Abstract
A Self-pairing es(P,P) is a special subclass of bilinear pairing where both input points in a group are equal. Self-pairings have some interest- ing applications in cryptographic scheme and protocols. Recently some novel methods for constructing self-pairings on supersingular elliptic curves have been proposed. In this paper we first give the construction of self-pairings on some supersingular elliptic curves. We will show that the proposed self pairings are efficient than the general pairings on the corresponding curves. Secondly, we present a digital signature scheme from self-pairing on elliptic curves. We also show that the signature scheme from self-pairing is more efficient than the pre- vious one.
Highlights
Pairing based cryptography [1] has become one of the most active areas in elliptic curve cryptography since 2000
They showed that the discrete logarithm problem can be shift from an elliptic curve to a finite field through the Weil pairing as the discrete logarithm problem is more solved over a finite field than over an elliptic curve
By using the distortion maps on supersingular elliptic curves with even embedding degree, the author of [14] proposed the self-pairing with a simple final exponentiation
Summary
Pairing based cryptography [1] has become one of the most active areas in elliptic curve cryptography since 2000. By using the distortion maps on supersingular elliptic curves with even embedding degree, the author of [14] proposed the self-pairing with a simple final exponentiation. Later this idea has been generalized to the hyper elliptic curves [19]. We use the distortion maps on the supersingular elliptic curves E1 : y2 + y = x3 over F2n, where n is odd and E2 : y2 = x3 − x + 1 over F3n , where n is odd, to proposed self-pairings on these curves. We present an efficient signature scheme from self-pairing on elliptic curves.
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