Low-Exponent RSA with Related Messages

In this paper we present a new class of attacks against RSA with low encrypting exponent. They enable the recovery of plaintext messages from their ciphertexts and a known polynomial relationship among the messages, provided that the ciphertexts were created using the same RSA public key with low encrypting exponent. These attacks differ from the low-exponent attacks described by Moore and Hastad and the common modulus attack identified by Simmons, which pertaGiven encryptions of $k$ messages under the same RSA public key with exponent $e$, together with knowledge of a polynomial relation among the messages of degree $\delta$, the goal of the attacks is to recover all messages. Our results were influenced by an attack presented by Franklin and Reiter for the case $k=2$, $e=3$, $\delta = 1$. Starting with this case, we generalize the exponent $e$ in Section 2, the degree $\delta$ in Section 3, and the number of messages $k$ in Section 4. Implications of the attack are considered in Section 5. in only to ciphertexts encrypted under different public keys.

By: Don Coppersmith, Matthew Franklin (AT&T Bell Labs.), Jacques Patarin (CPS Transac, France) and Michael Reiter (AT&T Bell Labs.)

Published in: RC20318 in 1995

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