We show how to solve a polynomial equation (mod N) of degree k in a single variable x, as long as there is a solution less than about N(sup 1/k). We give an application to an RSA encryption protocol: if messages are padded with truly random padding and then encrypted with an exponent 3, then two encryptions of the same message (with different padding) will reveal the message, as long as the padding is less than 1/9 of the length of N. With several encryptions, another technique can (heuristically) tolerate padding up to about 1/6 of the length of N.
By: Don Coppersmith
Published in: RC20223 in 1995
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