Fast modular multiplication using 2-power radix

Walter, Colin D.

doi:10.1080/00207169108803976

Cited by 12 publications

(5 citation statements)

References 6 publications

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“…Brickell [5] observes that R div M need only be approximated using the top bits of R and M in order to keep R bounded above. In particular [24], suppose that M is the approximation to M given by setting all but the k+3 most significant bits of M to zero, and that M is obtained from M by incrementing its k+3rd bit by 1.…”

Section: Modular Reduction and The Classical Algorithmmentioning

confidence: 99%

Montgomery’s Multiplication Technique: How to Make It Smaller and Faster

Walter¹

1999

Cryptographic Hardware and Embedded Systems

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Montgomery's modular multiplication algorithm has enabled considerable progress to be made in the speeding up of RSA cryptosystems. Perhaps the systolic array implementation stands out most in the history of its success. This article gives a brief history of its implementation in hardware, taking a broad view of the many aspects which need to be considered in chip design. Among these are trade-offs between area and time, higher radix methods, communications both within the circuitry and with the rest of the world, and, as the technology shrinks, testing, fault tolerance, checker functions and error correction. We conclude that a linear, pipelined implementation of the algorithm may be part of best policy in thwarting differential power attacks against RSA.

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Section: Modular Reduction and The Classical Algorithmmentioning

confidence: 99%

Montgomery’s Multiplication Technique: How to Make It Smaller and Faster

Walter¹

1999

Cryptographic Hardware and Embedded Systems

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“…It is claimed in this work that this shortens the cycle time of each iteration and gives a speedup factor of 70%. The second work was in the same year and it was about an algorithm which calculates a residue R and an integer quotient Q satisfying A × B = M × Q + R [198]. R is either the smallest non-negative residue of A × B mod M or differs by at most M from it.…”

Section: Other-non-montgomerymentioning

confidence: 99%

Hardware architectures for public key cryptography

et al. 2003

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This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e. RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems. Next an overview is given of the different hardware architectures which have been proposed in the literature.

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“…The techniques I-IV and VI are all used by Brickell [1]; V is found in [14] and [7] and VII in, for example, [7] and [10]. The look-up table, which might be used in VII, is more usually associated with III, as in [13].…”

Section: Existing Multipliersmentioning

confidence: 99%