A More Secure and Efficacious TTS Signature Scheme

In 2002 the authors introduced the new genre of digital signature scheme TTS (Tame Transformation Signatures) along with a sample scheme TTS/2. TTS is from the family of multivariate cryptographic schemes to which the NESSIE primitive SFLASH also belongs. It is a realization of T. Moh’s theory ([31]) for digital signatures, based on Tame Transformations or Tame Maps. Properties of multivariate cryptosystems are determined mainly by their central maps. TTS uses Tame Maps as their central portion for even greater speed than C∗-derived SFLASH family of schemes, which uses monomials in a large field for the central portion, previously usually acknowledged as fastest. We show a small flaw in TTS/2 and present an improved TTS implementation which we call TTS/4. We will examine in some detail how well TTS/4 performs, how it stands up to previously known attacks, and why it represents an advance over TTS/2. Based on this topical assessment, we consider TTS in general and TTS/4 in particular to be competitive or superior in several aspects to other schemes, partly because the theoretical roots of TTS induce many good traits. One specific area in which TTS/4 should excel is in low-cost smartcards. It seems that the genre has great potential for practical deployment and deserves further attention by the cryptological community.