TinyECCK: Efficient Elliptic Curve Cryptography Implementation over GF(2m) on 8-Bit Micaz Mote

Abstract

SUMMARYIn this paper, we revisit a generally accepted opinion: implementing Elliptic Curve Cryptosystem (ECC) over GF(2m) on sensor motes using smallt appropriate because XOR multiplication over GF(2m) is not efficiently supported by current low-powered microprocessors. Although there are some implementations over GF(2m) on sensor motes, their performances are not satisfactory enough to be used for wireless sensor networks (WSNs). We have found that a field multiplication over GF(2m) are involved in, a number of redundant memory accesses and its inefficiency is originated from this problem. Moreover, the field reduction process also requires many redundant memory accesses. Therefore, we propose some techniques for reducing unnecessary memory accesses. With the proposed strategies, the running time of field multiplication and reduction over GF(2163) can be decreased by 21.1% and 24.7%, respectively. These savings noticeably decrease execution times spent in Elliptic Curve Digital Signature Algorithm (ECDSA) operations (signing and verification) by around 15-19%. We present TinyECCK (Tiny Elliptic Curve Cryptosystem with Koblitz curve -a kind of TinyOS package supporting elliptic curve operations) which is the first implementation of Koblitz curve on sensor motes as far as we know. Through comparisons with existing software implementations of ECC built in C or hybrid of C and inline assembly on sensor motes, we show that TinyECCK outperforms them in terms of running time, code size and supporting services. Furthermore, we show that a field multiplication over GF(2m) can be faster than that over GF(p) on 8-bit Atmega128 processor by comparing TinyECCK with TinyECC, a well-known ECC implementation over GF(p). TinyECCK with sect163kl can generate a signature and verify it in 1.37 and 2.32 secs on a Micaz mote with 13,748-byte of ROM and 1,004-byte of RAM.

Shifting Primes: Extension of Pseudo-Mersenne Primes to Optimize ECC for MSP430-Based Future Internet of Things Devices

“…However, some interesting approaches have been defined for ECC implementations over GF (2 m ), for example [14] has showed that field multiplication is faster over GF (2 m ) than in GF (p) for new suggested hardware implementations, where the instructions set and arithmetic of the micro-controller are closer to GF (2 m ). Some of the most known software implementations over modular arithmetic for ECC are TinyECC [9,10] and NanoECC [11], which implement ECC-based operations. TinyECC adopted several optimization techniques such as optimized modular reduction using pseudo-Mersenne primes, sliding window method, Jacobian coordinate systems, in-line assembly and hybrid multiplication in order to achieve computational efficiency.…”

A DNA Sticker Algorithm for Parallel Reduction over Finite Field GF(2^n)

“…The implementation of the flexible ECC processor consumes only 1278 slices for 32-bit data path on Spartan III XC3S200. An elliptic curve cryptosystem (ECC) over GF (2 n ) was implemented in [14] on sensor motes using small word size for low-powered microprocessors. After that, these authors implemented another elliptic curve cryptosystem with Koblitz curve on 16-bit word on 16-bit Tmote Sky mote in [15].…”

Efficient Implementation of Pairing-Based Cryptography on a Sensor Node

“…On the other hand, TinyECCK is the fastest implementation of ECC on ATmega128L by Seo et al [23]. A multiplication in GF (2 163 ) is computed by the comb method and the window method with the width 4, and takes 2.9 msec.…”

“…TinyPBC [18] by Oliveira et al and NanoECC [25] by Szczechowiak et al are implementations of η T pairing over GF (2 m ) for m = 271. Currently pairing implementations (TinyPBC, TinyTate) are slower than RSA (TinyPK, [27]) and ECC (TinyECC [14], TinyECCK [23]). Therefore, it is a good research challenge to optimize the implementation of Pairing cryptosystems in resource-constrained sensor nodes.…”