# Attacks on RSA

*14 January 2011*.

A number of methods have been proposed for attacking the RSA cryptosystem. This article describes them.

Any efficient solution to the integer factorisation problem would break RSA; see the RSA article for discussion. The difficulty with that approach is that no efficient solution is known. Cracking a large (say 1024 bits or more) RSA key with current factoring algorithms is not practical, even with massive parallelism.

## [edit] Weiner attack

Michael Weiner proposed an attack ^{[1]} based on continued fractions which is effective if the exponent in the secret key is small. There have since been many papers proposing improvements on or variants of that attack.

## [edit] TWIRL

**The Weizmann Instiute Relation Locator** ^{[2]}, developed by Adi Shamir (The 'S' in RSA) and Eran Tromer, is a machine designed to speed up the seiving step in the number field seive technique for integer factorisation.

RSA Security have commented [1].

## [edit] References

- ↑ Wiener, M.J. (May 1990). "
*Cryptanalysis of short RSA secret exponents*". - ↑ Adi Shamir & Eran Tromer (2003).
*On the cost of factoring RSA-1024*.

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