Secure and Compact Elliptic Curve Cryptosystems

Jin, Yaoan; Miyaji, Atsuko

doi:10.1007/978-3-030-21548-4_36

Cited by 4 publications

(12 citation statements)

References 13 publications

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“…In [32], researchers presented secure ECC suitable for compact devices by using a modified addition formula for usual RLA. Although proposed method needs less space complexity, the time delay of the encryption process was increased because of using affine coordinates.…”

Section: Background and Related Workmentioning

confidence: 99%

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High-Speed and Secure Elliptic Curve Cryptosystem for Multimedia Applications

Al-Khatib¹

2020

IJACSA

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The last few years witnessed a rapid increase in the use of multimedia applications, which led to an explosion in the amount of data sent over communication networks. Therefore, it has become necessary to find an effective security solution that preserves the confidentiality of such enormous amount of data sent through unsecure network channels and, at the same time, meets the performance requirements for applications that process the data. This research introduces a high-speed and secure elliptic curve cryptosystem (ECC) appropriate for multimedia security. The proposed ECC improves the performance of data encryption process by accelerating the scaler multiplication operation, while strengthening the immunity of the cryptosystem against side channel attacks. The speed of the encryption process has been increased via the parallel implementation of ECC computations in both the upper scaler multiplication level and the lower point operations level. To accomplish this, modified version of the Right to Left binary algorithm as well as eight parallel multipliers (PM) were used to allow parallel implementation for point doubling and addition. Moreover, projective coordinates systems were used to remove the time-consuming inversion operation. The current 8-PM Montgomery ECC achieves higher performance level compared to previous ECC implementations, and can reduce the risk of side channel attacks. In addition, current research work provides performance and resources-consumption analysis for Weierstrass and Montgomery elliptic curve representations over prime field. However, the proposed ECC implementation consumes more resources. Presented ECCs were implemented using VHDL, and synthesized using the Xilinx tool with target FPGA.

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Section: Background and Related Workmentioning

confidence: 99%

“…However, the proposed algorithm did not utilize inherited parallelism in the different levels of computations in the encryption process, which is essential to develop high speed crypto processor. Moreover, ECCs presented in [32][33] are vulnerable to side channel attacks.…”

Section: Background and Related Workmentioning

confidence: 99%

High-Speed and Secure Elliptic Curve Cryptosystem for Multimedia Applications

Al-Khatib¹

2020

IJACSA

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“…Similarly, O + P and P + P are exceptional computations of Jacobian and projective addition formula. To reduce exceptional computations from affine coordinates, extended affine coordinates assign (0, 0) as the point at infinity for elliptic curves without point (0, 0), such as prime order elliptic curves [8]. Using the extended affine addition formulae, P + Q = O and 2P = O can be computed as (0, 0), which is exactly the point at infinity.…”

Section: Addition Formulae and Exceptional Computationsmentioning

confidence: 99%

“…Elliptic curve CA formulae [7,15,17] can achieve secure ECSM algorithms but are inefficient in terms of memory and computational costs. Another secure ECSM, which uses (extended) affine, is more efficient for both memory and computational costs [8]. However, it scans input scalars from right to left (RL).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose secure and compact left-to-right (LR) ECSM algorithms based on affine coordinates. We improve Joye's LR 2-ary algorithm to exclude exceptional computations of affine formulae and extended affine formulae [8]. We propose secure scalar multiplication algorithms, Algorithm 7 and Algorithm 8 through 2-bit scanning using the affine double and quadruple algorithm (DQ-algorithm) [12].…”

Section: Introductionmentioning

confidence: 99%

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Secure and Compact Elliptic Curve LR Scalar Multiplication

Jin

Miyaji

2020

Lecture Notes in Computer Science

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Elliptic curve cryptography (ECC) can ensure an equivalent security with much smaller key sizes. Elliptic curve scalar multiplication (ECSM) is a fundamental computation used in ECC. This paper focuses on ECSM resisting simple power attack and safe error attack of side-channel attack specifically. Elliptic curve complete addition (CA) formulae can achieve secure ECSM algorithms but are inefficient from memory and computational cost perspectives. Another secure ECSM, which uses (extended) affine, is more efficient for both memory and computational costs. However, it scans input scalars from right to left. In this paper, our developed scalar multiplication algorithms also use their extended affine, but scan from left to right (LR). We also prove the security of our LR ECSM algorithms and analyze them both theoretically and experimentally. Our new LR ECSM algorithms can reduce the amount of memory by 37.5% and reduce the computational time by more than 40% compared to Joye's regular 2-ary LR algorithm with CA formulae.

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