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The Rivest, Shamir, and Adleman (RSA) public-key encryption algorithm can be broken if the integer R used as the modulus can be factored. It my however be possible to break this system without factoring R . A modification of the RSA scheme is described. For this modified version it is shown that, if the encryption procedure can be broken in a certain number of operations, then R can be factored in only a few more operations. Furthermore, this technique can also be used to produce digital signatures, in much the same manner as the RSA scheme.
Hywel C Williams (Sat,) studied this question.