Efficient Prime-Field Arithmetic for Elliptic Curve Cryptography on Wireless Sensor Nodes
Public-Key Cryptography (PKC) is essential to ensure the authenticity and confidentiality of communication in open computer networks such as the Internet. While RSA is still the most widely used public-key cryptosystem today, it can be expected that Elliptic Curve Cryptography (ECC) will continue to gain importance and become the de-facto standard for PKC in the emerging Internet of Things. ECC is particularly attractive for use in resourcerestricted devices (e.g. wireless sensor nodes, RFID tags) due to its high level of security per bit, which allows for shorter keys compared to RSA. The performance of elliptic curve cryptosystems is primarily determined by the efficiency of certain arithmetic operations (especially multiplication and squaring) in the underlying finite field. In the present paper, we introduce a high-speed implementation of arithmetic in Optimal Prime Fields (OPFs) for the ATmegal28, an 8-bit processor used in a number of sensor nodes including the MICAz mote. An OPF is defined by a prime of the form p = u · 2k + v, whereby u and v are small compared to 2k; in our implementation u is a 16-bit integer and v = 1. A special property of these primes is their low Hamming weight since only a few bits near the MSB and LSB are one. We describe an optimized variant of Montgomery multiplication, based on Gura et als hybrid technique, that takes the low weight of such primes into account to minimize execution time. Our implementation for the ATmegal28 is able to perform a multiplication in a 160-bit OPF in 3,532 clock cycles, which represents a new speed record for 160-bit modular multiplication on an 8-bit processor.
Yang Zhang Johann GroBschadl
University of Luxembourg 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg
国际会议
哈尔滨
英文
459-466
2011-12-24（万方平台首次上网日期，不代表论文的发表时间）