 Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| Introduction |
| BACKGROUND |
| BACKGROUND |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Basic algorithmic number theory |
| Hash functions and MACs |
| Hash functions and MACs |
| Hash functions and MACs |
| Hash functions and MACs |
| Hash functions and MACs |
| ALGEBRAIC GROUPS |
| ALGEBRAIC GROUPS |
| Preliminary remarks on algebraic groups |
| Preliminary remarks on algebraic groups |
| Preliminary remarks on algebraic groups |
| Preliminary remarks on algebraic groups |
| Preliminary remarks on algebraic groups |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Varieties |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Tori, LUC and XTR |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Curves and divisor class groups |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Rational maps on curves and divisors |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Elliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| Hyperelliptic curves |
| EXPONENTIATION, FACTORING AND DISCRETE LOGARITHMS |
| EXPONENTIATION, FACTORING AND DISCRETE LOGARITHMS |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Basic algorithms for algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Primality testing and integer factorisation using algebraic groups |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Basic discrete logarithm algorithms |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms using pseudorandom walks |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| Factoring and discrete logarithms in subexponential time |
| LATTICES |
| LATTICES |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattices |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Lattice basis reduction |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Algorithms for the closest and shortest vector problems |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| Coppersmith’s method and related applications |
| CRYPTOGRAPHY RELATED TO DISCRETE LOGARITHMS |
| CRYPTOGRAPHY RELATED TO DISCRETE LOGARITHMS |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem and cryptographic applications |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| The Diffie–Hellman problem |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Digital signatures based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| Public key encryption based on discrete logarithms |
| CRYPTOGRAPHY RELATED TO INTEGER FACTORISATION |
| CRYPTOGRAPHY RELATED TO INTEGER FACTORISATION |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| The RSA and Rabin cryptosystems |
| ADVANCED TOPICS IN ELLIPTIC AND HYPERELLIPTIC CURVES |
| ADVANCED TOPICS IN ELLIPTIC AND HYPERELLIPTIC CURVES |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Isogenies of elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Pairings on elliptic curves |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| Background mathematics |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |
| References |