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**1 - 1**of**1**### The MMO Problem Oscar Garcı́a-Morchón

"... 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 ∈ Zp[x] and g ∈ Zq [x] of known degree, where p and q are two (un)known positive integers, from the values of f(t) mod p+ g( ..."

Abstract
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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 ∈ Zp[x] and g ∈ Zq [x] of known degree, where p and q are two (un)known positive integers, from the values of f(t) mod p+ g(t) mod q at polynomially many points t ∈ 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. 1.