Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith’s Methods
We analyze the security of the Elliptic Curve Linear Congruential Generator (EC-LCG). We show that this generator is insecure if sufficiently many bits are output at each iteration. In 2007, Gutierrez and Ibeas showed that this generator is insecure given a certain amount of most significant bits of some consecutive values of the sequence. Using the Coppersmith’s methods, we are able to improve their security bounds.
KeywordsElliptic Curve Linear Congruential Generator Lattice reduction Coppersmith’s methods Elliptic curves
The author was supported in part by the French ANR JCJC ROMAnTIC project (ANR-12-JS02-0004) and by the Simons foundation Pole PRMAIS. I would like to thank anonymous referees for their helpful comments.
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