Base extension using a convolution sum in residue number systems

Posch, Karl C.; Posch, Reinhard

doi:10.1007/bf02238608

Cited by 26 publications

(15 citation statements)

References 1 publication

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“…In this second case we observe that, using the classical ALU, we are restricted for the choice of moduli while our conditions (9) shows that taking more moduli without inducing errors is possible.…”

Section: New Rower Unitmentioning

confidence: 87%

“…One of them is that reduction over p is complex. Reduction over p is still possible when using Montgomery Reduction since it computes exactly the value using a base extension [9,10]. Thereafter, we recall the algorithm to compute the Montgomery Reduction in RNS [6,5,10].…”

Section: Rns and Montgomerymentioning

confidence: 99%

“…In [9,10], Posch and Posch introduced a floating approach to compute the base extension function. In [6], Kawamura came to a similar result, but the base extension function introduced by Kawamura supposes that the moduli m i are pseudo-Mersenne numbers of the form m i = 2 r − µ i with…”

Section: Base Extensionmentioning

confidence: 99%

“…We propose here a new ALU for the Rower unit to exploit the upper bound µ max ≤ 2 r α n given by our condition (9). Using this upper bound, we will be able to use smaller radix than the classical ALU for computing equivalent size of p (r = 16 for computing log 2 (p) = 521 whereas we need r = 18 with the classical ALU).…”

Section: New Rower Unitmentioning

confidence: 99%

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Double Level Montgomery Cox-Rower Architecture, New Bounds

Bajard

Merkiche²

2015

Smart Card Research and Advanced Applications

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Abstract. Recently, the Residue Number System and the Cox-Rower architecture have been used to compute efficiently Elliptic Curve Cryptography over FPGA. In this paper, we are rewriting the conditions of Kawamura's theorem for the base extension without error in order to define the maximal range of the set from which the moduli can be chosen to build a base. At the same time, we give a procedure to compute correctly the truncation function of the Cox module. We also present a modified ALU of the Rower architecture using a second level of Montgomery Representation. Such architecture allows us to select the moduli with the new upper bound defined with the condition. This modification makes the Cox-Rower architecture suitable to compute 521 bits ECC with radix downto 16 bits compared to 18 with the classical Cox-Rower architecture. We validate our results through FPGA implementation of a scalar multiplication at classical cryptography security levels (NIST curves). Our implementation uses 35% less LUTs compared to the state of the art generic implementation of ECC using RNS for the same performance [5]. We also slightly improve the computation time (latency) and our implementation shows best ratio throughput/area for RNS computation supporting any curve independently of the chosen base.

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Section: New Rower Unitmentioning

confidence: 87%

Section: Rns and Montgomerymentioning

confidence: 99%

Section: Base Extensionmentioning

confidence: 99%

Section: New Rower Unitmentioning

confidence: 99%

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Double Level Montgomery Cox-Rower Architecture, New Bounds

Bajard

Merkiche²

2015

Smart Card Research and Advanced Applications

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“…Since the MRS method is difficult to implement in a full-parallel fashion (c.f. Section 6), we choose the CRT method [15].…”

Section: Base Extensionmentioning

confidence: 99%

Novel RNS Parameter Selection for Fast Modular Multiplication

Yao

Fan

Cheung

et al. 2014

IEEE Trans. Comput.

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Abstract-The parameter selection of Residue Number Systems (RNS) has a great impact on its computational efficiency. This paper shows that a base extension, the most costly operation in RNS Montgomery multiplication, can be more efficient when the intervals between the RNS moduli are small. We propose a systematic RNS parameter selection procedure and two methods to select RNS moduli that lead to a reduced complexity. Our experimental results confirm the advantages of the selected moduli.

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Residue Number Systems in Cryptography: Design, Challenges, Robustness

Schinianakis

Stouraitis

2016

Secure System Design and Trustable Computing

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Base extension using a convolution sum in residue number systems

Cited by 26 publications

References 1 publication

Double Level Montgomery Cox-Rower Architecture, New Bounds

Double Level Montgomery Cox-Rower Architecture, New Bounds

Novel RNS Parameter Selection for Fast Modular Multiplication

Residue Number Systems in Cryptography: Design, Challenges, Robustness

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