Chapter

Public Key Cryptography – PKC 2011

Volume 6571 of the series Lecture Notes in Computer Science pp 335-350

Linear Recurring Sequences for the UOV Key Generation

  • Albrecht PetzoldtAffiliated withDepartment of Computer Science, Technische Universität DarmstadtCenter for Advanced Security Research Darmstadt - CASED
  • , Stanislav BulyginAffiliated withDepartment of Computer Science, Technische Universität DarmstadtCenter for Advanced Security Research Darmstadt - CASED
  • , Johannes BuchmannAffiliated withDepartment of Computer Science, Technische Universität DarmstadtCenter for Advanced Security Research Darmstadt - CASED

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.

Keywords

Multivariate Cryptography UOV Signature Scheme Key Size Reduction Linear Recurring Sequences