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Better key sizes (and attacks) for LWE-based encryption

By Richard Lindner and Chris Peikert


We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the “learning with errors ” (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple distinguishing attack considered in prior analyses; (2) concrete parameters and security estimates for an LWE-based cryptosystem that is more compact and efficient than the well-known schemes from the literature. Our new key sizes are up to 10 times smaller than prior examples, while providing even stronger concrete security levels

Topics: lattice-based cryptography, basis reduction, learning with errors
Year: 2011
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