Download PDF by San Ling: Algebraic Curves in Cryptography

Combinatorics

By San Ling

ISBN-10: 1420079468

ISBN-13: 9781420079463

The succeed in of algebraic curves in cryptography is going some distance past elliptic curve or public key cryptography but those different software components haven't been systematically coated within the literature. Addressing this hole, Algebraic Curves in Cryptography explores the wealthy makes use of of algebraic curves in various cryptographic functions, comparable to mystery sharing, frameproof codes, and broadcast encryption.

Suitable for researchers and graduate scholars in arithmetic and laptop technological know-how, this self-contained ebook is among the first to target many subject matters in cryptography concerning algebraic curves. After providing the mandatory historical past on algebraic curves, the authors talk about error-correcting codes, together with algebraic geometry codes, and supply an advent to elliptic curves. every one bankruptcy within the rest of the e-book bargains with a specific subject in cryptography (other than elliptic curve cryptography). the subjects lined contain mystery sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters start with introductory fabric ahead of that includes the applying of algebraic curves.

Show description

Read or Download Algebraic Curves in Cryptography PDF

Best combinatorics books

Maurice Frechet's Initiation to Combinatorial Topology (The Prindle, Weber & PDF

An ordinary textual content that may be understood through an individual with a heritage in highschool geometry, this article makes a speciality of the issues inherent to coloring maps, homeomorphism, functions of Descartes' theorem, and topological polygons. concerns of the topological category of closed surfaces hide common operations, use of standard different types of polyhedra, extra.

Read e-book online Discrete Mathematics with Ducks PDF

Containing routines and fabrics that have interaction scholars in any respect degrees, Discrete arithmetic with geese provides a gradual creation for college students who locate the proofs and abstractions of arithmetic demanding. This classroom-tested textual content makes use of discrete arithmetic because the context for introducing proofwriting.

Download e-book for kindle: Buildings and Schubert schemes by Carlos Contou-Carrere

The 1st a part of this e-book introduces the Schubert Cells and types of the final linear team Gl (k^(r+1)) over a box okay in accordance with Ehresmann geometric manner. soft resolutions for those forms are developed by way of Flag Configurations in k^(r+1) given via linear graphs known as minimum Galleries.

Additional resources for Algebraic Curves in Cryptography

Example text

1(i). 1(i). It is smooth and hence its genus is (3 − 1)(3 − 2)/2 = 1. Thus, for any k ≥ 1 and Fq rational point P , we have dimFq (L(kP )) = k + 1 − 1 = k. 1(ii). 7(iii) is smooth. Hence, its genus is (r + 1 − 1)(r + 1 − 2)/2 = r(r − 1)/2. 1(ii). 10(v). 3]). , X is an elliptic curve, then X is smooth and hence its genus is (3 − 1)(3 − 2)/2 = 1. Next, we generalize the Riemann-Roch spaces defined above. Let X be a smooth curve over Fq . A divisor is a formal sum P ∈X nP P , with nP ∈ Z for all P ∈ X , and nP = 0 for all but finitely many points P ∈ X .

As |wi | = r, we must have wi = −r for all 1 ≤ i ≤ 2g. Finally, we conclude that the zeta function of H is ZH (t) = (1 + rt)r(r−1) . (1 − t)(1 − r2 t) In particular, N2 = (r2 )2 + 1 − 2g(−r)2 = r3 + 1 = N1 . This implies that all the Fr4 -rational points are also Fr2 -rational. 20 Algebraic Curves in Cryptography For an algebraic curve X , we denote by N (X ) the number of Fq -rational points on X . By the Hasse-Weil bound, we know that the number of Fq rational points on a curve is upper bounded in terms of q and its genus.

15]) The Hamming code Ham(m, q) is a [(q m −1)/(q−1), (q m − 1)/(q − 1) − m, 3]-code. 16 The dual of the q-ary Hamming code Ham(m, q) is called a q-ary simplex code. It is sometimes denoted by S(m, q). The next bound, the Singleton bound, is an interesting one that is related to the well-known Reed-Solomon codes. 1]) For any integer q > 1, any positive integer n and any integer d such that 1 ≤ d ≤ n, we have Aq (n, d) ≤ q n−d+1 . In particular, when q is a prime power, the parameters [n, k, d] of any linear code over Fq satisfy k + d ≤ n + 1.

Download PDF sample

Algebraic Curves in Cryptography by San Ling


by John
4.1

Rated 4.42 of 5 – based on 35 votes