A scalable ECC processor implementation for high-speed and lightweight with side-channel countermeasures

Salman, Ahmad; Ahmed, Faraz; Homsirikamol, Ekawat; Yalla, Panasayya; Kaps, Jens-Peter; Gaj, Kris

doi:10.1109/reconfig.2017.8279769

Cited by 17 publications

(14 citation statements)

References 20 publications

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“…One example for the PM is presented in Algorithm 1, which requires r − 1 DBL and at most r − 1 ADD operations per PM, whereas the number of ADD operations varies with the key. We focus on the worst-case complexity because most implementations will try to balance the number of ADD operations in ordered to harden the calculation against timing attacks [32,33].…”

Section: Elliptic Curve Point Multiplication For Binary Keysmentioning

confidence: 99%

“…Consequently, an attacker can estimate the current bit of the secret key by observing the power consumption over time. To avoid TA and SPA attacks, many publications balance the number of applied point operations using additional dummy ADD operations [22,24,[31][32][33][34].…”

Section: Resistance Against Side-channel Attacksmentioning

confidence: 99%

“…In [26,28], arithmetic over binary extension field is considered, where the squaring operation is very efficient [29,30]. It was demonstrated in [22,24,25,[31][32][33][34] that non-binary expansions are beneficial to harden ECC implementations against attacks (SCA). Hardware implementations of the elliptic curve point multiplication are prone to SCA.…”

Section: Introductionmentioning

confidence: 99%

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A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

2020

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This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.

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Section: Elliptic Curve Point Multiplication For Binary Keysmentioning

confidence: 99%

Section: Resistance Against Side-channel Attacksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

2020

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“…With two parallel multipliers, we managed to reduce it to 6 clock cycles. Due to the special architecture of modular inversion to improve timing, calculating modular squaring as well as 2 2 th powering needs 2 clock cycles respectively and 2 5 th powering needs 3 clock cycles. Higher order powering operations are implemented by applying lower order powering units iteratively.…”

Section: Latency Calculationmentioning

confidence: 99%

“…However, among these applications, some of the time-critical applications such as network servers where millions of heterogeneous client devices need to be connected, the processing speed of identity authentication needs to be further improved. In recent years, several ECC processor designs over binary field Koblitz curve have been proposed to increase encryption speed [5]- [9]. Since point multiplication (PM) is the main and the most time-consuming iterative operation during the whole encryption process, most researches focus on exploiting novel hardware architectures to speed up the operation process.…”

Section: Introductionmentioning

confidence: 99%

Speed-Oriented Architecture for Binary Field Point Multiplication on Elliptic Curves

Zhong

Li³

et al. 2019

IEEE Access

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This paper introduces a novel speed-oriented architecture of point multiplication in elliptic curve cryptography. A balanced full-precision multiplier is proposed to shorten latency, and a new modular inversion architecture is integrated to reduce the total number of clock cycles in point multiplication. A modified Montgomery Ladder algorithm that takes three clock cycles to calculate one input bit is proposed to best utilize hardware resources. A mixed-pipeline technique is used to balance the delay of different paths and increase frequency. The proposed architecture is implemented on GF(2 163) and GF(2 571), based on

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Expanding Coverage of an Intelligent Transit Bus Monitoring System via ZigBee Radio Network

Salman

El-Tawab

Yorio

2019

Lecture Notes in Networks and Systems

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A scalable ECC processor implementation for high-speed and lightweight with side-channel countermeasures

Cited by 17 publications

References 20 publications

A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

Speed-Oriented Architecture for Binary Field Point Multiplication on Elliptic Curves

Expanding Coverage of an Intelligent Transit Bus Monitoring System via ZigBee Radio Network

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