By Mikael Goldmann, Mats NÄslund (auth.), Burton S. Kaliski Jr. (eds.)

ISBN-10: 3540633847

ISBN-13: 9783540633846

This ebook constitutes the refereed court cases of the seventeenth Annual foreign Cryptology convention, CRYPTO'97, held in Santa Barbara, California, united states, in August 1997 less than the sponsorship of the overseas organization for Cryptologic learn (IACR).

The quantity offers 35 revised complete papers chosen from a hundred and sixty submissions bought. additionally incorporated are invited shows. The papers are equipped in sections on complexity thought, cryptographic primitives, lattice-based cryptography, electronic signatures, cryptanalysis of public-key cryptosystems, details idea, elliptic curve implementation, number-theoretic structures, allotted cryptography, hash features, cryptanalysis of secret-key cryptosystems.

**Read or Download Advances in Cryptology — CRYPTO '97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings PDF**

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**Additional resources for Advances in Cryptology — CRYPTO '97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings**

**Example text**

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 — CRYPTO '97: 17th Annual International Cryptology Conference Santa Barbara, California, USA August 17–21, 1997 Proceedings by Mikael Goldmann, Mats NÄslund (auth.), Burton S. Kaliski Jr. (eds.)

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