Get Algebraic Geometry in Coding Theory and Cryptography PDF

By Harald Niederreiter

ISBN-10: 0691102880

ISBN-13: 9780691102887

This textbook equips graduate scholars and complex undergraduates with the mandatory theoretical instruments for utilising algebraic geometry to details conception, and it covers fundamental functions in coding conception and cryptography. Harald Niederreiter and Chaoping Xing give you the first unique dialogue of the interaction among nonsingular projective curves and algebraic functionality fields over finite fields. This interaction is prime to investigate within the box this present day, but beforehand no different textbook has featured whole proofs of it. Niederreiter and Xing hide classical functions like algebraic-geometry codes and elliptic-curve cryptosystems in addition to fabric no longer handled by means of different books, together with function-field codes, electronic nets, code-based public-key cryptosystems, and frameproof codes. Combining a scientific improvement of concept with a huge choice of real-world purposes, this is often the main finished but obtainable creation to the sector available.Introduces graduate scholars and complex undergraduates to the principles of algebraic geometry for functions to info concept offers the 1st special dialogue of the interaction among projective curves and algebraic functionality fields over finite fields comprises functions to coding conception and cryptography Covers the newest advances in algebraic-geometry codes beneficial properties purposes to cryptography no longer handled in different books

Show description

Read or Download Algebraic Geometry in Coding Theory and Cryptography PDF

Similar cryptography books

Song Y. Yan's Cryptanalytic Attacks on RSA PDF

На английском: RSA is a public-key cryptographic method, and is the main recognized and widely-used cryptographic procedure in todays electronic global. Cryptanalytic assaults on RSA, a qualified ebook, covers just about all significant recognized cryptanalytic assaults and defenses of the RSA cryptographic process and its editions.

Post-Quantum Cryptography by Daniel J. Bernstein (auth.), Daniel J. Bernstein, Johannes PDF

Quantum pcs will holiday brand new most well liked public-key cryptographic platforms, together with RSA, DSA, and ECDSA. This booklet introduces the reader to the following new release of cryptographic algorithms, the platforms that face up to quantum-computer assaults: particularly, post-quantum public-key encryption platforms and post-quantum public-key signature structures.

Henk C.A. van Tilborg's Fundamentals of Cryptology: A Professional Reference and PDF

The security of delicate details opposed to unauthorized entry or fraudulent adjustments has been of major difficulty through the centuries. smooth conversation strategies, utilizing desktops attached via networks, make all information much more susceptible for those threats. additionally, new concerns have arise that weren't appropriate ahead of, e.

Cas Cremers's Operational Semantics and Verification of Security Protocols PDF

Safeguard protocols are time-honored to make sure safe communications over insecure networks, akin to the net or airwaves. those protocols use robust cryptography to avoid intruders from examining or editing the messages. although, utilizing cryptography isn't adequate to make sure their correctness. mixed with their standard small measurement, which implies that you'll simply check their correctness, this usually leads to incorrectly designed protocols.

Additional resources for Algebraic Geometry in Coding Theory and Cryptography

Sample text

1≤i≤n Then b1 = 0 and n bi b1−1 z i = 0. z1 + i=2 By the condition on νP (b1 ), we have bi b1−1 ∈ OP for 2 ≤ i ≤ n. Passing to the residue classes modulo MQ , we get n ρ(bi b1−1 + MP )(z i + MQ ) = 0 + MQ , (z 1 + MQ ) + i=2 a contradiction to the choice of z 1 , . . , z n . 13, the following definition is meaningful. 14. The degree deg(P ) of a place P of F /k is defined to be the degree of the residue class field of P over k. A place of F /k of degree 1 is also called a rational place of F /k.

I) Let Fq n = Fq (β) and let f be the minimal polynomial of β over Fq . We will prove that f is irreducible over F . Suppose that f had a factorization f = gh over F with g and h monic and deg(g) ≥ 1, deg(h) ≥ 1. It is obvious that all roots of g and h are elements of Fq n . Hence, from the fact that the coefficients of a monic polynomial are polynomial expressions of its roots, it follows that g and h are polynomials over Fq n . Thus, all coefficients 28 CHAPTER 1 of g and h are algebraic over Fq .

Pr } ⊂ An is a finite set. Let Pj = (a1j , . . , anj ) for 1 ≤ j ≤ r and put gi = rj =1 (xi − aij ) for 1 ≤ i ≤ n. Then gi ∈ I (V ). Thus, in the coordinate ring k[V ] the monomial xir is a linear combination of 1, xi , . . , xir−1 . This means that the set { ni=1 xiei : 0 ≤ ei ≤ r − 1} generates the whole vector space k[V ]. This implies that k[V ] has a finite k-dimension. The following theorem provides an algebraic characterization of the dimension of an affine algebraic set. 2 for background on the Krull dimension of rings.

Download PDF sample

Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter


by James
4.4

Rated 4.54 of 5 – based on 16 votes