Samuel Freitas Antao
This thesis addresses the design of cryptographic accelerators, ranging from the embedded system to the high-performance computing device. New techniques are proposed to allow several cryptographic algorithms to be computed by the same target. Therefore, flexibility (to support several algorithms) and scalability (to extend the features of a designed accelerator) are two keywords in all […]
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Yuheng Liu
For a given level of security, elliptic curve cryptography (ECC) offers improved efficiency over classic public key implementations. Point multiplication is the most common operation in ECC and, consequently, any significant improvement in perfor- mance will likely require accelerating point multiplication. In ECC, the Montgomery algorithm is widely used for point multiplication. The primary purpose […]
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Utsab Bose, Anup Kumar Bhattacharya, Abhijit Das
Eta pairing on a supersingular elliptic curve over the binary field F_2_1223 used to offer 128-bit security, and has been studied extensively for efficient implementations. In this paper, we report our GPU-based implementations of this algorithm on an NVIDIA Tesla C2050 platform. We propose efficient parallel implementation strategies for multiplication, square, square root and inverse […]
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Joppe W. Bos
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 […]
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Joppe Willem Bos
Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice are studied and techniques are presented to speed-up the underlying arithmetic on parallel architectures. The fastest known approach to solve the discrete logarithm problem in groups of elliptic […]
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Ye Zhang, Chun Jason Xue, Duncan S. Wong, Nikos Mamoulis, S.M. Yiu
Recently, composite-order bilinear pairing has been shown to be useful in many cryptographic constructions. However, it is time-costly to evaluate. This is because the composite order should be at least 1024bit and, hence, the elliptic curve group order $n$ and base field become too large, rendering the bilinear pairing algorithm itself too slow to be […]
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Samuel Antao, Jean-Claude Bajard, Leonel Sousa
Acceleration of cryptographic applications on massive parallel computing platforms, such as Graphic Processing Units (GPUs), becomes a real challenge concerning practical implementations. In this paper, we propose a parallel algorithm for Elliptic Curve (EC) point multiplication in order to compute EC cryptography on these platforms. The proposed approach relies on the usage of the Residue […]
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Aaron E. Cohen, Keshab K. Parhi
This paper presents the Graphics Processing Unit (GPU) accelerated version of the LSB Invariant scalar point multiplication for binary elliptic curves. This method was implemented using the CUDA programming language for nVidia graphics cards. With a parallel factor of (length+1) and Lopez-Dahab projective coordinate Pi’s, on an nVidia GTX 285 graphics card precomputation takes 190.203995 […]
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Daniel Bernstein, Tien-Ren Chen, Chen-Mou Cheng, Tanja Lange, Bo-Yin Yang
This paper reports record-setting performance for the elliptic-curve 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 […]
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