Suppose that an eavesdropper Eve is able to solve the Diffie-Hellman problem; more precisely, suppose that...

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Suppose that an eavesdropper Eve is able to solve the Diffie-Hellman problem; more precisely, suppose that if Eve is given two powers g" and g" mod p then she is able to compute g mod p. With this ability, can Eve break the Elgamal public key cryptosystem? Suppose that an eavesdropper Eve is able to solve the Diffie-Hellman problem; more precisely, suppose that if Eve is given two powers g" and g" mod p then she is able to compute g mod p. With this ability, can Eve break the Elgamal public key cryptosystem?