Matrix groups of elliptic curve points:a new approach to simultaneous implementation of key agreement and privacy

Key agreement and privacy are two important security services in the fields of modern cryptography and information security. Based on informal matrices a novel way of researching into Elliptic Curve Cryptography (ECC) is proposed by Climent et al., but the concept of informal matrices is not perfect (they are not genuine matrices, severely lacking mathematical mechanism), and encryption service has not been provided. In this paper, a class of matrix groups of elliptic curve points with cryptographic significance is first constructed rigorously from the perspective of group theory. Combining the Hughes protocol with the ECIES (Elliptic Curve Integrated Encryption Scheme), a hybrid cryptosystem simultaneously implementing key agreement and privacy over the Internet is then proposed, which has three features: i) For enhancing the bit security of the shared secret in the standard model, a cryptographic hash function is used to derive a symmetric key from the sum of all the elliptic curve points in a block triangular matrix; ii) Oriented to real-time network applications, the sender can encrypt bulk data prior to agreeing upon a shared key with the receiver; and iii) the sizes of system parameters can be selected flexibly to strengthen system security. Finally, several corresponding aspects of cryptanalysis are investigated.