TY  - BOOK
AU  - Kendirli,Barış
ED  - Fatih Üniversitesi.
TI  - Number theory with cryptographic applications
T2  - Fatih University publications
SN  - 975303215
AV  - QA241 .K4613 2006
PY  - 2006///
CY  - İstanbul
PB  - Fatih University
KW  - Number theory
N1  - Includes bibliographical references (pages 521) and index; Contents; 1 Introduction		1; 2 Divisibility Properties of Integers	5; 2.1 The Greatest Common Divisor	10; 2.2 Linear Diophantirıe equations  	16; 2.3 Primes		19; 2.4 Fermat Faetorization	27; 3 Congruences		31; 3.1 Arithmetic Inverse:	36; 3.2 Linear Congruence	39; 3.3 Fermat's Little Theorem	45; 4 Cryptography		54; 4.1 Substitution Ciphers	54; 4.2 Block Ciphers		63; 4.3 Public- Key Cryptography	68; 5 Polynornial Congruences	75; 5.1 Chinese Remainder Theorem	75; 5.2 Solutions of congruences modulo prime power  78; 5.3 Reduction of polynomials    		88; 6 Primitive Roots:		95; 6.1 Existence of primitive root modulo prime		98; 6.2 Translation of muitiplicative problems into additive problems	103; 6.3 Application to Cryptography    		111; 7 Quadratic Polynomial    		113; 7.1 Quadratic Residues    		117; 7.2 The Law of Quadratic Reciprocity (GAUSS)	120; 7.3 Application to Diophantine Equations    		126; 7.4 Jacobi Symbol		129; 8 Arithmetic Functions	134; 8.1 Dirichlet Series		148; 8.2 Euler Products   		152; 9 Some Nonlinear Diophantine Equations	160; 9.1 The Equation x2 + y2 = z2 		161; 9.2 The equation x4+y4=z2	167; 9.3 FERMAT'S Last Theorem and the equation x4+y4=z4 	168; 9.4 The Equation n=x2+y2+z2+w2	169; 10 Continued Fractions:		172; 10.1 Infinite Continued Fractions		182; 10.2 Periodic continued fractions		184; 10.3 Pell's Equation x2 ~ dy2 = n for d > 0	192; 11 Primality Testing and Factoring		199; 11.1 Factorization by Continued Fraction	207; 11.2 Thep-1 Factoring Algorithm(Pollard)	211; 11.3 Rho-Method(Poüard)  		212; 11.4 Factor Base Method		214; 11.5 Quadratic Sieve Method		223; 12 Quadratic Fields		226; 12.1 Gaussian Integers	226; 12.2 General Quadratic Fields	 239; 13 Binary Quadratic Forms	247; 13.1 Connection Between Binary Quadratic Forms and free Z inodules of rank 2 in Quadratic Fields   248; 13.2 The Correspondence between Binary Quadratic Forms and Free Z Modules of rank 2	      252; 13.3 The order of a free Z modüle of rank 2		259; 14 Units in orders		267; 14.1 Determination of Elements of a Free Z Modüle of Rank 2 whose norms are a given rational number		276; 15 Factorization in the Orders of Quadratic Fields    291; 15.1 Properties of Ideals in Od 		299; 16 Product of free % modules of rank 2		315; 16.1 The factorization of prime integers in Q(Vd) 	334; 17 Kronecker Symbol		344; 17.1 Class Number:   		350; 17.2 Application to Diophantine Equations    358; 17.3 More about L functions   		365; 18 More on Binary Quadratic Forms	372; 18.1 The Representation of Integers by Binary Quadratic Forms 	385; 18.2 Operations on binary quadratic forms	394; 18.3 Genus Theory		410; 19 Elliptic Curves		430; 19.1 The Group Structure of an Elliptic Curve	434; 19.2 Rational Points on Elliptic Curves		448; 20 Finite Fields		458; 20.1 Some Maple Applications on Finite Fields	464; 21 Application to Cryptography		471; 21.1 Finite Field Cryptosystems		471; 21.2 Elliptic Curve Cryptosystems		490; 22 TABLES		503
ER  -