm1+m2rnmodn2$(4) where r is a random number. Set r = r1 × r2, then E(m1 + m2) = E(m1) × E(m2) are satisfied.

## 3.2 MapReduce Model

From the perspective of the software system, the hadoop system includes two parts: the distributed storage and the parallel computations. The Hadoop Distributed File System (denoted as HDFS) is mainly used for the distributed storage of massive-scale data, and among them, the master node controls and manages the whole system of distributed files which are named as NameNodes. Furthermore, each slave node which is responsible for data storage is defined as a DataNode.

In order to realize the parallel computation processing of the large data stored in the HDFS, Hadoop is used to propose a parallel computational framework (named MapReduce). The computational framework contains a master node (named JobTracker) and a multitude of slave nodes are defined as TaskTrackers. The JobTracker is mainly responsible for scheduling and managing the tasks in the operations, while the TaskTracker is responsible for executing the tasks distributed by the JobTracker.

The MapReduce parallel computing framework is a parallelized program execution system that provides a parallel processing model and a process comprising two stages of Map and Reduce. In the Map phase, the input tuples are partitioned by each Mapper, and tuples with the same partition value are passed to the same Reducer for correlation calculation.

## 4 An Encryption Scheme Based on the Additive Homomorphism

The encryption algorithm in this work mainly uses the additive homomorphism of the Paillier algorithm to encrypt, and is defined as follows.

$E(m)=E(m1+m2)=E(m1)×E(m2)$

To ensure the security of the encryption algorithm, the length of the public key is set to 256 bit, and the specific encryption scheme is listed as follows.

1. According to the definition of Paillier encryption algorithm, public keys (n, g) and private keys (p, q) are generated.

2. Assume that the length of the plaintext (L MB) can be divided into x groups of 256 bits in length, and the number of packets x is computed as follows $x=⌈L×8×220256⌉=⌈L×22032⌉$(5)

3. For each packet, the plaintext is firstly converted to BigInteger type, the value of which is represented as m, and m = m1 + m2 is satisfied. Afterwards, the values of m1 and m2 are computed. If m is an even number (m mod 2 = 0), then ${m}_{1}={m}_{2}=\frac{m}{2}$, else the values of m1 and m2 are given as follows.

$m1=(m−1)/2m2=(m+1)/2(m mod2)=1$(6)

4. E(m1) and E(m2) are calculated respectively, and the specific formula is given as follows.

$E(m1)=gm1r1n mod n2E(m2)=gm2r2n mod n2$(7)

The ciphertexts are E(m1) and E(m2). We let r1 = r2 while m1 = m2, hence, we just need to calculate E(m1) for E(m1) = E(m2).

During the decryption process, according to the additive homomorphism of Paillier, the algorithm can be figured out as follows.

$E(m)=E(m1)×E(m2)mod n2$(8)

Then, using the decryption formula (Eq. 3), the plaintext can be established.

## 5 Parallel Encryption Scheme based on the MapReduce

As is illustrated in this paper, the parallel encryption scheme based on the MapReduce combines the cloud environment and additive homomorphism of the Paillier algorithm, and realizes parallel encryptions by conducting blocking on the plaintexts. Thus, the encryption efficiency can be greatly enhanced.

## 5.1 Algorithm Flow

In the programming model of MapReduce, Split function is used to divide the input data into splints with fixed sizes based on the user's needs. Afterwards, the master node distributes them to different processors based on the relevant scheduling mechanism. The Map function conducts relevant operations on each splint after splinting blocks based on an algorithm self-defined by the user, with each Map accomplishing one part of the results. The Reduce function is responsible for integrating the results of all the Maps. The encryption calculation of each splint of the parallel scheme is independent. Therefore, it can be distributed to multiple Maps for encryption at the same time, and it can be defined as a tuple of polynomial time algorithms $∏=(Split,Map,Reduce)$(9)

The specific process is as shown in Fig. 1.

Figure 1

Parallel encryption process of Paillier

## 5.2 Split Algorithm

We assume that p is the number of the cores for set processing, and the primary file is divided into n blocks (n > 1), and blocksizei indicates the size of the i-th block (in). As the length of the encryption key is 256 bits, the size of the plaintext splint is an integral multiple of 32 bits, and specifically the size of each data block can be calculated with Eq. 10.

