Refinements of Miller's algorithm for computing the Weil/Tate pairing

• Published in: Journal of algorithms Vol. 58; no. 2; pp. 134 - 149
• Main Authors: Blake, Ian F., Kumar Murty, V., Xu, Guangwu
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.02.2006; Elsevier
• Subjects: Algebra; Algorithm; Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Cryptography; Elliptic curves; Exact sciences and technology; Information, signal and communications theory; Mathematics; Number theory; Sciences and techniques of general use; Signal and communications theory; Tate pairing; Telecommunications and information theory; Theoretical computing; Weil pairing; Elliptic curves; Weil pairing; Cryptography; Algorithm; Tate pairing; Integer; Cryptographic protocol; Finite field; Performance analysis; Elliptic curve; Taye pairing; Computing
• ISSN: 0196-6774; 1090-2678
• DOI: 10.1016/j.jalgor.2005.01.009

The efficient computation of the Weil and Tate pairings is of significant interest in the implementation of certain recently developed cryptographic protocols. The standard method of such computations has been the Miller algorithm. Three refinements to Miller's algorithm are given in this work. The first refinement is an overall improvement. If the binary expansion of the involved integer has relatively high Hamming weight, the second improvement suggested shows significant gains. The third improvement is especially efficient when the underlying elliptic curve is over a finite field of characteristic three, which is a case of particular cryptographic interest. Comment on the performance analysis and characteristics of the refinements are given.