Several variants of Rainbow or UOV using sparse private keys have been proposed to reduce the private key size.
As UOV can be considered as a single layer Rainbow, these two methods can also be applied to UOV.
Our Contributions: In this paper, we propose Circulant UOV with higher signature generating efficiency and shorter private key.
In this section, we will introduce UOV and its variants.
UOV is a modified version of the Oil and Vinegar scheme designed by J.
To figure out what UOV is, first of all, we'd like to introduce the concept of Oil-Vinegar polynomial with the following form:
For example, in the recent paper [5] the authors undertook an attempt to reduce the public key size, based on yet unbroken (under proper parameter choice) Unbalanced Oil and Vinegar (UOV) scheme [6].
Traditionally, basing on the four basic schemes MI [9], HFE [8], STS [10] and UOV [6], the MQ public key cryptosystems are divided in four groups.
For "generic" quadratic systems, experts believe that the Unbalanced Oil-Vinegar (UOV) scheme [6] is a feasible signature scheme with good efficiency and acceptable security.
In Section 2, we describe the preliminaries about hyper-spheres, signature models, multivariate cryptography and basic UOV signature scheme.
The UOV scheme is a single field construction, so we work solely in the polynomial ring K[X], where X = [x.sub.1],...,[x.sub.n].
The public key P of the UOV scheme consists of o quadratic polynomials in n variables: