You are here
Home > Applied

Applied Algebra, Algebraic Algorithms and Error-Correcting by Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain

By Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain Poli (eds.)

This ebook constitutes the refereed complaints of the fifteenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in may possibly 2003.

The 25 revised complete papers provided including 2 invited papers have been rigorously reviewed and chosen from forty submissions. one of the matters addressed are block codes; algebra and codes: jewelry, fields, and AG codes; cryptography; sequences; interpreting algorithms; and algebra: buildings in algebra, Galois teams, differential algebra, and polynomials.

Show description

Read Online or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings PDF

Similar applied books

The Belousov-Zhabotinskii Reaction

In 1958 B. P. Belousov found that the oxidation of citric acid via bromate within the presence of cerium ions doesn't continue to equilibrium methodically and uniformly, like such a lot chemical reactions, yet particularly oscillates with clocklike precision among a yellow and colorless kingdom. See Fig. eleven. 1, p.

The Relation of Theoretical and Applied Linguistics

The connection of theoretical and utilized linguistics has in recent times triggered numer­ ous debates. This quantity originated at considered one of them. The essence of many of the chapters, of them all other than Fraser's and Davies's, used to be truly offered on the around desk on "The Relationships of Theoretical and utilized Linguistics," equipped through the seventh international Congress of utilized Linguistics, held in Brus­ sels, in August 1984.

Extra info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings

Example text

Suitable for fast implementations; see Sect. 2. We do not consider the zero isogeny φ = [0]. 46 E. Brier and M. 4], such that φˆ ◦ φ = [m] and φ ◦ φˆ = [m] where m = deg φ and [m] (resp. [m] ) is the multiplication-by-m isogeny on E (resp. E ). Interestingly, this leads to a different way for computing Q = [rm]P as Q = φˆ [r] φ(P ) . [rm] P ∈ E(K) −−−−−→ Q = [rm]P ∈ E(K)  ˆ φ φ [r] P ∈ E (K) −−−−−→ Q = [r] P ∈ E (K) Fig. 1. Computing Q = [rm]P through isogenies Isogenies have been intensively studied in order to improve point counting algorithms.

Walker and P. Wild, The combinatorics of perfect authentication schemes, SIAM J. Disc. Math. 7 (1994), 102–107. 8. D. Pei, Information-theoretic bounds for authentication codes and block designs, J. Cryptography 8 (1995), 177–188. 9. S. R. Stinson, Combinatorial characterizations of authentication codes, Designs, Codes and Cryptography 7 (1996), 239–259. 10. U. Rosenbaum, A lower bound on authentication after having observed a sequence of messages, J. Cryptography 6 (1993), 135–156. 11. R, Safavi-Naini and L.

The authentication code of (3) provides at least log2 q n − 1 − 2(q − 1)q n/2 q bits of secrecy protection. Furthermore we have 1 2(q − 1)q n/2 1 2(q − 1)q n/2 − ≤ PI ≤ + n q q(q − 1) q q(q n − 1) and 2(q 2 − 1)q n/2 + q n − 1 −2(q 2 − 1)q n/2 + q n − 1 ≤ PS ≤ n/2 n q[2(q − 1)q + q − 1] q[−2(q − 1)q n/2 + q n − 1] 28 C. Ding et al. Optimality of the Codes We now prove that PI and PS of authentication code (3) meet the lower bound of Lemma 2 asymptotically. In the authentication code of (3), |S| = q n − 1, |M| = q(q n − 1) So the bound on PI given in Lemma 2 is P = Since lim n→∞ 1 .

Download PDF sample

Rated 4.83 of 5 – based on 17 votes
Top