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x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

Solution

Solution of problem 1 (2) Proposition If the permutation pairs are collision resistant, then the adaptive active attacker can’t sign any message with GMR. Proof A forged signature leads either to a collision in the tree of references (contradiction) or to an additional legal signature. So the attacker has inverted the collisionresistant permutation. With this ability he could generate collisions (contradiction). Example: R f 0 first differing bit position � Sig � � � � �R 1110 f 0 f 1 f 1 f 1 205

Note In the proof you dispose the “Oracle” (the attacked person) by showing that the attacker can generate „half“ the tree from the bottom or (exclusive) “half” the tree from the top with the same probability distribution as the attacked person. Lesson: randomly chosen references each used only once (compare one-time-pad) make adaptive active attacks ineffective � arrow explained (random number z') in figure signature system 206

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