Adnan Gutub - Efficient utilization of scalable multipliers in parallel to compute GF(p) elliptic curve cryptographic operations

Kuwait Journal of Science & Engineering (KJSE), Vol . 34, No. 2, December 2007

Efficient utilization of scalable multipliers in parallel to compute GF(p) elliptic curve cryptographic operations

ADNAN ABDUL-AZIZ GUTUB

King Fahd University of Petroleum & Minerals; Computer Engineering Department; Dhahran 31261; Saudi Arabia; Email: gutub@kfupm.edu.sa

ABSTRACT

This paper presents the design and implementation of an elliptic curve cryptographic core to realize point scalar multiplication operations used for the GF(p) elliptic curve encryption/decryption and the elliptic curve digital signature algorithm (ECDSA). The design makes use of projective coordinates together with scalable Montgomery multipliers for data size of up to 256-bits. We propose using four multiplier cores together with the ordinary projective coordinates which outperform implementations with Jacobean coordinates typically believed to perform better. The proposed architecture is particularly attractive for elliptic curve cryptosystems when hardware area optimization is the key concern.

Keywords: crypto hardware designs; elliptic curve cryptography; modulo arithmetic; projective coordinate cryptosystems; scalable multipliers

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