Cryptology ePrint Archive: Report 2012/588

Breaking Public Keys - How to Determine an Unknown RSA Public Modulus

Hans-Joachim Knobloch

Abstract: Not surprisingly, the common use of any public key crypto system involves publishing the public key and keeping the private key secret. There are however a few applications where both the private and public key are kept secret, thereby effectively converting a public key crypto algorithm to a symmetric algorithm. We show that if the RSA cryptosystem is used in such a symmetric application, it is possible to determine the public RSA modulus if the public exponent is known and short, such as 3 or F4=65537, and two or more plaintext/ciphertext (or, if RSA is used for signing, signed value/signature) pairs are known.

Category / Keywords: public-key cryptography / cryptanalysis block cipher RSA

Date: received 11 Oct 2012, last revised 16 Oct 2012

Contact author: hans-joachim knobloch at secorvo de

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Version: 20121025:121536 (All versions of this report)

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