$Bsizei(B)=⌈L×22032×n⌉×32i(10)

Fig. 2 shows the specific block algorithm. The content of the i-th splint is stored using the file buffer, and Key indicates the offset of the initial part of i-th splint in the file. Moreover, the value is stored in each file buffer.

Figure 2

shows the specific block algorithm

## 5.3 Map Functions and Reduce Functions

Map ( ) is a single task, and the Mapper class refers to the one for realizing the Map tasks. Hadoop provides an abstract Mapper base class. We inherit this base class, and realize the functions of the relevant interfaces among them. The detailed interface of the Map ( ) method is defined as follows: public void map (Object key, Text value, Context context) throws IOException Interrupted Exception. The parameter key is the key value transmitted into the map, and the values is the corresponding key value, the context is parameter of the environment subject that an environmental subject for the access of Hadoop by the programs. Map functions repeatedly on each group of data in each block data. Fig. 3 shows the encryption algorithm implemented in each Map ( ).

Figure 3

Map function

The detailed interface of Reduce ( ) is defined as follows: protected void reduce (KEYIN key, Iterable<VALUEIN>values, Context context) throws IOException, Interrupted Exception { }. The input parameter key is the key value that is input to reduce, and the values are the lists of the corresponding key value, the context is the parameter of the environment subjects, which were the environment subjects for the accesses of Hadoop by the programs.

The <key, value> are merged using the key values of the Map functions outputs, and the different values under the same keys are merged into the same list, they are sequenced based on the key values. When the files are written, only the value portion is output without recording the key values. As the key values are the offsets of the texts, the local ciphertext can be spliced into the complete ciphertext output in order.

## 5.4 Performance Analysis

We assume that the entire encryption time of the Paillier algorithm, key generation and the encryption times are Tseq, Tkey and TEnc respectively. Then Tseq can be expressed as Tseq = Tkey + TEnc. We can know that the main computation overhead in the encryption scheme is the modular exponentiation computation.

Assuming that the time cost for a single modular exponentiation operation is Tpd, then the time cost for conducting one encryption computation is represented as 2Tpd. Based on the above assumption, the plaintext with a length of L(MB) is divided into χ groups. Hence, the time needed to encrypt the plaintext of length L(MB) is defined as TEnc = 2 × χ × Tpd, the entire encryption time is Tseq = Tkey + 2 × χ × Tpd. Based on Eq. 5, the following equation can be obtained $Tseq=Tkey+2×⌈L×22032⌉×Tpd$(11)

When the value of L is bigger, Tkey can be ignored, and it can be seen that with the increase of L value, the encryption time Tseq basically presents a trend of linear rise.

During the process of the parallel encryptions, we assume that the operational process has no overlapping, the execution time Tn of the parallel encryption algorithm is composed of four parts, that is $Tn=Tcomm+Tkey+TMap+Treduce$(12) where Tcomm is the communication time, TMap is the parallel encryption time of Map, and Treduce is the time for conducting merging of the ciphertext based on the key values after encrypting.

Assume that the CPU has p cores, the plaintext with a length of L(MB) is divided into n blocks, and the processing time of the i-th block on the CPU core by a map is Ti, then $Tn=Tcomm+Tkey+Max(Ti)×⌈np⌉+Treduce$(13)

Based on the size of each splint given by Eq. 10, it can be inferred that each block of plaintext contains the number of packets $B{x}_{i}=⌈\frac{L×{2}^{20}}{32×n}⌉$, then $Ti=2×⌈L×22032×n⌉×Tpd$(14)

Assuming the same size of plaintext data, the size of the generated ciphertext is the same, and the Reduce time needed by each group of data for the generation of the ciphertext is Tric. Afterwards, the Reduce time Treduce needed by the entire ciphertexts is listed as follows $Treduce=x×Tric=⌈L×22032⌉×Tric$(15)

It can be learned that Treduce presents a proportional relation with the size of the generated ciphertext, and it can be derived as follows.

