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x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

to b) F : input n repeat

to b) F : input n repeat forever Calculating with and without p,q (16) choose w � Z n * at random, set x:= w 2 w´:= W(n,x) test whether w´ � � w, if so factor according to a) break • to determine the Jacobi symbol is easy (if p and q unknown: use quadratic law of reciprocity) x but note : If = 1, determine whether x � QRn is difficult n (i.e. it does not work essentially better than to guess) QRA = quadratic residuosity assumption 183

184 The s 2 -mod-n-Pseudo-random Bitstream Generator (PBG) Idea: short initial value (seed) � long bit sequence (should be random from a polynomial attacker’s point of view) Scheme: Requirements: security- parameter key and initial value l generation of key and initial value gen n, s PBG secret area real random number long bitstream b 0 b 1 b 2 ... length poly(l ) • gen and PBG are efficient • PBG is deterministic (� sequence reproducible) • secure: no probabilistic polynomial test can distinguish PBG-streams from real random streams

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X - Technische Universität Dresden
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