LEADER 04668nam 2200793Ia 450 001 9910954284503321 005 20250801110410.0 010 $a9781139012843 010 $a1-107-22971-5 010 $a1-280-39333-5 010 $a1-139-22286-4 010 $a9786613571250 010 $a1-139-01284-3 010 $a1-139-21806-9 010 $a1-139-21497-7 010 $a1-139-22458-1 010 $a1-139-22114-0 024 8 $a9786613571250 035 $a(CKB)2670000000177937 035 $a(EBL)866868 035 $a(SSID)ssj0000638367 035 $a(PQKBManifestationID)11354307 035 $a(PQKBTitleCode)TC0000638367 035 $a(PQKBWorkID)10714525 035 $a(PQKB)11257979 035 $a(UkCbUP)CR9781139012843 035 $a(OCoLC)793510851 035 $a(MiAaPQ)EBC866868 035 $a(Au-PeEL)EBL866868 035 $a(CaPaEBR)ebr10559486 035 $a(CaONFJC)MIL357125 035 $z(PPN)261330705 035 $a(PPN)234907878 035 $a(EXLCZ)992670000000177937 100 $a20111012d2012 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe mathematics of public key cryptography /$fSteven D. Galbraith 205 $a1st ed. 210 $aCambridge ;$aNew York $cCambridge University Press$d2012 215 $a1 online resource (xiv, 615 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 1 $a9781107013926 311 1 $a1-107-01392-5 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- Part I. Background -- 2. Basic algorithmic number theory -- 3. Hash functions and MACs -- Part II. Algebraic Groups -- 4. Preliminary remarks on algebraic groups -- 5. Varieties -- 6. Tori, LUC and XTR -- 7. Curves and divisor class groups -- 8. Rational maps on curves and divisors -- 9. Elliptic curves --10. Hyperelliptic curves -- Part III. Exponentiation, Factoring and Discrete Logarithms -- 11. Basic algorithms for algebraic groups -- 12. Primality testing and integer factorisation using algebraic groups --13. Basic discrete logarithm algorithms -- 14. Factoring and discrete logarithms using pseudorandom walks -- 15. Factoring and discrete logarithms in subexponential algorithms -- Part IV. Lattices -- 16. Lattices -- 17. Lattice basis reduction -- 18. Algorithms for the closest and shortest vector problems -- 19. Coppersmith's method and related applications -- Part V. Cryptography Related to Discrete Logarithms -- 20. The Diffie-Hellman problem and cryptographic applications -- 21. The Diffie-Hellman problem -- 22. Digital signatures based on discrete logarithms -- 23. Public key encryption based on discrete logarithms -- Part VI. Cryptography Related to Integer Factorisation -- 24. The RSA and Rabin cryptosystems -- Part VII. Advanced Topics in Elliptic and Hyperelliptic Curves -- 25. Isogenies of elliptic curves -- 26. Pairings on elliptic curves. 330 $aPublic key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more. 606 $aCoding theory 606 $aCryptography$xMathematics 606 $aCriptografia$2thub 606 $aTeoria de la codificació$2thub 608 $aLlibres electrònics$2thub 615 0$aCoding theory. 615 0$aCryptography$xMathematics. 615 7$aCriptografia 615 7$aTeoria de la codificació 676 $a003/.54 686 $aMAT008000$2bisacsh 700 $aGalbraith$b Steven D$0721516 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910954284503321 996 $aThe mathematics of public key cryptography$94412487 997 $aUNINA