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arXiv · 1401.7532

The MMO problem

Oscar Garcia-Morchon·Ronald Rietman·Ludo Tolhuizen·Domingo Gomez·Jaime Gutierrez
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Abstract

We consider a two polynomials analogue of the polynomial interpolation problem. Namely, we consider the Mixing Modular Operations (MMO) problem of recovering two polynomials $f\in \Z_p[x]$ and $g\in \Z_q[x]$ of known degree, where $p$ and $q$ are two (un)known positive integers, from the values of $f(t)\bmod p + g(t)\bmod q$ at polynomially many points $t \in \Z$. We show that if $p$ and $q$ are known, the MMO problem is equivalent to computing a close vector in a lattice with respect to the infinity norm. We also implemented in the SAGE system a heuristic polynomial-time algorithm. If $p$ and $q$ are kept secret, we do not know how to solve this problem. This problem is motivated by several potential cryptographic applications.

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BibTeXRIS

Oscar Garcia-Morchon, Ronald Rietman, Ludo Tolhuizen, Domingo Gomez, Jaime Gutierrez. 2014-01-29. The MMO problem. https://arxiv.org/abs/1401.7532

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