By Duong Hieu Phan, David Pointcheval (auth.), Chi-Sung Laih (eds.)
This publication constitutes the refereed lawsuits of the ninth overseas convention at the idea and alertness of Cryptology and knowledge defense, ASIACRYPT 2003, held in Taipei, Taiwan in November/December 2003.
The 32 revised complete papers awarded including one invited paper have been rigorously reviewed and chosen from 188 submissions. The papers are equipped in topical sections on public key cryptography, quantity idea, effective implementations, key administration and protocols, hash capabilities, workforce signatures, block cyphers, broadcast and multicast, foundations and complexity concept, and electronic signatures.
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This self-contained creation to trendy cryptography emphasizes the maths in the back of the speculation of public key cryptosystems and electronic signature schemes. The booklet specializes in those key themes whereas constructing the mathematical instruments wanted for the development and safety research of various cryptosystems.
На английском: The cryptosystems according to the Integer Factorization challenge (IFP), the Discrete Logarithm challenge (DLP) and the Elliptic Curve Discrete Logarithm challenge (ECDLP) are primarily the single 3 different types of useful public-key cryptosystems in use. the safety of those cryptosystems is based seriously on those 3 infeasible difficulties, as no polynomial-time algorithms exist for them thus far.
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Extra resources for Advances in Cryptology - ASIACRYPT 2003: 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30 – December 4, 2003. Proceedings
12. S. Goldwasser, S. Micali, and C. Rackoﬀ. The Knowledge Complexity of Interactive Proof Systems. In Proc. of the 17th STOC, pages 291–304. ACM Press, New York, 1985. 13. S. Goldwasser, S. Micali, and R. Rivest. A “Paradoxical” Solution to the Signature Problem. In Proc. of the 25th FOCS, pages 441–448. IEEE, New York, 1984. 14. S. Goldwasser, S. Micali, and R. Rivest. A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. SIAM Journal of Computing, 17(2):281–308, April 1988.
Thus the oracle O can correctly distinguish between SM ALLRSAK (n, e, α) and SM ALLRSAP (n, e, α). Therefore SM ALLRSAK ≈ SM ALLRSAP ≈ LARGERSAP ≈ LARGERSAK , where ≈ means indistinguishable. This implies that Reciprocal-Paillier assumption holds. 7 On Chosen Ciphertext Security For chosen ciphertext security, we can obtain a variant of our encryption scheme as follows by applying the technique of [Poi99]. c=( r+ α r e + mn mod n2 )||H(r, m) where H is a random hash function and || denotes concatenation.
Thus we have to compute: δ= Pr r1 ∈R Zλ/2 c∈G r ∈ Z 2 R N Pr = c∈G = c∈G r1 ∈R Zλ/2 g r1 +r2 λ/2 = c − [r1 = c1 ] Pr r1 ∈R Z(N +1)/4 r2 ∈R ZN Pr [r2 = c2 ] − r2 ∈R ZN g r1 (1 + r2 N ) = c Pr r1 ∈R Z(N +1)/4 r2 ∈R ZN g r1 (1 + r2 N ) = c 1 2 × − Pr g r1 (1 + r2 N ) = c λ N r1 ∈R Z(N +1)/4 r2 ∈R ZN Denoting g λ/2 = 1 + αN mod N 2 and β = α−1 mod N , we have g r1 (1 + r2 N ) = g r1 +r2 βλ/2 mod N 2 . Then we observe that for λ/2 ≤ r1 < N4+1 , we have the following “collision”: g r1 +r2 βλ/2 = g (r1 −λ/2)+(r2 β+1)λ/2 (mod N )2 Hence, two cases appear when summing up (of course, the probabilities that r2 or r2 β or r2 β + 1 equals a given c2 are all 1/N ): 4 1 N +1 λ 2 · N +1 × N if 0 ≤ c < 4 − 2 r1 +r2 βλ/2 c1 +c2 λ/2 Pr g = =g 1 · N4+1 × N1 if N4+1 − λ2 ≤ c < λ2 Consequently, we gets (recall that δ= N +1 4 8 p+q 2 − + 4 λN N (N + 1) ≤0 This is easily seen negligible.
Advances in Cryptology - ASIACRYPT 2003: 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30 – December 4, 2003. Proceedings by Duong Hieu Phan, David Pointcheval (auth.), Chi-Sung Laih (eds.)