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**2014/002**

**Title:**

Pseudorandom Generator Based on Hard Lattice Problem

**Authors:**
Kuan Cheng

**Abstract:**

This paper studies how to construct a pseudorandom generator using hard lattice problems. We use a variation of the classical hard problem \emph{Inhomogeneous Small Integer Solution} ISIS of lattice, say \emph{Inhomogeneous Subset Sum Solution} ISSS. ISSS itself is a hash function. Proving the preimage sizes ISSS hash function images are almost the same, we construct a pseudorandom generator using the method in \cite{GKL93}. Also, we construct a pseudoentropy generator using the method in \cite{HILL99}. Most theoretical PRG constructions are not feasible in fact as they require rather long random bits as seeds. Our PRG construction only requires seed length to be O(n^{2}\log_{2} n) which is feasible practically.

**ePrint:**
https://eprint.iacr.org/2014/002

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