# Breaking RSA May Be As Difficult As Factoring

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## Abstract

If factoring is hard, this paper shows that straight line programs cannot efficiently solve the low public exponent RSA problem. More precisely, no efficient algorithm can take an RSA public key as input and then output a straight line program that efficiently solves the low public exponent RSA problem for the given public key—unless factoring is easy.

## Keywords

RSA Factoring Straight line programs## Notes

### Acknowledgments

Steven Galbraith pointed out a major mistake in a previous paper of the author. The author’s efforts to correct this mistake ultimately led to this paper. Alfred Menezes provided extensive comments on the presentation of this paper.(One of which led to the correction: the condition that \(g(X)\) should be square-free, which can be used to factor if it fails.) Adrian Antipa, Rob Lambert, Scott Vanstone, Rene Struik and John Goyo also provided comments. Andy Rupp provided several comments. Anonymous reviewers provided valuable comments.

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