Diophantine m-tuples and Elliptic Curves

Extensions of a Diophantine triple by adjoining smaller elements II

An elliptic curve over Q(u) with torsion Z/4Z and rank 6

High-rank elliptic curves with given torsion group and some applications

On power values of pyramidal numbers, II,

Absolute root separation

Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields

On elliptic curves induced by rational Diophantine quadruples

Stjepan Bohniček (December 15, 1872 - March 14, 1956)

Extensions of a Diophantine triple by adjoining smaller elements

Construction of high rank elliptic curves

Number Theory

Rational Diophantine sextuples containing two regular quadruples and one regular quintuple

Diophantine triples with largest two elements in common

Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z

D(n)-quintuples with square elements

Diophantine m-tuples in finite fields and modular forms

Lie Groups, Number Theory, and Vertex Algebras

Triples, quadruples and quintuples which are D(n)- sets for several n's

Strong rational Diophantine D(q)-triples

Doubly regular Diophantine quadruples

Diophantine quadruples with the properties D(n1) and D(n2)

Rank zero elliptic curves induced by rational Diophantine triples

High rank elliptic curves induced by rational Diophantine triples

D(n)-sets with square elements

Products of factorials which are powers,

Number Theory

Triples and quadruples which are D(n)-sets for several n's

Elliptic curves induced by Diophantine triples

On fundamental units of real quadratic fields of class number 1

A Pellian equation with primes and applications to D(-1)-quadruples

On the largest element in D(n)-quadruples

Rational Diophantine sextuples with square denominators

Triples which are D(n)-sets for several n's

Strong Eulerian triples

On Diophantine m-tuples and D(n)-sets

More on Diophantine sextuples

Absolute real root separation

There are infinitely many rational Diophantine sextuples

Applications of continued fractions in factorization and primality testing

Root separation for reducible monic polynomials of odd degree

On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields

Triples which are D(n)-sets for several n's

Polynomial root separation

Absolute real root separation

Generating Elliptic Curves Using the Complex Multiplication Method

There are infinitely many rational Diophantine sextuples

Cryptanalysis of RSA and Its Variants

On rational Diophantine sextuples

Number theory and cryptography

Rational Diophantine sextuples

Transcendental numbers

Stream Cipher RC4

What is ... a Diophantine m-tuple?

Quadratic Residues and Square Roots in Public Key Cryptography

Finiteness results for F-Diophantine sets

Differential cryptanalysis

Number theory and cryptography

Elliptic curves with torsion group Z/6Z

Diophantine quadruples in finite fields and modular forms

There are infinitely many rational Diophantine sextuples

The rank and generators of Kihara's elliptic curve with torsion Z/4Z over Q(t)

The non-extensibility of D (-2k+ 1)-triples {;;1, k^ 2, k^ 2+ 2k-1};;

High-rank elliptic curves induced by Diophantine triples

Block Cipher Modes of Operation

NTRU Cryptosystem

Number theory and cryptography

Transposition Ciphers ADFGX and ADFGVX

The 2nd Department of Mathematical, Physical and Chemical Sciences

Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z

Some Diophantine properties of the sequence of S-units

High rank elliptic curves with torsion Z/2Z × Z/4Z induced by Diophantine triples

Ranks of elliptic curves with prescribed torsion over number fields

High rank elliptic curves with prescribed torsion group over quadratic fields

Diophantine Problems With Sums of Divisors

Mordell-Weil Groups and Isogenies of the Families of Elliptic Curves

Root separation for integer polynomials

Mordell-Weil groups of elliptic curves induced by Diophantine triples

Root separation for integer polynomials

Root separation for integer polynomials

Products of three factorials

On the torsion group of elliptic curves induced by D(4)-triples

Diophantine m-tuples with elements in arithmetic progressions

Root separation for reducible integer polynomials

On quadratic twists of elliptic curves y^2=x(x-1)(x-lambda)

On the high rank π/3 and 2π/3 - congruent number elliptic curves

Elliptic curves coming from Heron tringles

Stream ciphers

Applications of Elliptic Curves in Cryptography

Arithmetic progressions and Pellian equations

Elliptic curves and triangles with three rational medians

Sumsets being squares

Geometric approach to continued fractions

Diffie-Hellman Problem and Discrete Logarithm Problem

Indefinite binary quadratic forms

On the existence of rational Diophantine quintuples with the property D(q)

