Cryptology ePrint Archive: Report 2012/064

Ron was wrong, Whit is right

Arjen K. Lenstra and James P. Hughes and Maxime Augier and Joppe W. Bos and Thorsten Kleinjung and Christophe Wachter

Abstract: We performed a sanity check of public keys collected on the web. Our main goal was to test the validity of the assumption that different random choices are made each time keys are generated. We found that the vast majority of public keys work as intended. A more disconcerting finding is that two out of every one thousand RSA moduli that we collected offer no security. Our conclusion is that the validity of the assumption is questionable and that generating keys in the real world for ``multiple-secrets'' cryptosystems such as RSA is significantly riskier than for ``single-secret'' ones such as ElGamal or (EC)DSA which are based on Diffie-Hellman.

Category / Keywords: public-key cryptography / Sanity check, RSA, 99.8\% security, ElGamal, DSA, ECDSA, (batch) factoring, discrete logarithm, Euclidean algorithm, seeding random number generators, $K_9$.

Date: received 14 Feb 2012, last revised 17 Feb 2012

Contact author: akl at epfl ch

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Version: 20120217:134904 (All versions of this report)

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