IEICE TRANSACTIONS on Fundamentals
Unified Dual-Radix Architecture for Scalable Montgomery Multiplications in GF(P) and GF(2n)
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.9 pp.2304-2317
- Publication Date
- 2009/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.2304
- Type of Manuscript
- PAPER
- Category
- VLSI Design Technology and CAD
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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},}
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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 -
English
