Paper 2015/421
VLSI Implementation of DoubleBase Scalar Multiplication on a Twisted Edwards Curve with an Efficiently Computable Endomorphism
Zhe Liu, Husen Wang, Johann Großschädl, Zhi Hu, and Ingrid Verbauwhede
Abstract
The verification of an ECDSA signature requires a doublebase 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 $[1, n1]$. We introduce in this paper an areaoptimized VLSI design of a PrimeField Arithmetic Unit (PFAU) that can serve as a looselycoupled or tightlycoupled hardware accelerator in a systemonchip to speed up the execution of doublebase 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 207bit 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 $0.13\mu$ standardcell library. It can be clocked with a frequency of up to 50 MHz and is capable to perform a constanttime multiplication in the mentioned 207bit prime field in only 198 clock cycles. A complete doublebase scalar multiplication has an execution time of some 365k cycles and requires the precomputation of 15 points. Our design supports many tradeoffs between performance and RAM requirements, which is a highly desirable property for future InternetofThings (IoT) applications.
Metadata
 Available format(s)
 Category
 Implementation
 Publication info
 Preprint. MINOR revision.
 Keywords
 elliptic curve cryptosystemdigital signatures
 Contact author(s)
 husen wang @ esat kuleuven be
 History
 20150505: received
 Short URL
 https://ia.cr/2015/421
 License

CC BY
BibTeX
@misc{cryptoeprint:2015/421, author = {Zhe Liu and Husen Wang and Johann Großschädl and Zhi Hu and Ingrid Verbauwhede}, title = {{VLSI} Implementation of DoubleBase Scalar Multiplication on a Twisted Edwards Curve with an Efficiently Computable Endomorphism}, howpublished = {Cryptology ePrint Archive, Paper 2015/421}, year = {2015}, note = {\url{https://eprint.iacr.org/2015/421}}, url = {https://eprint.iacr.org/2015/421} }