On the size of sets in a polynomial variant of a problem of Diophantus

On the rank of elliptic curves coming from rational Diophantine triples

Finite field and polynomial congruences

On a conjecture regarding balancing with powers of Fibonacci numbers

On Hall's conjecture

On Hall's conjecture and related polynomial Pell's equation

On a problem of Diophantus for rationals

Polynomial root separation and applications

On power values of pyramidal numbers

On the sum of two divisors of (n^2 + 1)/2

Some Diophantine Problems over the Imaginary Quadratic Fields

LLL Algorithm and Some Applications to Cryptography

Internet Security

On a variation of a congruence of Subbarao

Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

Root separation for reducible monic quartics

Elliptic curves of large rank over quadratic fields

Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

Solving a family of quartic Thue inequalities using continued fractions

Some Diophantine triples and quadruples for quadratic polynomials

On Hall's conjecture

Root separation for irreducible integer polynomials

Mordell-Weil groups of elliptic curves over number fields of small degree

On the size of sets whose elements have perfect power n-shifted products

Root separation for reducible monic quartics

Continued fraction convergents and Newton's approximants for quadratic irrationalities

Ranks of families of elliptic curves and applications to Diophantine problems

Diophantine quadruples in Z[√ -2]

Polynomial Variants of a Problem of Diophantus

Cryptography in the Second World War

Smart Card Security in Banking

Sieve Methods

Elliptic Curves over Finite Fields

Compact Representation of Quadratic Integers and Integer Points on Elliptic Curves

Quadratic Fields and Quadratic Forms

On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z

Diophantine m-tuples

Elliptic curves

High rank elliptic curves induced by Diophantine triples and congruent numbers

On the size of sets in a polynomial variant of a problem of Diophantus

Rational Diophantine sextuples with mixed signs

A search for high rank congruent number elliptic curves

Security of Micropayment Systems

Distribution of Prime Numbers

Generating Random Numbers

Technologies for E-Commerce

Smart Cards

Perfect Numbers

Micropayments

Fermat Numbers

Strong Diophantine triples

Elliptic equations

Heights in Diophantine Geometry and Consequences of the abc-conjecture

Digital Cash and Digital Checks

Periodic Continued Fractions

A variant of Wiener's attack on RSA

A problem of Diophantus, Fermat and Euler and its generalizations

Conjectures and results on the size and number of Diophantine tuples

On the number of Diophantine m-tuples

Security of Bank Systems

Cryptography in School

Public Key Infrastructure

Public Key Cryptography

Factorization and ideals

Cryptosystems with Public Key

Solving Congruences

Cryptography in school

Mestre's Polynomial Method for Construction of High-rank Elliptic Curves

Digital Signature Authentication

RSA Cryptosystem

A polynomial variant of a problem of Diophantus for pure powers

On arithmetic progressions on Pellian equations

Polygraphic Substitution Ciphers

Pell Equation and Pythagorean Triples

On Worley's theorem in Diophantine approximations

Strong Diophantine triples

A variant of Wiener's attack on RSA

Applications of Continued Fractions in Diophantine Approximations and Cryptanalysis

Strong Diophantine triples

Convex Sets

A variant of Wiener's attack on RSA with small secret exponent

Mordell-Weil groups of elliptic curves induced by Diophantine triples

Decomposition of a recursive family of polynomials

Principles of Design of Modern Block Cryptosystems

On the family of Diophantine triples {;k-1, k+1, 16k^3-4k};

On differences of two squares in some quadratic fields

Construction of high rank elliptic curves and related Diophantine problems

Effective solution of the D(-1)-quadruple conjecture

Diophantine m-tuples and generalizations

On Mordell-Weil groups of elliptic curves induced by Diophantine triples

On a problem of Diophantus with polynomials

Primitive Roots and Quadratic Residues

ENIGMA

Representation of Primes by Quadratic Forms

Security of Electronic Commerce

Euclidean Algorithm

Distribution of Quadratic Residues

Complex continued fractions

Cryptography

Error-correcting Codes and McEliece Cryptosystem

Digital Watermarking

Diophantine Equations over Function Fields

Systems of Pellian Equations and the Problem of Extension of Some Diophantine Triples

