## Cryptology ePrint Archive: Report 2021/1006

UOV-Pepper: New Public Key Short Signature in Degree 3

Gilles Macario-Rat and Jacques Patarin

Abstract: In this paper, we present a new perturbation for the design of multivariate schemes that we call Pepper''. From this idea, we present some efficient multivariate signature schemes with explicit parameters that resist all known attacks. In particular they resist the two main (and often very powerful) attacks in this area: the Gröbner attacks (to compute a solution of the system derived from the public key) and the MinRank attacks (to recover the secret key). Pepper can also be seen as a new perturbation that can be used to strengthen many other multivariate schemes. The Pepper'' perturbation works only for public key equations of degree (at least) 3. Despite this, the size of the public key may still be reasonable since we can use larger fields (and also maybe non dense equations). Furthermore, the size of the signatures can be very short.

Category / Keywords: public-key cryptography / public-key cryptography, post-quantum multivariate cryptography, UOV, HFE