Single Base Modular Multiplication for Efficient Hardware RNS Implementations of ECC

Bigou, Karim; Tisserand, Arnaud

doi:10.1007/978-3-662-48324-4_7

Cited by 28 publications

(27 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The single cox unit computes the appropriate reduction factor h i,j and distributes it to the rowers. KBE algorithm and cox-rower architecture have been used in several hardware implementations of asymmetric cryptosystems using RNS: e.g., [15] for RSA; [16] and [17] for ECC. Fig.…”

Section: B Rns Base Extensionmentioning

confidence: 99%

“…Output: S A and S B with S = XA −1 mod P + δP and δ ∈ {0, 1, 2} the interest in using HBE instead of KBE for other RNS MM algorithms: [17] and [27].…”

Section: 95mentioning

confidence: 99%

“…A specific RNS MM approach for ECC has been proposed in [17] and generalized in [27]. These methods propose to use specific P values with pseudo-Mersenne like properties in RNS.…”

Section: 95mentioning

confidence: 99%

“…These methods propose to use specific P values with pseudo-Mersenne like properties in RNS. They mainly mix RNS with a polynomial representation of a small degree d. The MM algorithms from [17] and [27] are respectively referred as HPR with d = 2 and HPR with d = 4 below.…”

Section: 95mentioning

confidence: 99%

See 3 more Smart Citations

Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography

Djath

Bigou

Tisserand

2019

2019 IEEE 26th Symposium on Computer Arithmetic (ARITH)

Self Cite

View full text Add to dashboard Cite

Base extension is a critical operation in RNS implementations of asymmetric cryptosystems. In this paper, we propose a new way to perform base extensions using a hierarchical approach for computing the Chinese remainder theorem. For well chosen parameters, it significantly reduces the computational cost and still ensures a high level of internal parallelism. We illustrate the interest of the proposed approach on the cost of typical arithmetic primitives used in asymmetric cryptography. We also demonstrate improvements in FPGA implementations of base extensions on typical elliptic curve cryptography field sizes using high-level synthesis tools.

show abstract

Section: B Rns Base Extensionmentioning

confidence: 99%

“…Output: S A and S B with S = XA −1 mod P + δP and δ ∈ {0, 1, 2} the interest in using HBE instead of KBE for other RNS MM algorithms: [17] and [27].…”

Section: 95mentioning

confidence: 99%

“…A specific RNS MM approach for ECC has been proposed in [17] and generalized in [27]. These methods propose to use specific P values with pseudo-Mersenne like properties in RNS.…”

Section: 95mentioning

confidence: 99%

Section: 95mentioning

confidence: 99%

See 2 more Smart Citations

Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography

Djath

Bigou

Tisserand

2019

2019 IEEE 26th Symposium on Computer Arithmetic (ARITH)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Methods are either based on the CRT as used by Shenoy and Kumaresan [67], Posch and Posch [60], and Kawamura, Koike, Sano, and Shimbo [46] or on an intermediate representation denoted by a mixed radix system as presented in Szabo and Tanaka in [71]. Carefully selected RNS bases can significantly impact the performance in practice as shown by Bajard, Kaihara, and Plantard in [3] and Bigou and Tisserand in [8]. Another RNS approach is presented by Phillips, Kong, and Lim [59].…”

Section: Montgomery Multiplication Using the Residue Number System Rementioning

confidence: 99%

Montgomery Arithmetic from a Software Perspective

Bos

Montgomery²

Topics in Computational Number Theory Inspired by Peter L. Montgomery

View full text Add to dashboard Cite

This chapter describes Peter L. Montgomery's modular multiplication method and the various improvements to reduce the latency for software implementations on devices which have access to many computational units.We propose a representation of residue classes so as to speed modular multiplication without affecting the modular addition and subtraction algorithms. Peter L. Montgomery [55]* This material has been published as Chapter 2 in "Topics in

show abstract

A high‐speed RSD‐based flexible ECC processor for arbitrary curves over general prime field

Shah

Javeed

Azmat

et al. 2018

Circuit Theory & Apps

View full text Add to dashboard Cite

SummaryThis workpresents a novel high‐speed redundant‐signed‐digit (RSD)‐based elliptic curve cryptographic (ECC) processor for arbitrary curves over a general prime field. The proposed ECC processor works for any value of the prime number and curve parameters. It is based on a new high speed Montgomery multiplier architecture which uses different parallel computation techniques at both circuit level and architectural level. At the circuit level, RSD and carry save techniques are adopted while pre‐computation logic is incorporated at the architectural level. As a result of these optimization strategies, the proposed Montgomery multiplier offers a significant reduction in computation time over the state‐of‐the‐art. At the system level, to further enhance the overall performance of the proposed ECC processor, Montgomery ladder algorithm with (X,Y)‐only common Z coordinate (co‐Z) arithmetic is adopted. The proposed ECC processor is synthesized and implemented on different Xilinx Virtex (V) FPGA families for field sizes of 256 to 521 bits. On V‐6 platform, it computes a single 256 to 521 bits scalar point multiplication operation in 0.65 to 2.6 ms which is up to 9 times speed‐up over the state‐of‐the‐art.

show abstract

Single Base Modular Multiplication for Efficient Hardware RNS Implementations of ECC

Cited by 28 publications

References 27 publications

Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography

Hierarchical Approach in RNS Base Extension for Asymmetric Cryptography

Montgomery Arithmetic from a Software Perspective

A high‐speed RSD‐based flexible ECC processor for arbitrary curves over general prime field

Contact Info

Product

Resources

About