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Abstract. The complexity of breaking cryptosystems of which security is based on the discrete logarithm problem is explored. The cryptosystems mainly discussed are the DiffieHellman key exchange scheme (DH), the BellareMicali noninteractive oblivious transfer scheme (BM), the ElGamal public-key cryptosystem (EG), the Okamoto conference-key sharing scheme (CONF), and the Shamir 3-pass key-transmission...
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