New polynomial basis versatile multiplier over GF(2m) for low-power on-chip crypto-systems

This paper presents a low-power, reduced-area finite field multiplier over GF(2m) for ultra-low-power devices. The proposed design supports any field GF(2m) with low-weight irreducible polynomial. The different implementations presented in this paper support 99% of fields with prime m <; 4096. The proposed design is advantageous in terms of flexibility and hardware complexity. The design can perform multiplication over fields whose m > 1024, and all standard elliptic curves consuming 28.7μW and 4μW respectively, using the TSMC 65nm technology library. The design is demonstrated to operate at frequencies up to 500 MHz, allowing various trade-offs between power, energy and performance. The proposed design is shown to use around 40% less area and 40% less power than the other designs proposed in the literature. Hence, it enables implementing more secure ciphers for almost the lower cost than other available designs.

[1]  Chih-Tsun Huang,et al.  Design of low-cost elliptic curve cryptographic engines for ubiquitous security , 2014, Technical Papers of 2014 International Symposium on VLSI Design, Automation and Test.

[2]  Faruk Göloglu,et al.  On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in F21971 , 2013, IACR Cryptol. ePrint Arch..

[3]  John Viega,et al.  The Use of Galois/Counter Mode (GCM) in IPsec Encapsulating Security Payload (ESP) , 2005, RFC.

[4]  Vipul Gupta,et al.  Energy analysis of public-key cryptography for wireless sensor networks , 2005, Third IEEE International Conference on Pervasive Computing and Communications.

[5]  Gadiel Seroussi,et al.  Table of low-weight binary irreducible polynomials , 1998 .

[6]  Huong Ho,et al.  Design and Implementation of a Polynomial Basis Multiplier Architecture Over GF(2m) , 2014, J. Signal Process. Syst..

[7]  Jean-Pierre Deschamps,et al.  Efficient Elliptic Curve Point Multiplication Using Digit-Serial Binary Field Operations , 2013, IEEE Transactions on Industrial Electronics.

[8]  Faruk Göloglu,et al.  Solving a 6120 -bit DLP on a Desktop Computer , 2013, Selected Areas in Cryptography.

[9]  Morteza Nikooghadam,et al.  Low-power and high-speed design of a versatile bit-serial multiplier in finite fields GF(2m) , 2013, Integr..

[10]  Lynn Batten,et al.  Public Key Cryptography: Applications and Attacks , 2013 .

[11]  José Luis Imaña Low Latency $GF(2^{m})$ Polynomial Basis Multiplier , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  Jean-Pierre Deschamps Hardware Implementation of Finite-Field Arithmetic , 2009 .

[13]  Ricardo Dahab,et al.  Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation , 1999, CHES.