Elliptic Curve point multiplication on GPUs

Antão, Samuel; Bajard, Jean-Claude; Sousa, Leonel

doi:10.1109/asap.2010.5541000

Cited by 36 publications

(16 citation statements)

References 7 publications

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“…Our approach differs from the previous reports implementing ECC schemes on GPUs [5,3,53,2] in that we divide the elliptic curve arithmetic over multiple threads instead of dividing a single finite field operation over the available resources. The presented algorithms are based on methods originating in cryptographic side-channel analysis [31] and are designed for a parallel computer architecture with a 32-bit instruction set.…”

Section: Introductionmentioning

confidence: 62%

“…This is an order of magnitude faster, in term of response time, compared to the previous fastest low-latency implementation [2]. Figure 1 shows the latencies when varying the amount of threads, eight threads are scheduled to work on a single ECSM, for different block-sizes on the GTX 580.…”

Section: Resultsmentioning

confidence: 94%

“…This might be one of the few available options to lower the latency for schemes which perform a sequence of data-dependent modular multiplications, such as in RSA where the main operation is modular exponentiation, but different approaches can be tried in the setting of elliptic curve arithmetic. We follow the ideas from [27,25] and choose, in contrast to for instance [2], to let a single thread compute a single modular multiplication. The parallelism is exploited at the elliptic curve arithmetic level where multiple instances of the finite field arithmetic are computed in parallel to implement the elliptic curve group operation.…”

Section: Parallel Algorithmsmentioning

confidence: 99%

“…These papers report performance benchmark results to demonstrate that the GPU architecture can already be used as a cryptologic workhorse. Previous published GPU implementations cover asymmetric cryptography, such as RSA [39,53,24], and ECC [53,2], and symmetric cryptography [35,22,56,23,45,12]. The GPU has also been considered to enhance the performance of cryptanalytic computations in the setting of finding hash collisions [8], integer factorization [5,3] and computing elliptic curve discrete logarithms [4].…”

Section: Introductionmentioning

confidence: 99%

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Low-Latency Elliptic Curve Scalar Multiplication

Bos

2012

Int J Parallel Prog

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This paper presents a low-latency algorithm designed for parallel computer architectures to compute the scalar multiplication of elliptic curve points based on approaches from cryptographic side-channel analysis. A graphics processing unit implementation using a standardized elliptic curve over a 224-bit prime field, complying with the new 112-bit security level, computes the scalar multiplication in 1.9 milliseconds on the NVIDIA GTX 500 architecture family. The presented methods and implementation considerations can be applied to any parallel 32-bit architecture.

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Section: Introductionmentioning

confidence: 62%

Section: Resultsmentioning

confidence: 94%

Section: Parallel Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-Latency Elliptic Curve Scalar Multiplication

Bos

2012

Int J Parallel Prog

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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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Vectorizing and distributing number‐theoretic transform to count Goldbach partitions on Arm‐based supercomputers

Jesus,

Oliveira e Silva,

Weiland

2023

Concurrency and Computation

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SummaryIn this article, we explore the usage of scalable vector extension (SVE) to vectorize number‐theoretic transforms (NTTs). In particular, we show that 64‐bit modular arithmetic operations, including modular multiplication, can be efficiently implemented with SVE instructions. The vectorization of NTT loops and kernels involving 64‐bit modular operations was not possible in previous Arm‐based single instruction multiple data architectures since these architectures lacked crucial instructions to efficiently implement modular multiplication. We test and evaluate our SVE implementation on the A64FX processor in an HPE Apollo 80 system. Furthermore, we implement a distributed NTT for the computation of large‐scale exact integer convolutions. We evaluate this transform on HPE Apollo 70, Cray XC50, HPE Apollo 80, and HPE Cray EX systems, where we demonstrate good scalability to thousands of cores. Finally, we describe how these methods can be utilized to count the number of Goldbach partitions of all even numbers to large limits. We present some preliminary results concerning this problem, in particular a histogram of the number of Goldbach partitions of the even numbers up to 240.

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Elliptic Curve point multiplication on GPUs

Cited by 36 publications

References 7 publications

Low-Latency Elliptic Curve Scalar Multiplication

Low-Latency Elliptic Curve Scalar Multiplication

Cofactorization on Graphics Processing Units

Vectorizing and distributing number‐theoretic transform to count Goldbach partitions on Arm‐based supercomputers

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