Transposition Ciphers

Markov Chain

PGP - Pretty Good Privacy

Steganography: Hiding Information in Images

Elliptic Curves and Elliptic Functions

Algebraic Numbers

Diophantine m-tuples for linear polynomials. II. Equal degrees

Indecomposability of polynomials and related Diophantine equations

Modern Block Ciphers

High rank elliptic curves with prescribed torsion group

Algorithms for Large-Integer Multiplications

Methods for computing the rank of elliptic curves over Q(T)

On the D(-1)-quadruple conjecture

Roth's Theorem

Digital Signature and Digital Money

Diophantine m-tuples for primes

Arithmetic Functions

On the indecomposabilty of polynomials

Steganography

Complete solution of a problem of Diophantus and Euler

Internet Security and SSL Protocol

Square roots with many good approximants

Diophantine m-tuples

Diophantine m-tuples and connections with eliptic curves

Asymptotic estimates for the number of Diophantine m-tuples

Fibonacci numbers and sets with the property D(4)

Discrete logarithm problem for elliptic curves

Topological Convex Structures

Diophantine quadruples in quadratic fields

Vigenere Cipher

History of Cryptography

A family of quartic Thue inequalities

Mathematical Basis of Public-Key Cryptography

Application of LLL-algorithm in solving Diophantine equations

There are only finitely many Diophantine quintuples

Newton's approximants and continued fractions

Shannon's Theory

Complete solution of the polynomial version of a problem of Diophantus

Continued fractions and RSA with small secret exponent

On a problem of Diophantus and Euler

RC6 Cryptosystem

Monoalphabetic Substitution Ciphers

Bounds for the size of sets with the property D(n)

Mordell-Weil theorem

Continued Fractions and Their Applications

Fermat's Little Theorem and Its Consequences

Construction of elliptic curves over Q with large rank

Continued fractions and RSA with small secret exponent

Mersenne Numbers and Perfect Numbers

Primality Testing

A polynomial variant of a problem of Diophantus and Euler

Knapsack Problem and Applications in Cryptography

On a problem of Diophantus for higher powers

On Diophantine quintuple conjecture

Kneser's Theorem

Congruent numbers and elliptic curves

Modular functions and complex multiplication of elliptic curves

Mordell's theorem

DES Cryptosystem

Zero-knowledge Proofs

Congruences of Integers and Polynomials

Statistical Properties of Arithmetic Functions

An example of elliptic curve over Q with rank equal to 15

A parametric family of quartic Thue equations

On the size of Diophantine m-tuples

Hash Functions in Cryptography

Discrete Logarithm Problem

An interesting property of a recurrence related to the Fibonacci sequence

Polyalphabetic Ciphers

Construction of high-rank elliptic curves with non-trivial torsion group

Primality Tests

Fibonacci Numbers and the Golden Section

Diffie-Hellman Key Distribution Protocol

Diophantine m-tuples for linear polynomials

An extension of an old problem of Diophantus and Euler. II

Newton's formula and continued fraction expansion of sqrt(d)

Twoparametric family of quartic Thue equations

Diophantine m-tuples and elliptic curves

An absolute bound for the size of Diophantine m-tuples

Pierre de Fermat (1601.-1665.)

Diophantine equations for second order recursive sequences of polynomials

Diophantine triples and construction of high-rank elliptic curves over Q with three non-trivial 2-torsion points

A parametric family of elliptic curves

Integer points on a family of elliptic curves

Irregular Diophantine m-tuples and elliptic curves of high rank

A note on Diophantine quintuples

The Fibonacci numbers

A proof of the Hoggatt-Bergum conjecture

A bijective proof of Riordan's theorem on powers of Fibonacci numbers

An extension of an old problem of Diophantus and Euler

A generalization of a theorem of Baker and Davenport

Some estimates of the number of Diophantine quadruples

On the exceptional set in the problem of Diophantus and Davenport

Complete solution of a family of simultaneous Pellian equations

A problem of Diophantus and Pell numbers

Diophantine quadruples and quintuples modulo 4

A problem of Diophantus and Dickson's conjecture

The problem of Diophantus and Davenport for Gaussian integers

The problem of Diophantus and Davenport

On Diophantine quintuples

The problem of the extension of a parametric family of Diophantine triples

Complete solutions of certain families of simultaneous Pellian equations

Generalized Fibonacci numbers and the problem of Diophantus

Mathematical competitions of high-school students

Some polynomial formulas for Diophantine quadruples

Diophantine quadruples for squares of Fibonacci and Lucas numbers

Generalization of a problem of Diophantus