TY - JOUR

T1 - Unified dual-radix architecture for scalable montgomery multiplications in GF(P) and GF(2n)

AU - Tanimura, Kazuyuki

AU - Nara, Ryuta

AU - Kohara, Shunitsu

AU - Shi, Youhua

AU - Togawa, Nozomu

AU - Yanagisawa, Masao

AU - Ohtsuki, Tatsuo

PY - 2009/9

Y1 - 2009/9

N2 - Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of publickey 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.

AB - Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of publickey 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.

KW - Dual-radix

KW - Elliptic curve cryptography

KW - Modular multiplication

KW - Montgomery multiplication

KW - Scalability

KW - Unified

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U2 - 10.1587/transfun.E92.A.2304

DO - 10.1587/transfun.E92.A.2304

M3 - Article

AN - SCOPUS:84883894071

VL - E92-A

SP - 2304

EP - 2317

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 9

ER -