The security of many currently used cryptosystems, in particular that of all public-key cryptosystems, is based on the hardness of an underlying computational problem, such as factoring integers or computing discrete logarithms. Security proofs for these systems show that the ability of an adversary to perform a successful attack contradicts the assumed difficulty of the computational problem. Security proofs of this type were presented in Chapter 9. For example, we proved that public-key one-time pads induced by one-way permutations with a hard-core predicate are ciphertext-indistinguishable. The security of the encryption scheme is reduced to the one-way feature of function families, such as the RSA or modular squaring families, and the one-way feature of these families is, in turn, based on the assumed hardness of inverting modular exponentiation or factoring a large integer (see Chapter 6). The security proof is conditional, and there is some risk that in the future, the underlying condition will turn out to be false.
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