An Elliptic Curve Threshold Group Signature Scheme

Abstract

In a (t,n) threshold group signature scheme, only t or more signers of the group can sign messages on behalf of the group. Elliptic Curve Cryptography (ECC) was introduced by Victor Miller and Neal Koblitz in 1985. ECC proposed as an alternative to established public-key systems such as DSA and RSA. The main reason for the attractiveness of ECC isthe fact that there is no sub-exponential algorithm known to solve the discrete logarithm problem on a properly chosen elliptic curve. This means that significantly smaller parameters can be used in ECC than in other competitive systems such RSA and DSA, but with equivalent levels of security. Some benefits of having smaller key sizes include faster computations, and reductions in processing power, storage space and bandwidth. This makes ECC ideal for constrained environment such as pagers, PDAs, cellular phones and smart cards. In this paper, we propose a threshold group signature scheme based on elliptic curve discrete logarithm problem. The advantages of the proposed scheme are justified through extensive simulations.