Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups

Authors:
Danilo Gligoroski;Smile Markovski;Svein Johan Knapskog
Affiliations:
Centre for Quantifiable Quality, of Service in Communication Systems, Norwegian University of Science and Technology, Trondheim, Norway;Ss "Cyril and Methodius" University, Institute of Informatics, Faculty of Sciences, Skopje, Republic of Macedonia;Centre for Quantifiable Quality of Service in Communication Systems, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
MATH'08 Proceedings of the American Conference on Applied Mathematics
Year:
2008

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Abstract

We have designed a new class of multivariate quadratic trapdoor functions. The trapdoor functions are generated by quasigroup string transformations based on a class of quasigroups called multivariate quadratic quasi-groups (MQQ). The public key schemes using these trapdoor functions are bijective mappings, they do not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n = 140; 160; 180,.... A particular characteristic of our public key scheme is that it is very fast; it has the speed of decryption/signature generation as a typical symmetric block cipher.