An FPGA implementation of a GF(p) ALU for encryption processors

Daly, Alan J.; Marnane, William P.; Kerins, Tim; Popovici, Emanuel

doi:10.1016/j.micpro.2004.03.006

Cited by 55 publications

(31 citation statements)

References 11 publications

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“…But the maximum frequency was reduced to a very low level, because too many arithmetic operations have to be completed within one clock cycle. Similar drawbacks in frequency can also be found in [2,17].…”

Section: High-radix Montgomery Multiplicationsupporting

confidence: 63%

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A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$

Liu

Pan

et al. 2014

Lecture Notes in Computer Science

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Abstract. Elliptic curve cryptography (ECC) is preferred for highspeed applications due to the lower computational complexity compared with other public-key cryptographic schemes. As the basic arithmetic, the modular multiplication is the most time-consuming operation in publickey cryptosystems. The existing high-radix Montgomery multipliers performed a single Montgomery multiplication either in approximately 2n clock cycles, or approximately n cycles but with a very low frequency, where n is the number of words. In this paper, we first design a novel Montgomery multiplier by combining a quotient pipelining Montgomery multiplication algorithm with a parallel array design. The parallel design with one-way carry propagation can determine the quotients in one clock cycle, thus one Montgomery multiplication can be completed in approximately n clock cycles. Meanwhile, by the quotient pipelining technique applied in digital signal processing (DSP) blocks, our multiplier works in a high frequency. We also implement an ECC processor for generic curves over GF(p) using the novel multiplier on FPGAs. To the best of our knowledge, our processor is the fastest among the existing ECC implementations over GF(p).

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Section: High-radix Montgomery Multiplicationsupporting

confidence: 63%

“…From the perspective of the radix, the Montgomery multiplication implementations can be divided into two categories: radix-2 based [7,21] and high-radix based [1,2,9,11,17,19,20,22,23]. Compared with the former one, the latter, which can significantly reduce the required clock cycles, are preferred for high-speed applications.…”

Section: Introductionmentioning

confidence: 99%

A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$

Liu

Pan

et al. 2014

Lecture Notes in Computer Science

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“…While addition and subtraction are relatively easy to implement, modular multiplication is much more complex. An in depth review of modular arithmetic and architectures can be found in [8] The processor architecture in Figure 1 is capable of controlling a number a arithmetic units. There are two architecture types available for the processor.…”

Section: A Arithmetic Unitsmentioning

confidence: 99%

SPA resistant elliptic curve cryptosystem using addition chains

Byrne

Crowe

Marnane

et al. 2007

IJHPSA

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Abstract-There has been a lot of interest in recent years in the problems faced by cryptosystems due to side channel attacks. Algorithms for elliptic curve point scalar multiplication such as the double and add method are prone to such attacks. By making use of special addition chains, it is possible to implement a Simple Power Analysis(SPA) resistant cryptosystem. In this paper a reconfigurable architecture for a cryptographic processor is presented. A SPA resistant algorithm for point multiplication is implemented and is shown to be faster than the double-and-add method. Post place and route results for the processor are given.

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“…Therefore ECC has become final choice in smart cards, credit cards and mobile phones due to its strength to provide equivalent security compared to RSA. It is estimated that security level of 160 and 224 bits ECC cryptosystem is equivalent to the 1024 and 2048 bits RSA respectively [3,4] The research on efficient algorithms and hardware accelerations have concentrated on efficient implementation of elliptic curve point multiplication which is the fundamental operation of all elliptic curve cryptosystems. The elliptic curve point multiplication is computed with point operations which, further are computed using finite field arithmetic.…”

Section: Introductionmentioning

confidence: 99%

A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography

Sridhar¹,

N²

2012

IJCA

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This paper presents a technique to speed up the computation of inversion of NIST recommended elliptic curve with modulus p 521 -1. The property of multiplicative inverse between pair of numbers over Meresenne"s prime is used to reduce the number of iterations in the Binary Inversion Algorithm in GF(p). This increases the speed requirement for point operations applicable to Elliptic Curve Cryptography. This paper proposes an model of the architecture to achieve the above objective which uses parallelism in multiplicative inversion arithmetic block to speed up the computation.

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An FPGA implementation of a GF(p) ALU for encryption processors

Cited by 55 publications

References 11 publications

A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$

A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$

SPA resistant elliptic curve cryptosystem using addition chains

A Technique to Speed up the Modular Multiplicative Inversion over GF(P) Applicable to Elliptic Curve Cryptography

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