Toward Acceleration of RSA Using 3D Graphics Hardware

Moss, Andrew; Page, Daniel; Smart, Nigel P.

doi:10.1007/978-3-540-77272-9_22

Cited by 52 publications

(29 citation statements)

References 14 publications

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“…GPUs have now developed into a powerful, highly parallel computing platform that finds more and more interest outside graphics-processing applications. In cryptography so far mostly secretkey applications were implemented (see, e.g., [14] and the book [15]) while taking full advantage of GPUs for public-key cryptography remained a challenge [38].…”

Section: Review Of Gpus and Gpu Programmingmentioning

confidence: 99%

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ECM on Graphics Cards

Bernstein

Chen

Cheng

et al. 2009

Advances in Cryptology - EUROCRYPT 2009

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Abstract. This paper reports record-setting performance for the ellipticcurve method of integer factorization: for example, 926.11 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers on a single PC. The state-of-the-art GMP-ECM software handles 124.71 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers using all four cores of a 2.4 GHz Core 2 Quad Q6600.The extra speed takes advantage of extra hardware, specifically two NVIDIA GTX 295 graphics cards, using a new ECM implementation introduced in this paper. Our implementation uses Edwards curves, relies on new parallel addition formulas, and is carefully tuned for the highly parallel GPU architecture. On a single GTX 295 the implementation performs 41.88 million modular multiplications per second for a general 280-bit modulus. GMP-ECM, using all four cores of a Q6600, performs 13.03 million modular multiplications per second. This paper also reports speeds on other graphics processors: for example, 2414 280-bit elliptic-curve scalar multiplications per second on an older NVIDIA 8800 GTS (G80), again for a general 280-bit modulus. For comparison, the CHES 2008 paper "Exploiting the Power of GPUs for Asymmetric Cryptography" reported 1412 elliptic-curve scalar multiplications per second on the same graphics processor despite having fewer bits in the scalar (224 instead of 280), fewer bits in the modulus (224 instead of 280), and a special modulus (2 224 − 2 96 + 1).

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Section: Review Of Gpus and Gpu Programmingmentioning

confidence: 99%

“…Aoki et al in [2] discovered small prime factors by sieving, discarded any unfactored parts above 2 105 , and then used ECM to discover primes up to 2 38 . Kleinjung reported in [29,Section 5] on ECM "cofactorisation" for a 1024-bit n consuming, overall, a similar amount of time to sieving.…”

Section: Introductionmentioning

confidence: 99%

ECM on Graphics Cards

Bernstein

Chen

Cheng

et al. 2009

Advances in Cryptology - EUROCRYPT 2009

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“…There are two recent papers employing modular techniques on the GPU ( [18], [24]). Despite the fact that they are concentrated on the acceleration of modular exponentiation, it is interesting within our context how they deal with the modular reduction after multiplication.…”

Section: Related Workmentioning

confidence: 99%

Efficient Multiplication of Polynomials on Graphics Hardware

Emeliyanenko

2009

Lecture Notes in Computer Science

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Abstract. We present the algorithm to multiply univariate polynomials with integer coefficients efficiently using the Number Theoretic transform (NTT) on Graphics Processing Units (GPU). The same approach can be used to multiply large integers encoded as polynomials. Our algorithm exploits fused multiply-add capabilities of the graphics hardware. NTT multiplications are executed in parallel for a set of distinct primes followed by reconstruction using the Chinese Remainder theorem (CRT) on the GPU. Our benchmarking experiences show the NTT multiplication performance up to 77 GMul/s 1 . We compared our approach with CPU-based implementations of polynomial and large integer multiplication provided by NTL and GMP 2 libraries.

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“…Cryptologic applications of GPUs have been considered before: symmetric cryptography in [33,20,56,21,44,11,18], asymmetric cryptography in [39,54,22] for RSA and in [54,1,9] for ECC, and enhancing symmetric [8] and asymmetric [7,5,6,10] cryptanalysis.…”

Section: Introductionmentioning

confidence: 99%

Cofactorization on Graphics Processing Units

Miele

Bos

Kleinjung

et al. 2014

Advanced Information Systems Engineering

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Abstract. We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core CPUs simultaneously. This allows those processors to focus on the memory-intensive sieving and results in more useful NFS-relations found in less time.

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Toward Acceleration of RSA Using 3D Graphics Hardware

Cited by 52 publications

References 14 publications

ECM on Graphics Cards

ECM on Graphics Cards

Efficient Multiplication of Polynomials on Graphics Hardware

Cofactorization on Graphics Processing Units

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