LEADER 03781nam 22005655 450 001 996418186403316 005 20200704113335.0 010 $a3-030-44074-5 024 7 $a10.1007/978-3-030-44074-9 035 $a(CKB)5280000000218457 035 $a(MiAaPQ)EBC6215573 035 $a(DE-He213)978-3-030-44074-9 035 $a(PPN)248595792 035 $a(EXLCZ)995280000000218457 100 $a20200601d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebra for Applications$b[electronic resource] $eCryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression /$fby Arkadii Slinko 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (376 pages) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 $a3-030-44073-7 327 $a1 Integers -- 2 Cryptology -- 3 Groups -- 4 Fields -- 5 Polynomials -- 6 Secret Sharing -- 7 Error-Correcting Codes -- 8 Compression -- Appendix A: GAP -- Appendix B: Miscellanea -- Solutions to Exercises -- Index. 330 $aModern societies are awash with data that needs to be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorised access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory and can only be properly understood with a good knowledge of these fields. This textbook provides the mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Designed for an undergraduate lecture course, this textbook provides all of the background in arithmetic, polynomials, groups, fields, and elliptic curves that is required to understand real-life applications such as cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. It explains in detail how these applications really work. The book uses the free GAP computational package, allowing the reader to develop intuition about computationally hard problems and giving insights into how computational complexity can be used to protect the integrity of data. The first undergraduate textbook to cover such a wide range of applications, including some recent developments, this second edition has been thoroughly revised with the addition of new topics and exercises. Based on a one semester lecture course given to third year undergraduates, it is primarily intended for use as a textbook, while numerous worked examples and solved exercises also make it suitable for self-study. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aAlgebra 606 $aInformation theory 606 $aDiscrete mathematics 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aInformation and Communication, Circuits$3https://scigraph.springernature.com/ontologies/product-market-codes/M13038 606 $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000 615 0$aAlgebra. 615 0$aInformation theory. 615 0$aDiscrete mathematics. 615 14$aAlgebra. 615 24$aInformation and Communication, Circuits. 615 24$aDiscrete Mathematics. 676 $a512.9 700 $aSlinko$b Arkadii$4aut$4http://id.loc.gov/vocabulary/relators/aut$0734115 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418186403316 996 $aAlgebra for applications$91522741 997 $aUNISA