$Tn=Tcomm+Tkey+2×⌈L×22032×n⌉×Tpd×⌈np⌉+⌈L×22032⌉×Tric$(16)

If the value of L is bigger, Tkey and Tcomm can be ignored. According to the Eq. 16, we can conclude that with the value increasing, the main overhead of the encryption time Tn is shifted from being dominated by Map to Reduce.

The integral speed-up ratio Sp can be expressed as follows $Sp=TseqTn=Tkey+TEncTcomm+Tkey+TMap+Treduce$(17)

As Tcomm and Tkey can be ignored, then the following equation can be obtained.

$Sp≈2×⌈L×22032⌉×Tpd2×⌈L×22032×n⌉×Tpd×⌈np⌉+⌈L×22032⌉×Tric≈11n×⌈np⌉+Tric2×Tpd$(18)

We can know that when the total core number p is fixed and n ∈ (kp, kp + p], the speed-up ratio ηT presents an increasing trend, and the maximum will not exceed p with k a natural number.

## 5.5 Security Analysis

This scheme is homomorphic, and under the selection of the plaintext attacks, it is semantically secure. In paper [6], the encryption scheme proposed by Paillier is designed based on the calculations among the ${Z}_{{N}^{2}}^{\ast }$ group, of which N is a module of RSA. As < N, g > ∈ Pn is satisfied, the following equation can be satisfied ${P}_{N,g}:Z×{Z}_{N}^{\ast }\to {Z}_{{N}^{2}}^{\ast }$.

Paillier has proved that PN,g is a one-way trapdoor permutation. As Pn is a bijection, it is known as < N, g > ∈ Pn. For an element $c\in {Z}_{{N}^{2}}^{\ast }$, there exists a sole $\left(m,r\right)\in {Z}_{N}×{Z}_{N}^{\ast }$, which satisfies c = gm rN mod N2, m is known as a class that c relates to N and g, and is recorded as ClassN, g(c). In case the decomposition of N is known, it is easy to calculate ClassN, g(c). On the other hand, if the decomposition of N is not known, up till now, no polynomial time algorithm for calculating ClassN, g(c) has been found. We represent the unidirectional polarity of PN,g as Pailier1[N, g]. This is where the hardness in the calculations of composite residuosity class, i.e. Pailier1[N, g] = Class[N, g].

## 6.1 Experiment settings

The hardware platform used in this experiment includes a Master node and three slave nodes. Particularly, the Master node is responsible for the monitoring and scheduling of jobs, while the slave node is in charge of storage file distribution and calculation. The specific hardware configurations and software environment of each node are listed in the node configurations of experiment cluster in Table 1.

Table 1

Software and hardware configuration

## 6.2 Experiment Results Analysis

In this experiment, encryption tests are conducted on the plaintexts with respective sizes of 256MB, 512MB, 768MB, 1024 MB,1280 MB,1536 MB,1792 MB and 2048 MB. The experiment involves two kinds of serial and the parallel test. In the serial environment, direct encryption is conducted on the plaintexts without the need of splinting. In contrast, the data needs to be splinted into lots of blocks in the parallel environment. The block size used in this experimental environment is set to 64MB, therefore, these files are divided into different data blocks, with the number of data blocks being 4, 8, 12, 16, 20, 24,28 and 32 respectively.

In the experiments, four computational nodes are used, with the core number of the CPU being 4, and the total core number for the CPU is 16. Table 2 respectively records the sizes of the different files, the encryption time of the files and the total speed-up ratio under the serial and the parallel environment. FS, SET, PET, MMT and RT respectively mean File size, Serial encryption time, Parallel encryption time, Max Map time and Reduce time. Fig. 4 indicates the encryption time of files of different sizes under the serial and the parallel environments, Fig. 5 indicates the integral speed-up ratio of files of different sizes under the serial and the parallel environments.

Figure 4

The contrast diagram of encryption time

Figure 5

The speed-up rate of the different size file

Table 2

The test results of different files

From the above experimental results (shown in Table 2, Fig. 4 and Fig. 5), the following conclusions can be drawn.

1. Under the circumstance of fixed node numbers, the time needed by the serial encryption presents a proportional relation with the plaintext size.

