Since Diffie and Hellman proposed the concept of the public key cryptosystem (PKC), key agreement protocol (KAP) and digital signature scheme (DSS) in 1976, various PKC, KAP and DSS were proposed.The signcryption which is a new public-key technology that combines signing and encrypting a message, that is ,DSS+PKC or DSS+KAP in a single step was proposed by Y. Zheng in 1997. The signcryption is particularly useful in cloud computing for ensuring confidential, authenticated transmissions. I propose the new method for performing the function of both KAP and DSS simultaneously (signcryption) on octonion ring. Because the security of this system is based on the computational difficulty to solve the multivariate algebraic equations of high degree, proposed system is against the Gröbner basis attack. In addition to message confidentiality, non-repudiation and unforgeability, the proposed scheme has forward secrecy, public verifiability and encrypted message authentication.

Masahiro Yagisawa received the B.E. and M.E. degrees from the University of Tokyo in 1974 and 1976. I am a member of IEICE (The Institute of Electronics, Information and Communication Engineers), IPSJ (Information Processing Society of Japan) and JSIAM (The Japan Society for Industrial and Applied Mathematics).