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 |