Advances in Cryptology — ASIACRYPT 2002: 8th International by Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang

By Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang Zheng (eds.)

This booklet constitutes the refereed complaints of the eighth overseas convention at the thought and alertness of Cryptology and data defense, ASIACRYPT 2002, held in Singapore, in December 2002.
The 34 revised complete papers provided including invited contributions have been conscientiously reviewed and chosen from 173 submissions at the foundation of 875 evaluate reviews. The papers are prepared in topical sections on public key cryptography, authentication, concept, block ciphers, disbursed cryptography, cryptanalysis, public key cryptanalysis, mystery sharing, electronic signatures, functions, Boolean features, key administration, and ID-based cryptography.

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Extra resources for Advances in Cryptology — ASIACRYPT 2002: 8th International Conference on the Theory and Application of Cryptology and Information Security Queenstown, New Zealand, December 1–5, 2002 Proceedings

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However, these conclusions are based on numerous assumptions, some quite optimistic. Much more research, and possibly actual relation collection experiments, would have to be carried out to get a clearer Analysis of Bernstein’s Factorization Circuit 23 grasp of the actual cost (time and money) of both the relation collection and matrix steps for 1024-bit moduli. 7). , the “large” matrix) already minimize the cost of relation collection (cf. 6). For improved NFS that is applied to a single factorization (cf.

Given two values g2 ∈R QRN and u1 ∈R QRN with logg (u1 ) = r, it is infeasible to find the value u2 = g2r . 5 Assumption: (factoring assumption for N ) Given N , it its infeasible to find P or Q. Theorem 1 (Factoring assumption ⇒ CDH assumption). If the factoring N is infeasible, the CDH assumption for QRN holds. The proof is in Section C of the appendix. 5 Some Technicalities Lemma 5. Let g be a generator of QRN and w ∈R ZZpq . The value g2 = g w is a uniformly distributed random value in QRN . With overwhelming probability, g2 is a generator for QRN .

Else compute τ = T ∗ h(2, K , U1 , U2 ) and output K∗ = K ∗ h(3, τ , U1 , U2 ). Theorem 3 (Security of h-extended scheme in standard model). Let h be any efficient function h : {1, 2, 3} × QR3N → QRN . If H is TC-resistant and both the DDH assumption for QRN and the factoring assumption for N hold, the Cramer-Shoup cryptosystem in QRN is ACC-secure. A Variant of the Cramer-Shoup Cryptosystem for Groups of Unknown Order 37 Proof. Observe that the simulator described in Section 5 computes the values k and t when dealing with an encapsulation query.

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Advances in Cryptology — ASIACRYPT 2002: 8th International by Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang
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