SECURITY OF NUMBER THEORETIC PUBLIC KEY CRYPTOSYSTEMS AGAINST RANDOM ATTACK, III

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Abstract
This paper concludes the discussion we began in the last two issues of CRYPTOLOGIA. A typical message receiver using an RSA public key cryptosystem believes that the secret nontrivial factors p and q of his public coding modulus m are primes. But he need not know that p or q are prime, or even square free. We give a few examples below. In some of them the “RSA public key cryptosystem” based on integers P and Q erroneously thought both to be prime works perfectly, but is more vulnerable to a cryptanalytic attack of the type G. J. Simmons and J. N. Norris [7] have suggested. In other cases these cryptosystems malfunction in an obvious fashion likely to be apprehended quickly by the message receiver. After the examples we prove all the results in I and II except a few which, like Theorems 1.1, 1.2 and 1.3, are obvious corollaries of other results in those papers.

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