Linear recurring sequences for the UOV key generation

Authors:
Albrecht Petzoldt;Stanislav Bulygin;Johannes Buchmann
Affiliations:
Technische Universität Darmstadt, Department of Computer Science, Darmstadt, Germany and Center for Advanced Security Research Darmstadt, Darmstadt, Germany;Technische Universität Darmstadt, Department of Computer Science, Darmstadt, Germany and Center for Advanced Security Research Darmstadt, Darmstadt, Germany;Technische Universität Darmstadt, Department of Computer Science, Darmstadt, Germany and Center for Advanced Security Research Darmstadt, Darmstadt, Germany
Venue:
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Year:
2011

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Abstract

Multivariate public key cryptography is one of the main approaches to guarantee the security of communication in the post-quantum world. Due to its high efficiency and modest computational requirements, multivariate cryptography seems especially appropriate for signature schemes on low cost devices. However, multivariate schemes are not much used yet, mainly because of the large size of their public keys. In [PB10] Petzoldt et al. presented an idea how to create a multivariate signature scheme with a partially cyclic public key based on the UOV scheme of Kipnis and Patarin [KP99]. In this paper we use their idea to create a multivariate signature scheme whose public key is mainly given by a linear recurring sequence (LRS). By doing so, we are able to reduce the size of the public key by up to 86%. Moreover, we get a public key with good statistical properties.