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5 years ago

x - Faculty of Computer Science - Technische Universität Dresden

x - Faculty of Computer Science - Technische Universität Dresden

About cryptographically

About cryptographically strong systems (2) application: s 2 -mod-n-generator, GMR and many others, e.g., only well analyzed systems like RSA (significant alternative: only “discrete logarithm”, based on number theory, too, similarly well analyzed) necessary: 1. factoring is difficult 2. to generate p,q is easy 3. operations on the message with n alone, you can only invert using p, q 163

clear: in NP � but difficulty cannot be proved yet complexity at present , c � 1,9 “sub-exponential” practically up to 155 decimal digits in the year 1999 174 decimal digits in the year 2003 200 decimal digits in the year 2005 232 decimal digits in the year 2010 (www.crypto-world.com/FactorRecords.html) (notice : L( n) � e � e � faster algorithms, e.g., for 2 r � 1, but this doesn’t matter) assumption: factoring is hard c� 3 l 3 Factoring ln( n) �(lnln( n)) (notice : If an attacker could factor, e.g., every 1000 th n, this would be unacceptable.) 2 164

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