Welcome to the resource topic for 2015/421
Title:
VLSI Implementation of Double-Base Scalar Multiplication on a Twisted Edwards Curve with an Efficiently Computable Endomorphism
Authors: Zhe Liu, Husen Wang, Johann Großschädl, Zhi Hu, Ingrid Verbauwhede
Abstract:The verification of an ECDSA signature requires a double-base scalar multiplication, an operation of the form k \cdot G + l \cdot Q where G is a generator of a large elliptic curve group of prime order n, Q is an arbitrary element of said group, and k, l are two integers in the range of [1, n-1]. We introduce in this paper an area-optimized VLSI design of a Prime-Field Arithmetic Unit (PFAU) that can serve as a loosely-coupled or tightly-coupled hardware accelerator in a system-on-chip to speed up the execution of double-base scalar multiplication. Our design is optimized for twisted Edwards curves with an efficiently computable endomorphism that allows one to reduce the number of point doublings by some 50% compared to a conventional implementation. An example for such a special curve is -x^2 + y^2 = 1 + x^2y^2 over the 207-bit prime field F_p with p = 2^{207} - 5131. The PFAU prototype we describe in this paper features a (16 \times 16)-bit multiplier and has an overall silicon area of 5821 gates when synthesized with a 0.13\mu standard-cell library. It can be clocked with a frequency of up to 50 MHz and is capable to perform a constant-time multiplication in the mentioned 207-bit prime field in only 198 clock cycles. A complete double-base scalar multiplication has an execution time of some 365k cycles and requires the pre-computation of 15 points. Our design supports many trade-offs between performance and RAM requirements, which is a highly desirable property for future Internet-of-Things (IoT) applications.
ePrint: https://eprint.iacr.org/2015/421
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