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

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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 feel that they move all probabilistic polynomial time statistical checks. in spite of the fact that, regardless of those great houses, the safe turbines identified 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. Pseudc-random quantity g- erators which are at present utilized in perform output n bits consistent with multiplication (n2 steps). a tremendous open challenge used to be to output even bits on each one multiplication in a cryptographically safe method. This challenge was once said by means of Blum, Blum & Shub [3] within the context in their z2 mod N generator. They extra ask: what number bits should be o- placed according to multiplication, preserving cryptographic protection? during this paper we nation an easy , the XOR-Condition and convey that any generator pleasant this situation can output logn bits on each one multiplication. We exhibit that the XOR-Condition is chuffed via the lop least major bits of the z2-mod N generator. the safety of the z2 mod N generator used to be according to Quadratic Residu- ity [3]. This generator is an instance of a Trapdoor Generator [13], and its trapdoor homes were utilized in protocol layout. We increase the protection of this gene- tor by way of proving it as tough as factoring.

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Additional info for Advances in Cryptology: Proceedings of CRYPTO 84

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303-308. [Ah0741 A V. Aho, J. E. Hopcroft, and J. D. Ullman, Tbe Resign and Ana/ysis of COmpUter A/gor ifhms, Addison-Wesley, 1974. [BIum831 fl. Blwn. 'How to exchange (secret) keys,' ACM rransacrions on Computer Systems 1,2 (May 1985). pp. 175- 193. [Boon591 W. Boone, 'The word problem,' Anna/s o f Math. 70 ( 198 1 1, pp. 207-265. [Bras791 G. Brassard, "A note on the complexity of cryptography,' /ffE Transactions on /nformation Theory, IT-25,2 (Mar. 19791, pp. 232-233. lBras8 11 G. A report on CRYPT0 81, ed.

The secret t h a t h e l p s A l i c e s o l v e t h e e q u a t i o n ( 1 ) i s an i n t e g e r ( d , d ) - m a t r i x A w h i c h modulo n i s i n v e r t i b l e . I f t h e t r a n s f o r m a t i o n 39 x - = A s (mod n ) t r a n s f o r m s P i n t o a polynomial x P ' ( x 2 1 . . , X d ) = 1 , s d ) (mod n ) t h e n A l i c e can e a s i l y s o l v e e q u a t i o n ( 1 ) . = P ( s l,.. p i c k s random v a l u e s x 2 , . . , x d . She E Zn, evaluates . (21 x1 := m / P ' ( x 2 , . , x d ) (mod n ) and t r a n s f o r m s s (3) := A -1 5 (mod n ) .

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 . The messages m a r e numbers i n Zn.

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