International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 29 May 2012

Yun-Ju Huang, Feng-Hao Liu, Bo-Yin Yang
ePrint Report ePrint Report
In this work, we study a new multivariate quadratic (MQ) assumption that can be used to construct public-key encryption schemes. In particular, we research in the following two directions:

We establish a precise \\emph{asymptotic} formulation of a family of hard MQ problems, and provide empirical evidence to confirm the hardness. %Since there are many practical solvers studied and implemented during the studies of algebraic attacks, we use

We construct public-key encryption schemes, and prove their security under the hardness assumption of this family. Also, we provide a new \\emph{perspective} to look at MQ systems that plays a key role to our design and proof of security.

As a consequence, we construct the \\emph{first} public-key encryption scheme that is \\emph{provably secure} under the MQ assumption.

Moreover, our public-key encryption scheme is efficient in the sense that it only needs a ciphertext length $L + \\poly(k)$ to encrypt a message $M\\in \\{0, 1 \\}^{L}$ for any un-prespecified polynomial $L$, where $k$ is the security parameter. This is essentially \\emph{optimal} since an additive overhead is the best we can hope for.

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