Download Advances in Cryptology: Proceedings of CRYPTO 84 by S C Serpell, C B Brookson, B L Clark (auth.), George Robert PDF

By S C Serpell, C B Brookson, B L Clark (auth.), George Robert Blakley, David Chaum (eds.)

Recently, there was loads of curiosity in provably "good" pseudo-random quantity turbines [lo, four, 14, 31. those cryptographically safe turbines are "good" within the experience that they go all probabilistic polynomial time statistical checks. even though, regardless of those great homes, the safe turbines identified up to now be afflicted by the han- cap of being inefiicient; the main efiicient of those take n2 steps (one modular multip- cation, n being the size of the seed) to generate one bit. Pseudc-random quantity g- erators which are presently utilized in perform output n bits in step with multiplication (n2 steps). a tremendous open challenge was once to output even bits on every one multiplication in a cryptographically safe method. This challenge was once acknowledged through Blum, Blum & Shub [3] within the context in their z2 mod N generator. They additional ask: what number bits may be o- placed according to multiplication, preserving cryptographic safeguard? during this paper we kingdom an easy situation, the XOR-Condition and exhibit that any generator enjoyable this can output logn bits on each one multiplication. We express that the XOR-Condition is chuffed through the lop least major bits of the z2-mod N generator. the safety of the z2 mod N generator was once in response to Quadratic Residu- ity [3]. This generator is an instance of a Trapdoor Generator [13], and its trapdoor houses were utilized in protocol layout. We enhance the protection of this gene- tor by means of proving it as not easy as factoring.

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Advances in Cryptology: Proceedings of CRYPTO 84

Lately, there was loads of curiosity in provably "good" pseudo-random quantity turbines [lo, four, 14, 31. those cryptographically safe turbines are "good" within the feel that they move all probabilistic polynomial time statistical exams. besides the fact that, regardless of those great houses, the safe turbines recognized to this point be afflicted by the han- cap of being inefiicient; the main efiicient of those take n2 steps (one modular multip- cation, n being the size of the seed) to generate one bit.

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The modulus n i s t h e p r o d u c t of two l a r g e random primes p f q . The f a c t o r i z a t i o n of n s h o u l d b e unknown, e x c e p t p o s s i b l y t o A l i c e . I n o r d e r t o p r e v e n t f a c t o r i n g of n by known f a c t o r i n g a l g o r i t h m s n s h o u l d b e a t l e a s t 6 0 0 b i t s l o n g . The c o e f f i c i e n t s of P a r e i n t e g e r s i n t h e r a n g e Zn := { c E Z? : 0 2 c 'n ) . f o r th e r i n g Z/nZ o f i n t e g e r s modulo n. T y p i c a l l y P w i l l o n l y h a v e a The e l e m e n t s i n Zn a r e used a s r e p r e s e n t a t i v e s few c o e f f i c i e n t s .

These v a l u e s c a n be made p u b l i c , b u t t h e f a c t o r i z a t i o n of n s h o u l d be known o n l y t o t h e key g e n e r a t i o n c e n t e r . The o n l y d i f f e r e n c e between u s e r s i s t h e v a l u e of i , a n d t h e secret k e y w h i c h c o r r e s p o n d s t o i i s t h e ( u n i q u e ) number g such t h a t ge = i (mod n ) . T h i s g c a n be e a s i l y computed by t h e key g e n e r a t i o n c e n t e r , b u t if t h e RSA scheme i s s e c u r e n o o n e e l s e c a n e x t r a c t e - t h r o o t s mod n .

274-275. [Rive831 R. L. Proceedings of Crypt0 82 ed. by D. C h u m et. , Plenum, 1983, pp. 145-163. iRotrn731 J. J. Rotman, Theory of Groups: A n /ntroduction, Second Edition, Allyn and Bacon, 1973. Proceedings of Crypto 82 ed. by D. , Plenum, 1983, pp. 279-288. ' (presentation at Crypto 82). 36 iSna83cI A Shamir, "On the generation of cryptograPhlcally strong pseudorandom sequences,' ACM Tfansaclfons on Computer Systems I , I (Feb. 19831, pp. 38-44. [Tarfa31 R. E. Tarjan, Data Structures andNetwork Algorithms, SIAM, 1983.

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