2. The time needed by the parallel encryption increases along with the increase of the plaintext.

3. When n < p, the time consumption of the map functions is the main time consumption of the encryption process, and when n is increasingly approaching p, the difference between the time consumed by the reduce functions and the map functions gradually decreases.

4. When n > p, and along with the increase of n, the time consumption of reduce functions becomes the main time consumption during the encryption process. The main reason being that only one node is responsible for Reduce, and this also constrains the speed-up ratio.

5. When n < p, the speed-up ratio Sp increases faster, and when n = p, the maximum value of Sp is reached. When n > p, at each n ∈ (kp, kp + P), the speed-up ratio presents a trend of slow increase, and when n = (k + 1) × p, the maximum value is reached.

## 7 Conclusion

In this paper, we propose a novel privacy-preserving PHE scheme based on MapReduce, which uses the additive homomorphism of the Paillier algorithm. The proposed scheme is suitable for cloud computing environments due to its parallelism. Experimental results indicate that the scheme enabled the speed-up ratio to reach 7.1 through the parallelism of clusters.

In the future, we will extend this work in the following aspects: (1) To conduct the optimization of the Reduce functions and then adopt two or more Reducers. (2) To study the parallelism of other HE algorithms, and then compare them with the efficiency of this algorithm so as to find out the optimal HE algorithm.

## Acknowledgement

This research is supported by the National Natural Science Foundation of China under the Grants nos. 61572263, 61502251 and 61502243, Natural Science Foundation of Jiangsu Province under the Grants nos. BK20151511, BK20141429 and BK20161516, Colleges and Universities in Jiangsu Province plans to graduate research and innovation under Grant no. KYLX_0816, Natural Science Research Project of Jiangsu University under the Grants nos.(14KJB520031 and 15KJB520027),the Nature Science Project of Nanjing University of Posts and Telecommunications under the Grants nos.(NY215097 and NY214127).

## References

• [1]

Huang R.W., Gui X.L., Yu S., et al., Privacy-preserving computable encryption scheme of cloud computing, CJC., 2011, 34, 2391-2402. Google Scholar

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• [3]

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Paillier P., Public-key cryptosystems based on composite degree residuosity classes, EUROCRYPT'99 (2-6 May 1999,Prague, Czech republic), Springer, Berlin, Heidelberg, 1999, 223-238. Google Scholar

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Boneh D., Goh E.J., Nissim K., Evaluating 2-DNF formulas on ciphertexts, Second Theory of Cryptography Conference (10-12, February 2005, Cambridge, MA, United states), Springer, Berlin, Heidelberg, 2005, 325-341. Google Scholar

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Gentry C., Fully homomorphic encryption using ideal lattices, ACM symposium on Theory of Computing (May 31-June 2, 2009, Bethesda, MD, United states), Association for Computing Machinery, New York, 2009, 169-178. Google Scholar

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Dijk M., Gentry C., Halevi S., et al., Full homomorphic encryption over the integers, Advances in Cryptology EUROCRYPT 2010, Springer, Berlin Heidelberg, 2009, 24-43. Google Scholar

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Brakerski Z., Gentry C., Vaikuntanathan V., (Leveled) Full homomorphic encryption without bootstrapping, the 3th Innovations in Theoretical Computer Science Conference (8-10, January, 2012, Cambridge, Massachusetts, UK), ACM, New York, 2012, 309-325. Google Scholar

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Gentry C., Sahai A., Waters B., Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based, 33rd Annual International Cryptology Conference (18-22, August, 2013, Santa Barbara, CA, United states), Springer, Heidelberg, 2013, 75-92. Google Scholar

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López-Alt A., Tromer E., On-the-fly multiparty computation on the cloud via multikey full homomorphic encryption, 44rd annual ACM symposium on Theory of computing (19-22, May, 2012, New York, NY, United states), ACM, New York, 2012, 1219-1234. Google Scholar

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Accepted: 2016-12-16

Published Online: 2017-04-06

Citation Information: Open Physics, Volume 15, Issue 1, Pages 135–142, ISSN (Online) 2391-5471,

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text:
## Beautiful Skylines

Points: 1 (partial)
Time limit: 5.0s
Memory limit: 512M

Authors:
Problem types

You are an architect designing a city, and you have decided that you are going to make it beautiful, or more specifically, that it is going to have a beautiful skyline. A skyline consists of $$N$$ consecutive, unit width buildings, each with a height between $$0$$ and $$H$$ inclusive. It is considered beautiful if the height of two directly adjacent buildings differs by no more than $$K$$. In order to design your beautiful city, you first want to know how many different beautiful skylines are possible.

