Download e-book for kindle: Advances in Cryptology — CRYPTO '97: 17th Annual by Mikael Goldmann, Mats NÄslund (auth.), Burton S. Kaliski Jr.

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

ISBN-10: 3540633847

ISBN-13: 9783540633846

This booklet constitutes the refereed lawsuits of the seventeenth Annual overseas Cryptology convention, CRYPTO'97, held in Santa Barbara, California, united states, in August 1997 below the sponsorship of the overseas organization for Cryptologic examine (IACR).
The quantity provides 35 revised complete papers chosen from a hundred and sixty submissions got. additionally integrated are invited shows. The papers are equipped in sections on complexity thought, cryptographic primitives, lattice-based cryptography, electronic signatures, cryptanalysis of public-key cryptosystems, info concept, elliptic curve implementation, number-theoretic platforms, dispensed cryptography, hash capabilities, cryptanalysis of secret-key cryptosystems.

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

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1 Following the naming analogy of the Tate and ate pairing we might call this pairing also the eil pairing. Note that eil is the german word for hurry. For a suitable choice of s the eil pairing can indeed be computed faster than the Weil pairing. 22 3 F. Hess Pairing Functions of Lowest Degree Let s be an integer. For h = di=0 hi xi ∈ Z[x] with h(s) ≡ 0 mod r let fs,h,R ∈ Fqk (E) for R ∈ E(Fqk )[r] be the uniquely defined monic function satisfying d hi ((si R) − (O)). (fs,h,R ) = i=0 Furthermore, define d ||h||1 = |hi |.

An easy calculation with cyclic groups shows that it is always possible to choose d ≥ 0 such that u = sq −d mod r has order e modulo r for some e | #Aut(E). The value of s can be changed modulo r2 without changing the pairings as , atwist and es . s Possible cases. Since the automorphism group of an ordinary elliptic curve can only be cyclic of order 2, 4 or 6 there are only few new cases in which Theorem 2 can be applied. On the other hand, there is some freedom of choice regarding the parameters e, d.

Let as : I (1) → W, h → as,h be a map with the following properties: 1. as,g+h = as,g as,h for all g, h ∈ I (1) , 2. as,hx = ass,h for all h ∈ I (1) with as,h ∈ W bilin , 3. as,r ∈ W bilin \{1} and as,t−s = 1. Then im(as ) = W bilin and ker(as ) = I (2) . More precisely, as,h = ah(s)/r s,r for all h ∈ I (1) . There exists an efficiently computable h ∈ I (1),ϕ(n) with ||h||1 = O(r1/ϕ(n) ) and as,h = 1. The O-constant depends only on n. Any h ∈ I (1) with as,h = 1 satisfies ||h||1 ≥ r1/ϕ(n) . Proof.

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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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