Multivariate Quadratic Trapdoor Functions Based on Multivariate Quadratic Quasigroups

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 quasigroups (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. Key–Words: Public Key Cryptosystems, Fast signature generation, Multivariate Quadratic Polynomials, Quasigroup String Transformations, Multivariate Quadratic Quasigroup