Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter

By Harald Niederreiter

This textbook equips graduate scholars and complicated undergraduates with the mandatory theoretical instruments for utilizing algebraic geometry to info concept, and it covers fundamental purposes in coding concept and cryptography. Harald Niederreiter and Chaoping Xing give you the first special dialogue of the interaction among nonsingular projective curves and algebraic functionality fields over finite fields. This interaction is key to investigate within the box this present day, but beforehand no different textbook has featured entire proofs of it. Niederreiter and Xing conceal classical purposes like algebraic-geometry codes and elliptic-curve cryptosystems in addition to fabric now not taken care of via 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 vast number of real-world functions, this is often the main finished but obtainable creation to the sphere available.

  • Introduces graduate scholars and complicated undergraduates to the principles of algebraic geometry for functions to info idea
  • Provides the 1st distinct dialogue of the interaction among projective curves and algebraic functionality fields over finite fields
  • Includes functions to coding concept and cryptography
  • Covers the most recent advances in algebraic-geometry codes
  • Features functions to cryptography no longer handled in different books

Show description

Read or Download Algebraic Geometry in Coding Theory and Cryptography PDF

Similar cryptography books

Contemporary Cryptology (Advanced Courses in Mathematics - CRM Barcelona)

The purpose of this article is to regard chosen themes of the topic of up to date cryptology, dependent in 5 particularly self sustaining yet comparable issues: effective allotted computation modulo a shared mystery, multiparty computation, smooth cryptography, provable defense for public key schemes, and effective and safe public-key cryptosystems.

Advanced Statistical Steganalysis (Information Security and Cryptography)

Steganography is the artwork and technology of hiding details in inconspicuous hide information in order that even the life of a mystery message is stored private, and steganalysis is the duty of detecting mystery messages in covers. This learn monograph specializes in the function of canopy indications, the distinguishing function that calls for us to regard steganography and steganalysis in a different way from different secrecy suggestions.

The Information Security Dictionary: Defining the Terms that Define Security for E-Business, Internet, Information and Wireless Technology (The ... Series in Engineering and Computer Science)

Whatever for everybody If this ebook is to be successful and aid readers, its cardinal advantage needs to be to supply an easy reference textual content. it's going to be a necessary addition to a data safeguard library. As such it may additionally serve the aim of being a brief refresher for phrases the reader has no longer obvious because the days whilst one attended a computing technology software, details safeguard path or workshop.

Additional resources for Algebraic Geometry in Coding Theory and Cryptography

Example text

Bn z n ) are all distinct, and so the strict triangle inequality yields n ν = min ν(bi z i ) < ∞, bi z i 1≤i≤n i=1 which is again a contradiction. In the above proof, we have shown, in particular, that the restriction of a valuation of F /k to k(x) yields a valuation of k(x). Obviously, for equivalent valuations of F the restrictions are again equivalent. Thus, a place Q of F corresponds by restriction to a unique place P of k(x). We say that Q lies over P or that P lies under Q. Therefore, every place of F lies either over a place of k(x) corresponding to a monic irreducible polynomial in k[x] or over the infinite place of k(x).

7, |{σ (P ) : σ ∈ Gal(Fq /Fq )}| = |{σ (P ) : σ ∈ Gal(Fq m /Fq )}| ≤ |Gal(Fq m /Fq )| = m. This completes the proof. We define the degree of an Fq -closed point P to be the cardinality of P, denoted by deg(P). For a point P = [a0 , a1 , . . , an ] ∈ Pn with ai = 0, the definition field of P over k, denoted by k(P ), is defined by k(a0 /ai , a1 /ai , . . , an /ai ). 10. (i) The definition field of a point is well defined. First of all, if (b0 , b1 , . . , bn ) = (λa0 , λa1 , . . , λan ) with λ = 0, we have bj /bi = aj /ai for all j = 0, 1, .

Define the map θi : Ui → An , [a0 , a1 , . . , ai ai ai ai . 2) It is clear that θi is well defined and bijective. 1). Via θi , the space An can be viewed as an open subset of Pn . We claim that the map θi is a homeomorphism from Ui (with its induced Zariski topology from Pn ) onto An (with the Zariski topology). It suffices to check this for i = 0. Indeed, let V = Zh (S) ⊆ U0 be an algebraic set of Pn . Then it is easy to verify that θ0 (V ) = Z({f (1, y1 , . . , yn ) : f (x0 , x1 , . . , xn ) ∈ S homogeneous}).

Download PDF sample

Rated 4.84 of 5 – based on 13 votes