000			03977cam a2200325 i 4500
001			18345
005			20260202142823.0
008			070723s2006 tu a b 001 0 eng d
020			_a975303215 _qpbk.
035			_a(OCoLC)
040			_aBAUN _beng _cBAUN _erda
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA241 _b.K4613 2006
100	1		_aKendirli, Barış. _989776 _eaut
245	1	0	_aNumber theory with cryptographic applications / _cby Barış Kendirli.
264		1	_aİstanbul : _bFatih University, _c2006.
300			_avolume, 525 pages ; _c28 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aFatih University publications ; _v21
504			_aIncludes bibliographical references (pages 521) and index.
505	0	0	_tContents _t1 Introduction 1 _t2 Divisibility Properties of Integers 5 _t2.1 The Greatest Common Divisor 10 _t2.2 Linear Diophantirıe equations 16 _t2.3 Primes 19 _t2.4 Fermat Faetorization 27 _t3 Congruences 31 _t3.1 Arithmetic Inverse: 36 _t3.2 Linear Congruence 39 _t3.3 Fermat's Little Theorem 45 _t4 Cryptography 54 _t4.1 Substitution Ciphers 54 _t4.2 Block Ciphers 63 _t4.3 Public- Key Cryptography 68 _t5 Polynornial Congruences 75 _t5.1 Chinese Remainder Theorem 75 _t5.2 Solutions of congruences modulo prime power 78 _t5.3 Reduction of polynomials 88 _t6 Primitive Roots: 95 _t6.1 Existence of primitive root modulo prime 98 _t6.2 Translation of muitiplicative problems into additive problems 103 _t6.3 Application to Cryptography 111 _t7 Quadratic Polynomial 113 _t7.1 Quadratic Residues 117 _t7.2 The Law of Quadratic Reciprocity (GAUSS) 120 _t7.3 Application to Diophantine Equations 126 _t7.4 Jacobi Symbol 129 _t8 Arithmetic Functions 134 _t8.1 Dirichlet Series 148 _t8.2 Euler Products 152 _t9 Some Nonlinear Diophantine Equations 160 _t9.1 The Equation x2 + y2 = z2 161 _t9.2 The equation x4+y4=z2 167 _t9.3 FERMAT'S Last Theorem and the equation x4+y4=z4 168 _t9.4 The Equation n=x2+y2+z2+w2 169 _t10 Continued Fractions: 172 _t10.1 Infinite Continued Fractions 182 _t10.2 Periodic continued fractions 184 _t10.3 Pell's Equation x2 ~ dy2 = n for d > 0 192 _t11 Primality Testing and Factoring 199 _t11.1 Factorization by Continued Fraction 207 _t11.2 Thep-1 Factoring Algorithm(Pollard) 211 _t11.3 Rho-Method(Poüard) 212 _t11.4 Factor Base Method 214 _t11.5 Quadratic Sieve Method 223 _t12 Quadratic Fields 226 _t12.1 Gaussian Integers 226 _t12.2 General Quadratic Fields 239 _t13 Binary Quadratic Forms 247 _t13.1 Connection Between Binary Quadratic Forms and free Z inodules of rank 2 in Quadratic Fields 248 _t13.2 The Correspondence between Binary Quadratic Forms and Free Z Modules of rank 2 252 _t13.3 The order of a free Z modüle of rank 2 259 _t14 Units in orders 267 _t14.1 Determination of Elements of a Free Z Modüle of Rank 2 whose norms are a given rational number 276 _t15 Factorization in the Orders of Quadratic Fields 291 _t15.1 Properties of Ideals in Od 299 _t16 Product of free % modules of rank 2 315 _t16.1 The factorization of prime integers in Q(Vd) 334 _t17 Kronecker Symbol 344 _t17.1 Class Number: 350 _t17.2 Application to Diophantine Equations 358 _t17.3 More about L functions 365 _t18 More on Binary Quadratic Forms 372 _t18.1 The Representation of Integers by Binary Quadratic Forms 385 _t18.2 Operations on binary quadratic forms 394 _t18.3 Genus Theory 410 _t19 Elliptic Curves 430 _t19.1 The Group Structure of an Elliptic Curve 434 _t19.2 Rational Points on Elliptic Curves 448 _t20 Finite Fields 458 _t20.1 Some Maple Applications on Finite Fields 464 _t21 Application to Cryptography 471 _t21.1 Finite Field Cryptosystems 471 _t21.2 Elliptic Curve Cryptosystems 490 _t22 TABLES 503
650		0	_aNumber theory. _914928
710	2		_9109674 _aFatih Üniversitesi.
830		0	_9109673 _aFatih Üniversitesi yayınları ; _v21.
900			_bbağış
942			_2lcc _cKT
999			_c15743 _d15743