Consider a skyline where $$N=6$$ and $$H=4$$. We represent a building a single column, where x indicates where a building is:

..x...
x.x...
xxx.x.
xxxxx.

The third and fourth buildings differ in height by $$3$$. Thus, this is only a beautiful skyline if $$K\geq 3$$.

#### Input Specification

The input will start with an integer $$T$$, the number of test cases to follow. Each test case consists of a line containing three integers: $$N$$, the number of buildings in your skyline, $$H$$, the maximum possible height of a building in the skyline and $$K$$, the maximum number of units of height that two adjacent buildings can differ by in order to be a beautiful skyline.

#### Output Specification

For each test case in the order given, output a single line containing a single integer, the number of beautiful skylines there are modulo $$10^9+7$$.

#### Bounds

Note this problem includes sub-problems of increasing difficulty worth different numbers of points:

• 50 points: $$1 \leq N, H, K \leq 100$$
• 100 points: $$1 \leq N, H, K \leq 2000$$
• 150 points: $$1 \leq N \leq 10^9$$ and $$1 \leq H, K \leq 100$$

Important Note: Observe that the 150 point sub-problem is not a superset of the 100 point sub-problem. You may need to implement some sort of conditional logic to switch algorithms.

For all sub-problems:

$$1 \leq T \leq 10$$

#### Sample Input

4
2 2 2
2 2 1
3 2 1
50 50 20

#### Sample Output

9
7
17
785605991

## Comments

There are no comments at the moment.


text:
# Usual sources of cigarettes

Usual sources of cigarettes were reported in previous editions, but this measure is not included on the CTNS.


text:
Well, it's been almost two months since my last update. I suppose if this were a blog, that would be unacceptable.

Anyway, I still don't have anything interesting to say, so I'll have to defer to others.

And, fortunately, some decent articles from Evangelicals Now appeared in my Bloglines feeds this morning.


text:
# Why not use Beta(1,1) as boundary avoiding prior on a transformed correlation parameter?

In Bayesian Data Analysis, chapter 13, page 317, second full paragraph, in the modal and distributional approximations, Gelman et al. write:

If the plan is to summarize inference by the posterior mode of $\rho$ [the correlation parameter in a bivariate normal distribution], we would replace the U(-1,1) prior distribution with $p(\rho) \propto (1 - \rho)(1 + \rho)$, which is equivalent to a Beta(2,2) on the transformed parameter $\frac{\rho + 1}{2}$. The prior and resulting densities are zero at the boundaries and thus the posterior mode will never be -1 or 1. However,...the prior density for $\rho$ is linear near the boundaries and thus will not contradict any likelihood.

Below is a plot of the PDF for the Beta(2,2) distribution.

Although the plot is given for the domain [0,1], the shape is the same for the domain [-1,1] obtained by performing the inverse of the transformation described in the quote above. This is a fairly informative distribution! It gives about seven times the density to $\frac{\rho + 1}{2} = 0.5$ than it does to $\frac{\rho + 1}{2} = 0.3,0.97$. So in fact it would contradict the likelihood if the likelihood pointed toward something far from the boundaries, but even further from $\rho = 0$. Wouldn't a better boundary avoiding prior be Beta(1 + $\delta$,1 + $\delta$), where $\delta \rightarrow 0$. Take, for example, Beta(1.0001, 1.0001), plotted below:

The trouble with this prior, of course, is that the density drops very sharply near zero, which may contradict the likelihood of it points to a space that is very very near a boundary. Which brings me to my question:

Why not just set the prior of the transformed correlation parameter to Beta(1,1)? Because the beta distribution density is zero for $\frac{\rho + 1}{2} = 0,1$, this is equivalent to the uniform distribution over the open interval (-1,1) rather than the closed interval [-1,1], and so is it not a boundary avoiding prior, and is it not preferable to a prior that places fairly strong belief in the probability that $\rho = 0$, which is only desirable if you actually have that belief?

