Cryptographic Application of Elliptic Curve with High Rank

Abstract: Elliptic curve cryptography is better than traditional cryptography based on RSA and discrete logarithm of finite field in terms of efficiency and security. In this paper, we show how to exploit elliptic curve with high rank, which has not been used in cryptography before, to construct cryptographic schemes. Concretely we demonstrate how to construct public key signature scheme with hierarchy revocation based on elliptic curve with high rank, where the rank determines the height of the revocation tree. Although our construction is not very efficient in some sense, our construction shows elliptic curve with high rank is valuable and important for cryptographic usage. The technique and assumption presented can surely be used for other cryptographic constructions.