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**2012/602**

**Title:**

A note on invariant linear transformations in multivariate public key cryptography

**Authors:**
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).

**ePrint:**
https://eprint.iacr.org/2012/602

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