The security of public-key cryptosystems is based on the intractability of certain computational problems. The security of the RSA and Rabin schemes is based on the hardness of integer factorization. The security of the ElGamal protocols and of DSA is based on the intractability of computing discrete logarithms in finite prime fields. However, none of those computational problems is provably intractable. Algorithmic progress has almost always been faster than predicted and it is known that quantum computers will make integer factorization and discrete logarithm computation in the relevant groups easy. Therefore, it is necessary to find public-key cryptosystems that are based on new intractable problems. In particular, it is necessary to find public key cryptosystems that remain secure even when quantum computers can be built.
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