A Scheme Of Data Encryption Based On Threshold Scheme And Elliptic Curve Cryptosystem

This thesis proposes a scheme of data encryption based on the (m,n)-threshold scheme and elliptic curve cryptosystem in which users are handled as an individual-user and a group-user. A group-user is a group made up of many (may be n) participants, each of whom holds a shadow of a common key (private key) different from one another. The key can be recovered by the minimum of m (m≤n) participants in the group. An individual-user is one who holds the key all by himself. The functions of this scheme are as follows: ①The encryption of plaintext based on the (m,n)-threshold scheme by a group-user and the decryption of ciphertext by an individual-user; ②The encryption of plaintext by an individual-user and the decryption of ciphertext based on the (m,n)-threshold scheme by an group-user; ③The encryption of plaintext and the decryption of ciphertext by individual-users; ④ The encryption of plaintext and the decryption of ciphertext based on the (m,n)-threshold scheme by group-users. The (m,n)-threshold scheme, which is constructed on polynomial equation over finite field (based on LaGrange interpolation formula), is secure as one-time pad's. Its security is ensured by the difficulty of elliptic curve's discrete logarithm problem by means of the exclusion of supersingle and anomalous elliptic curves and the adoption of a big prime (more than 160 bits) for the order of base-point in elliptic curve in this scheme of data encryption.