LEADER 03512nam 22006495 450 001 9911003695103321 005 20251212134144.0 010 $a3-031-82626-4 024 7 $a10.1007/978-3-031-82626-9 035 $a(CKB)38859021100041 035 $a(MiAaPQ)EBC32125988 035 $a(Au-PeEL)EBL32125988 035 $a(DE-He213)978-3-031-82626-9 035 $a(EXLCZ)9938859021100041 100 $a20250520d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebra for Applications $eCryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression /$fby Arkadii Slinko 205 $a3rd ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (686 pages) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 311 08$a3-031-82625-6 327 $aIntegers -- Cryptology -- Groups -- Fields -- Polynomials -- Secret Sharing -- Error-Correcting Codes -- Compression -- Appendix A: GAP -- Appendix B: Miscellanea -- Solutions to Exercises -- Index. 330 $aThis textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study. This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version. 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aAlgebra 606 $aComputer science$xMathematics 606 $aDiscrete mathematics 606 $aAlgebra 606 $aMathematical Applications in Computer Science 606 $aDiscrete Mathematics 606 $aĀlgebra$2thub 606 $aMatemātica discreta$2thub 606 $aInformātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aAlgebra. 615 0$aComputer science$xMathematics. 615 0$aDiscrete mathematics. 615 14$aAlgebra. 615 24$aMathematical Applications in Computer Science. 615 24$aDiscrete Mathematics. 615 7$aĀlgebra 615 7$aMatemātica discreta 615 7$aInformātica 676 $a004.01512 700 $aSlinko$b A. M$g(Arkadii M.)$0734115 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911003695103321 996 $aAlgebra for applications$91522741 997 $aUNINA