**A note on invariant linear transformations in multivariate public key cryptography**

*Andreas Wiemers*

**Abstract: **Imai and Matsumoto introduced a public key cryptosystem based on
multivariate quadratic polynomials. In a simplified way, the essence of their cryptosystem can be described in the following way: Start with a central monomial F. The secret key comprises
two invertible linear transformations T and L such that TFL is the public key. In order to study equivalent public keys it is natural to ask for the "invariant" secret keys (T,L), i.e. TFL=F. Lin, Faugere, Perret and Wang give a partial answer to this question by considering such L which fulfill FL=F. In this paper we will determine all invariant invertible linear transformations (T,L).

**Category / Keywords: **public-key cryptography / multivariate public key cryptography

**Date: **received 24 Oct 2012

**Contact author: **wiemers bonn at freenet de

**Available format(s): **PDF | BibTeX Citation

**Version: **20121025:131729 (All versions of this report)

**Short URL: **ia.cr/2012/602

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