05143nam0 22008413i 450 VAN0024864320260914022333.197N9783030440749127746339820220726d2020 |0itac50 baengCH|||| |||||i e bcrAlgebra for applicationscryptography, secret sharing, error-correcting, fingerprinting, compressionArkadii Slinko2. edChamSpringer20201 testo elettronico (xiv, 368 p.ill.)Modern societies are awash with data that needs to be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorised access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory and can only be properly understood with a good knowledge of these fields. This textbook provides the mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Designed for an undergraduate lecture course, this textbook provides all of the background in arithmetic, polynomials, groups, fields, and elliptic curves that is required to understand real-life applications such as cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. It explains in detail how these applications really work. The book uses the free GAP computational package, allowing the reader to develop intuition about computationallyhard problems and giving insights into how computational complexity can be used to protect the integrity of data [...]. (Estratto dal sito dell'editore)001VAN000294432001 Springer undergraduate mathematics series210 Berlin [etc.]Springer1998-VAN00234845Algebra for applications152274111A05Multiplicative structure; Euclidean algorithm; greatest common divisors [MSC 2020]VANC023952MF11A51Factorization; primality [MSC 2020]VANC023242MF11C08Polynomials in number theory [MSC 2020]VANC022428MF11C20Matrices, determinants in number theory [MSC 2020]VANC033735MF11T06Polynomials over finite fields [MSC 2020]VANC022071MF11T71 Algebraic coding theory; cryptography [MSC 2020]VANC020456MF11Y05Factorization [MSC 2020]VANC021737MF11Y11Primality [MSC 2020]VANC021730MF11Y16Number-theoretic algorithms; complexity [MSC 2020]VANC021420MF12E20Finite fields (field-theoretic aspects) [MSC 2020]VANC026983MF14G50Applications to coding theory and cryptography of algebraic geometry [MSC 2020]VANC020731MF14H52Elliptic curves [MSC 2020]VANC021174MF20A05Axiomatics and elementary properties of groups [MSC 2020]VANC033736MF20B30Symmetric groups [MSC 2020]VANC029251MF68P25Data encryption [MSC 2020]VANC021877MF68P30Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [MSC 2020]VANC019979MF94A60Cryptography [MSC 2020]VANC019699MF94A62Authentication, digital signatures and secret sharing [MSC 2020]VANC024292MFBCH CodeKW:KDiffie-HellmanKW:KDigital signatureKW:KElgamal CryptosystemKW:KError-Correcting CodesKW:KEuler Totient FunctionKW:KFingerprinting CodesKW:KFitingof Compression CodeKW:KHuffman compression codeKW:KIdeal secret sharing schemeKW:KLagrange InterpolationKW:KLinear Secret Sharing SchemeKW:KMiller-Rabin Pseudoprimality TestKW:KPrefix CodesKW:KPrimality TestingKW:KPublic key cryptographyKW:KRSA CryptosystemKW:KReed-Solomon CodesKW:KSecret key cryptographyKW:KShamir’s Secret Sharing SchemeKW:KCHChamVANL001889SlinkoArkadiiVANV087802734115Springer <editore>VANV108073650Slinko, A.Slinko, ArkadiiVANV276787ITSOL20260918RICAhttp://doi.org/10.1007/978-3-030-44074-9E-book – Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o ShibbolethBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICAIT-CE0120VAN08NVAN00248643BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08DLOAD e-book 4544 08eMF4544 20220726 Algebra for applications1522741UNICAMPANIA