• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.1
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• pp.127-132
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• 2007

This paper proposed receding methods for a radix-${\gamma}$ representation of the secret scalar which are resistant to SPA. Unlike existing receding method, these receding methods are left-to-right so they can be interleaved with a left-to-right scalar multiplication, removing the need to store both the scalar and its receding. Hence, these left-to-right methods are suitable for implementing on memory limited devices such as smart cards and sensor nodes

• JSTS:Journal of Semiconductor Technology and Science
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• v.16 no.1
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• pp.118-125
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• 2016

This paper presents a new high-efficient algorithm and architecture for an elliptic curve cryptographic processor. To reduce the computational complexity, novel modified Lopez-Dahab scalar point multiplication and left-to-right algorithms are proposed for point multiplication operation. Moreover, bit-serial Galois-field multiplication is used in order to decrease hardware complexity. The field multiplication operations are performed in parallel to improve system latency. As a result, our approach can reduce hardware costs, while the total time required for point multiplication is kept to a reasonable amount. The results on a Xilinx Virtex-5, Virtex-7 FPGAs and VLSI implementation show that the proposed architecture has less hardware complexity, number of clock cycles and higher efficiency than the previous works.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.8
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• pp.30-37
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• 2007

An exponentiation in $GF(2^m)$ is a basic operation for several algorithms used in cryptography, digital signal processing, error-correction code and so on. Existing hardware implementations for the exponentiation operation organize by Right-to-Left method since a merit of parallel circuit. Our paper proposes a polynomial exponentiation structure with a trinomial that is organized by Left-to-Right method and that utilizes a weakly dual basis. The basic idea of our method is to decrease time delay using precomputation tables because one of two inputs in the Left-to-Right method is fixed. Since $T_{sqr}$ (squarer time delay) + $T_{mul}$(multiplier time delay) of ow method is smaller than $T_{mul}$ of existing methods, our method reduces time delays of existing Left-to-Right and Right-to-Left methods by each 17%, 10% for $x^m+x+1$ (irreducible polynomial), by each 21%, 9% $x^m+x^k+1(1, by each 15%, 1% for $x^m+x^{m/2}+1$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.3
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• pp.419-426
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• 2021

A high-performance elliptic curve cryptography processor (HP-ECCP) was designed to support five field sizes of 192, 224, 256, 384 and 521 bits over GF(p) defined in NIST FIPS 186-2, and it provides eight modes of arithmetic operations including ECPSM, ECPA, ECPD, MA, MS, MM, MI and MD. In order to make the HP-ECCP resistant to side-channel attacks, a modified left-to-right binary algorithm was used, in which point addition and point doubling operations are uniformly performed regardless of the Hamming weight of private key used for ECPSM. In addition, Karatsuba-Ofman multiplication algorithm (KOMA), Lazy reduction and Nikhilam division algorithms were adopted for designing high-performance modular multiplier that is the core arithmetic block for elliptic curve point operations. The HP-ECCP synthesized using a 180-nm CMOS cell library occupied 620,846 gate equivalents with a clock frequency of 67 MHz, and it was evaluated that an ECPSM with a field size of 256 bits can be computed 2,200 times per second.