Implementation of Boneh - Lynn - Shacham short digital signature scheme using Weil bilinear pairing based on supersingular elliptic curves

Abstract

One option for a digital signature solution for devices with low memory and low bandwidth transmission over channels uses a short digital signature scheme based on Weil bilinear pairing aimed at short processing times, fast computation, and convenient deployment on applications. The computational technique of non-degenerate bilinear pairings uses supersingular elliptic curves over a finite field F p l (where p is a sufficiently large prime number) and has the advantage of being able to avoid Weil-descent, Menezes-Okamoto-Vanstone (MOV) attacks, and attacks by the Number Field Sieve algorithm. Compared to Elliptic Curve Digital Signature Algorithm (ECDSA) digital signature schemes, generating a digital signature for a Boneh-Lynn-Shacham (BLS) scheme using Weil bilinear pairing on a supersingular elliptic curve is simple. In this study, the authors replace non-degenerate bilinear pairing calculations on a supersingular elliptic curve with a Weil pairing with PϵE(F p ), QϵE(F p 1) and a higher security multiplier α=12 in the BLS short digital signature scheme. The execution time of the BLS short digital signature program showed improvement compared to the commercial ECDSA digital signature scheme.

Keywords

• digital signature
• ECDSA
• elliptic curve cryptography
• tate pairing
• Weil pairing