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x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

Scheme

Scheme of security proofs (2) (adaptive) active attacker attacked person � � call result Alg.2: solve the number theoretic problem result Alg.3: get secret key ciphertext plaintext . . . . . . Alg.1: get to know something about the plaintext (or provide signature, respectively) Seemingly, there are no provably secure cryptosystems against adaptive active attacks. A constructive security proof seems to be a game with fire. 197

Alg.2: has to demand uniformity Why fallacy ? attacker attacked person Alg.1: uniform for any key GMR – signature system Alg.1: non uniform: only own key Shafi Goldwasser, Silvio Micali, Ronald Rivest: A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks; SIAM J. Comput. 17/2 (April 1988) 281 – 308 Main ideas 1) Map a randomly chosen reference R, which is only used once. 2) Out of a set of collision-resistant permutations (which are invertible using a secret) assign to any message m one permutation. - 1 F n,m (R) R Sig R m F n,m (Sig ) R m 198

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