An RNS-Enhanced Microprocessor Implementation of Public Key Cryptography

Lim, Zhining; Phillips, Braden J.

doi:10.1109/acssc.2007.4487465

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…More recently, RNS was used in cryptographic applications to speed up computations over very large operands for RSA (1024-4096 bits) [23,2,21], elliptic curve cryptography [28,22,14] (ECC, 160-550 bits), and pairings [7,11]. Nonpositional property of RNS can be used to randomize internal computations as a protection against side channel attacks [3,8] or fault ones [8,15].…”

Section: Improving Modular Inversion In Rns Using the Plus-minus Methmentioning

confidence: 99%

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Improving Modular Inversion in RNS Using the Plus-Minus Method

Bigou

Tisserand

2013

Cryptographic Hardware and Embedded Systems - CHES 2013

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Abstract. The paper describes a new RNS modular inversion algorithm based on the extended Euclidean algorithm and the plus-minus trick. In our algorithm, comparisons over large RNS values are replaced by cheap computations modulo 4. Comparisons to an RNS version based on Fermat's little theorem were carried out. The number of elementary modular operations is significantly reduced: a factor 12 to 26 for multiplications and 6 to 21 for additions. Virtex 5 FPGAs implementations show that for a similar area, our plus-minus RNS modular inversion is 6 to 10 times faster.

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Section: Improving Modular Inversion In Rns Using the Plus-minus Methmentioning

confidence: 99%

“…Efficient RNS modular reduction and RNS modular multiplication methods have been proposed in [27,19,1,26] RNS modular multiplication for RSA was studied in [27,19,1]. Full RSA in RNS implementations can be found in [23,2,21]. As far as we know, the best RNS exponentiation algorithm is described in [12].…”

Section: Notations and Definitionsmentioning

confidence: 99%

Improving Modular Inversion in RNS Using the Plus-Minus Method

Bigou

Tisserand

2013

Cryptographic Hardware and Embedded Systems - CHES 2013

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“…An inner-product-step-processor (IPSP) consists of a series of multiply-add-delay operations. Such IPSP-like architectures [Con04], [Lim99], [Lim07], [Re01], [Sha85], [Sod86] are prevalent in finite impulse response (FIR) filter, infinite impulse response (IIR) filter, discrete wavelet transform (DWT), fast Fourier transform (FFT), convolution, etc. Although RNS has been proven to be useful in the datapath optimization of these DSP applications, the iterative IPSP computations often result in temporarily expansion of dynamic range.…”

Section: Motivationmentioning

confidence: 99%

VLSI efficient RNS scalers and arbitrary modulus residue generators

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Carry propagation has been identified as the main timing bottleneck of the datapath elements of application-specific digital signal processors in the accustomed positional number system. Residue Number System (RNS), being a non-weighted number system, emerges as a good remedy to this problem. RNS gains phenomenal successes in speeding up the datapath of digital signal processing applications dominated by additions/subtractions and multiplications, such as digital filters, convolution, channelizers, equalizers, discrete transforms, etc. Despite xii

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