Fully Homomorphic Encryption on Octonion Ring: Fully homomorphic encryption with multivariate polynomials on non-associative ring - Softcover

Yagisawa, Masahiro

Softcover

ISBN 10: 3659773913 ISBN 13: 9783659773914

Publisher: LAP LAMBERT Academic Publishing, 2015

Synopsis

Gentry’s bootstrapping technique is still the only known method for obtaining fully homomorphic encryption. I propose a new fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The security of the proposed fully homomorphic encryption scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack. The key size of this system and complexity for enciphering/ deciphering become to be small enough to handle.

About this title

About the Author

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).

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2015
• Language: English
• ISBN 10: 3659773913
• ISBN 13: 9783659773914
• Binding: Paperback
• Number of pages: 80