The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
모듈식 곱셈은 공개 키 암호화의 일종인 타원 곡선 암호화(ECC)에서 가장 지배적인 산술 연산입니다. 몽고메리 곱셈기는 모듈식 곱셈을 계산하는 데 일반적으로 사용되며 피연산자의 비트 길이가 보안 수준에 따라 달라지므로 확장성이 필요합니다. 또한 ECC는 다음과 같이 수행됩니다. GF(P) 또는 GF(2n) 및 승수에 대한 통합 아키텍처 GF(P) and GF(2n)이 필요합니다. 그러나 이전 연구에서는 주파수 간의 지연 시간 차이를 처리하기 위해 주파수 변경이 필요했습니다. GF(P) and GF(2n)의 임계 경로 때문에 승수 GF(P) 승수가 더 깁니다. 본 논문은 확장 가능한 몽고메리 곱셈을 위한 통합 이중 기수 아키텍처를 제안합니다. GF(P) and GF(2n). 제안된 아키텍처는 2개의 병렬 기수-XNUMX를 통합합니다.16 승수 GF(P) 및 기수-264 승수 GF(2n)을 하나의 단위로 묶었습니다. 더 낮은 기수 적용 GF(P) 곱셈기는 임계 경로를 단축하고 동일한 주파수에서 동일한 곱셈기를 사용하여 두 필드의 피연산자를 계산할 수 있도록 하므로 지연 시간 차이를 처리하기 위한 클록 분배기가 필요하지 않습니다. 게다가 병렬 아키텍처는 GF(P)는 이중 기수 접근 방식으로 증가된 클록 주기를 줄입니다. 결과적으로 제안된 아키텍처는 다음을 계산합니다. GF(P) 256μs의 0.28비트 몽고메리 곱셈. 구현 결과 제안 면적은 이전 작업과 거의 동일한 39kgate인 것으로 나타났습니다.
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Kazuyuki TANIMURA, Ryuta NARA, Shunitsu KOHARA, Youhua SHI, Nozomu TOGAWA, Masao YANAGISAWA, Tatsuo OHTSUKI, "Unified Dual-Radix Architecture for Scalable Montgomery Multiplications in GF(P) and GF(2n)" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 9, pp. 2304-2317, September 2009, doi: 10.1587/transfun.E92.A.2304.
Abstract: Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of public-key cryptography. Montgomery multiplier is commonly used to compute the modular multiplications and requires scalability because the bit length of operands varies depending on its security level. In addition, ECC is performed in GF(P) or GF(2n), and unified architecture for multipliers in GF(P) and GF(2n) is required. However, in previous works, changing frequency is necessary to deal with delay-time difference between GF(P) and GF(2n) multipliers because the critical path of the GF(P) multiplier is longer. This paper proposes unified dual-radix architecture for scalable Montgomery multiplications in GF(P) and GF(2n). This proposed architecture unifies four parallel radix-216 multipliers in GF(P) and a radix-264 multiplier in GF(2n) into a single unit. Applying lower radix to GF(P) multiplier shortens its critical path and makes it possible to compute the operands in the two fields using the same multiplier at the same frequency so that clock dividers to deal with the delay-time difference are not required. Moreover, parallel architecture in GF(P) reduces the clock cycles increased by dual-radix approach. Consequently, the proposed architecture achieves to compute a GF(P) 256-bit Montgomery multiplication in 0.28 µs. The implementation result shows that the area of the proposal is almost the same as that of previous works: 39 kgates.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2304/_p
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@ARTICLE{e92-a_9_2304,
author={Kazuyuki TANIMURA, Ryuta NARA, Shunitsu KOHARA, Youhua SHI, Nozomu TOGAWA, Masao YANAGISAWA, Tatsuo OHTSUKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Unified Dual-Radix Architecture for Scalable Montgomery Multiplications in GF(P) and GF(2n)},
year={2009},
volume={E92-A},
number={9},
pages={2304-2317},
abstract={Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of public-key cryptography. Montgomery multiplier is commonly used to compute the modular multiplications and requires scalability because the bit length of operands varies depending on its security level. In addition, ECC is performed in GF(P) or GF(2n), and unified architecture for multipliers in GF(P) and GF(2n) is required. However, in previous works, changing frequency is necessary to deal with delay-time difference between GF(P) and GF(2n) multipliers because the critical path of the GF(P) multiplier is longer. This paper proposes unified dual-radix architecture for scalable Montgomery multiplications in GF(P) and GF(2n). This proposed architecture unifies four parallel radix-216 multipliers in GF(P) and a radix-264 multiplier in GF(2n) into a single unit. Applying lower radix to GF(P) multiplier shortens its critical path and makes it possible to compute the operands in the two fields using the same multiplier at the same frequency so that clock dividers to deal with the delay-time difference are not required. Moreover, parallel architecture in GF(P) reduces the clock cycles increased by dual-radix approach. Consequently, the proposed architecture achieves to compute a GF(P) 256-bit Montgomery multiplication in 0.28 µs. The implementation result shows that the area of the proposal is almost the same as that of previous works: 39 kgates.},
keywords={},
doi={10.1587/transfun.E92.A.2304},
ISSN={1745-1337},
month={September},}
부
TY - JOUR
TI - Unified Dual-Radix Architecture for Scalable Montgomery Multiplications in GF(P) and GF(2n)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2304
EP - 2317
AU - Kazuyuki TANIMURA
AU - Ryuta NARA
AU - Shunitsu KOHARA
AU - Youhua SHI
AU - Nozomu TOGAWA
AU - Masao YANAGISAWA
AU - Tatsuo OHTSUKI
PY - 2009
DO - 10.1587/transfun.E92.A.2304
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2009
AB - Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of public-key cryptography. Montgomery multiplier is commonly used to compute the modular multiplications and requires scalability because the bit length of operands varies depending on its security level. In addition, ECC is performed in GF(P) or GF(2n), and unified architecture for multipliers in GF(P) and GF(2n) is required. However, in previous works, changing frequency is necessary to deal with delay-time difference between GF(P) and GF(2n) multipliers because the critical path of the GF(P) multiplier is longer. This paper proposes unified dual-radix architecture for scalable Montgomery multiplications in GF(P) and GF(2n). This proposed architecture unifies four parallel radix-216 multipliers in GF(P) and a radix-264 multiplier in GF(2n) into a single unit. Applying lower radix to GF(P) multiplier shortens its critical path and makes it possible to compute the operands in the two fields using the same multiplier at the same frequency so that clock dividers to deal with the delay-time difference are not required. Moreover, parallel architecture in GF(P) reduces the clock cycles increased by dual-radix approach. Consequently, the proposed architecture achieves to compute a GF(P) 256-bit Montgomery multiplication in 0.28 µs. The implementation result shows that the area of the proposal is almost the same as that of previous works: 39 kgates.
ER -