Multivariate Signature using Algebraic Techniques

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Farshid Delgosha, Faramarz Fekri

Published: 2006, Last Modified: 17 Mar 2026ISIT 2006EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We propose an algebraic framework for designing trap-door one-way functions with applications in multivariate signature schemes. Multivariate schemes are attractive because of their efficiency. The proposed framework involves paraunitary matrices, a special subset of invertible polynomial-matrices. Using the algebraic framework, we propose the general template of paraunitary digital-signature scheme (PDSS). The general framework paves the way for a computational-security analysis of the PDSS. We also propose a practical instance of the PDSS that operates on the field GF (28). The message block and the secret key both consist of 16 symbols from GF (28). The signature is a block of length 26 symbols from GF (28). The complexity analysis of this instance reveals that it is, at least, as efficient as the hidden-field equations (HFE) scheme. In addition, our cryptanalysis shows that the proposed instance is secure