By Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang Zheng (eds.)
This booklet constitutes the refereed lawsuits of the eighth foreign convention at the idea and alertness of Cryptology and knowledge safety, ASIACRYPT 2002, held in Singapore, in December 2002.
The 34 revised complete papers provided including invited contributions have been rigorously 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, conception, block ciphers, disbursed cryptography, cryptanalysis, public key cryptanalysis, mystery sharing, electronic signatures, functions, Boolean features, key administration, and ID-based cryptography.
Read or Download 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 PDF
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Additional info 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
ASIACRYPT 2002, LNCS 2501, pp. 27–45, 2002. c Springer-Verlag Berlin Heidelberg 2002 28 Stefan Lucks this paper, we deal with another variation, based on the Diﬃe-Hellman problem in speciﬁc groups of non-prime order. Set N = P Q, P = 2p + 1, Q = 2q + 1, p = q, and let P , Q, p, and q be odd primes. In the remainder of this paper, we assume N to be of that form. Consider the group QRN of the Quadratic Residues mod N and the CramerShoup Cryptosystem in this group. ) As it will turn out, the legal user will not need to know the factorisation of N for either encryption, decryption or key generation (with the possible exception of generating an appropriate N itself).
Assume g2 to be a generator for QRN . ) Let the ciphertext (U1 , U2 , T ) be invalid. Thus, R1 = R2 exist with U1 = g R1 and U2 = g2R2 . To answer the query, the values K = U1z1 U2z2 (or K = U1z ), A = H(U1 , U2 ), and T = U1x1 +y1 A U2x2 +y2 A = g R1 x1 +R1 y1 A g2R2 x2 +R2 y2 A are computed, which provides the equation lT := logg (T ) = R1 x1 + R1 y1 A + wR2 x2 + wR2 y2 A . (3) Equations 1 and 2 can be used to eliminate the variables x1 and y1 : lT = R1 lc − R1 wx2 + R1 ld A − R1 wy2 A + wR2 x2 + wR2 y2 A = R1 lc + R1 ld A + wx2 (R2 − R1 ) + wy2 A (R2 − R1 ) 7 It is vital that lc and ld are uniquely deﬁned.
However, usually the uj are chosen to have weight 1 or 2, so the cost of computing these inner products can be kept very low. Also, note that the number of routed messages is now doubled, because previously only half the nodes sent non-nil messages. However, empirically it appears that the clockwise transposition routing algorithm handles the full load without any slowdown. It remains to determine the optimal values of K and ρ. This involves implementation details and technological quirks, and obtaining precise ﬁgures appears rather hard.