Elliptic curve cryptography on embedded multicore systems

Fan, Junfeng; Sakiyama, Kazuo; Verbauwhede, Ingrid

doi:10.1007/s10617-008-9021-3

Cited by 29 publications

(19 citation statements)

References 17 publications

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“…In [10, Section 5.2.1] Hankerson, Menezes and Vanstone outline a hierarchy of operations in ECC as protocols, point multiplication, elliptic-curve addition and doubling, finite-field arithmetic. Fan, Sakiyama & Verbauwhede expand this in [7] to describe a 5-layer pyramid of 1. Integrity, confidentially, authentication, 2.…”

Section: Implementation Hierarchymentioning

confidence: 99%

Fast Elliptic-Curve Cryptography on the Cell Broadband Engine

Costigan

Schwabe

2009

Progress in Cryptology – AFRICACRYPT 2009

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Abstract. This paper is the first to investigate the power of the Cell Broadband Engine for state-of-the-art public-key cryptography. We present a high-speed implementation of elliptic-curve Diffie-Hellman (ECDH) key exchange for this processor, which needs 777000 cycles on one Synergistic Processor Unit for a scalar multiplication on a 255-bit elliptic curve, including the costs for key verification and key compression. This cycle count is independent of inputs therefore protecting against timing attacks. This speed relies on a new representation of elements of the underlying finite field suited for the unconventional instruction set of this architecture. Furthermore we demonstrate that an implementation based on the multiprecision integer arithmetic functions provided by IBM's multi-precision math (MPM) library would take at least 2227040 cycles. Comparison with implementations of the same function for other architectures shows that the Cell Broadband Engine is competitive in terms of cost-performance ratio to other recent processors such as the Core 2 for public-key cryptography. Specifically, the state-of-the-art Galbraith-Lin-Scott ECDH software performs 27370 scalar multiplications per second using all four cores of a 2.5GHz Intel Core 2 Quad Q9300 inside a $400 computer, while the new software reported in this paper performs 24528 scalar multiplications per second on a Playstation 3 that costs just $279. Both of these speed reports are for high-security 256-bit elliptic-curve cryptography.

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Section: Implementation Hierarchymentioning

confidence: 99%

Fast Elliptic-Curve Cryptography on the Cell Broadband Engine

Costigan

Schwabe

2009

Progress in Cryptology – AFRICACRYPT 2009

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“…The use of multi-core processors is an emerging research topic in the context of cryptographic implementation, for example Fan et al investigate modular multiplication [16] and ECC [17] on this type of platform. Intra-pairing parallelism is clearly possible at the field arithmetic level as evidenced by related hardware based approaches [26].…”

Section: Multi-core Processorsmentioning

confidence: 99%

On Software Parallel Implementation of Cryptographic Pairings

Grabher

Großschädl

Page

2009

Selected Areas in Cryptography

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Abstract. A significant amount of research has focused on methods to improve the efficiency of cryptographic pairings; in part this work is motivated by the wide range of applications for such primitives. Although numerous hardware accelerators for pairing evaluation have used parallelism within extension field arithmetic to improve efficiency, similar techniques have not been examined in software thus far. In this paper we focus on parallelism within one pairing evaluation (intra-pairing), and parallelism between different pairing evaluations (inter-pairing). We identify several methods for exploiting such parallelism (extending previous results in the context of ECC) and show that it is possible to accelerate pairing evaluation by a significant factor in comparison to a naive approach.

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“…However, the number of Block RAMs necessary for the architecture is much larger than of Pöpper et al [32] or Varchola et al [38]. Fan et al [17] created an architecture for special primes and curves, namely the standardized NIST P-192. The approach was to parallelize Montgomery multiplication and formulas for point addition and doubling on the curve.…”

Section: Introductionmentioning

confidence: 99%

Implementing Complete Formulas on Weierstrass Curves in Hardware

Massolino¹,

Renes²,

Batina³

2016

Security, Privacy, and Applied Cryptography Engineering

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Abstract. This work revisits the recent complete addition formulas for prime order elliptic curves of Renes, Costello and Batina in light of parallelization. We introduce the first hardware implementation of the new formulas on an FPGA based on three arithmetic units performing Montgomery multiplication. Our results are competitive with current literature and show the potential of the new complete formulas in hardware design. Furthermore, we present algorithms to compute the formulas using anywhere between two and six processors, using the minimum number of parallel field multiplications.

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Elliptic curve cryptography on embedded multicore systems

Cited by 29 publications

References 17 publications

Fast Elliptic-Curve Cryptography on the Cell Broadband Engine

Fast Elliptic-Curve Cryptography on the Cell Broadband Engine

On Software Parallel Implementation of Cryptographic Pairings

Implementing Complete Formulas on Weierstrass Curves in Hardware

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