More generally, isn't using the beta distribution by definition a boundary avoiding prior because its support is $0 < \frac{\rho + 1}{2} < 1$?

In cases where the likelihood function is maximized at $\rho=-1$, using Beta(1,1) over an open interval doesn't help since then there is no well-defined posterior mode. There is no point in the open interval that you could say is the posterior mode.


text:
# Posts published in “Mathematics”

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Also read, Circle Formulas Circle Theorems Lines and Angles Straight Line Coordinate Geometry Conic Section Formulas: Since we have read simple geometrical figures in earlier…

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Also, read Matrix Formulas Determinant Formulas Set Theory Mean Median Mode Formula: Nowadays, you must be aware of the use of data through statistics almost…

Also, read Matrix Formulas Mean, Median, Mode Formulas Set Theory Determinant formulas: In the previous section we discussed matrices. Now you are much aware of…

Also, read Determinant formulas Mean, Median, Mode Formulas Set Theory Matrix Algebra: Matrix has emerged as a great mathematical tool which simplifies our work to…

Differentiability of a function: Differentiability applies to a function whose derivative exists at each point in its domain. Actually, differentiability at a point is defined…

Continuity: We can say a function f ( x ) to be continuous at x = a if \(\mathop {\lim }\limits_{x \to a} f\left( x…

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Also read, Circle Formulas Area Formulas Lines and Angles Coordinate Geometry Conic Section Formula The Straight line: Straight line definition is simple according to euclidian…

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text:
# GENERALIZED INVERSES IN NUMERICAL SOLUTIONS OF CAUCHY SINGULAR INTEGRAL EQUATIONS

• Kim, S. (Department of Mathematics Ewha Womans University)
• Published : 1998.10.01

#### Abstract

The use of the zeros of Chebyshev polynomial of the first kind $T_{4n＋4(x}$ ) and second kind $U_{2n＋1}$ (x) for Gauss-Chebyshev quad-rature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_{n}$ /(x) and $U_{m}$(x) as in [8]. We show that the coefficient matrix of the overdetermined system has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.e.


text:
## No relationship between inter- and intra-subject CV [Power / Sample Size]

Hi arl_stat,

» Mostly in public domain, the inter subject CV of drug is not mentioned.

You fell into trap of wrong terminology. Even if a study was performed in a parallel design, one gets the total (a.k.a. pooled) CV – not the inter-subject CV.$$CV_{\textrm{total}}=\sqrt{\exp\left(\log_{e}(CV_{\textrm{inter}}^{2}+1)+\log_{e}(CV_{\textrm{intra}}^{2}+1)\right)-1}\tag{1}$$
Simply: The total variance (which you observe in any design) is the sum of inter- and intra-subject variances.$$s_{\textrm{total}}^{2}=s_{\textrm{inter}}^{2}+s_{\textrm{intra}}^{2}\tag{2}$$ The inter-subject CV is only accessible in a crossover study (see this post).

» […] can we use this intra-subject CV to estimate sample size for parallel study design?

No.

» Is there any formula to calculate inter-subject CV using 90% confidence interval ranges and number of subjects?

No, since you need the CVtotal calculated acc. to $$(1)$$ from a crossover – or directly observed in a parallel design – and there is no relationship between CVinter and CVintra. Hence, CVintra from a crossover alone does not help.

» First can we calculate the sample size of 2 way crossover study design and then double the subjects and finalize the sample size for parallel study design?

No (see above). For ages rumors are swirling around a factor of two but that’s plain nonsense. Think about a drug with low CVintra and polymorphic metabolism. Then the factor can easily be >5 and by doubling the sample size of a crossover the parallel study will be grossly underpowered. BTW, in rare cases CVintra > CVinter.

Run a – not too small! – pilot study or a TSD.*

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes


text:
LATEST NONSENSE
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