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x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

Method s 2

Method s 2 -mod-n-generator • key value: p,q prime, big, � 3 mod 4 n = p • q • initial value (seed): s � Z n * • PBG: s 0 := s 2 mod n Example: n = 3 � 11 = 33, s = 2 index 0 1 2 3 4 s i : b i : s i+1 := s i 2 mod n bi := s i mod 2 ... (last bit) Note: length of period no problem with big numbers (Blum / Blum / Shub 1983 / 86) ... 4 16 25 31 4 0 0 1 1 0 16 2 mod 33 = 8 � 32 = 8 � (-1) = 25 25 2 = (-8) 2 � 64 � 31 31 2 = (-2) 2 = 4 185

s 2 -mod-n-generator as symmetric encryption system Purpose: application as symmetric encryption system: “Pseudo one-time pad” Compare: one-time pad: add long real random bit stream with plaintext Pseudo one-time pad: add long pseudo-random stream with plaintext Scheme: secret area n, s security- parameter secret key = key and initial value = x0x1x2 ... encryption: create b0 b1 b2 ..., add = x0 � b0, x1 � b1, ... key generation = generation of key and initial value n, s plaintext ciphertext plaintext decryption: create b0 b1 b2 ..., add real random number x k(x) x l 186

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