Secure Key Transfer Protocol Using Goldbach Sequences

Cryptography has been most successfully deployed in protocols where a client-server relationship exists, such as Secure Socket Layer(SSL) and Transport Layer security(TSL). A data can be encrypted using an encryption algorithm along with a public key. This encrypted data could be read by the node which has the private key of this encrypted data which can decrypt the message. A signature is formed together with a message digest and a private key. It makes it impossible to detect the message digest given a key and also it would be impossible to detect the key given a message digest. Other variations are given in [13],[14].In this thesis we consider a new way to develop a key distribution protocol using the standard Goldbach conjecture and its constrained forms. According to this conjecture any even number can be represented as a sum of two prime numbers. We have looked at random sequences obtained from the count of partitions of different even numbers and we have derived new variant sequences of this partition random sequence. Random sequences can be good candidates for cryptographic keys [15]-[18] and they have other applications in cryptography. When random sequences from different sources are used, their independence may be checked by a cross correlation analysis [19]-[21].Goldbach partitions will be shown to have excellent cross correlation properties. We also present the use of Goldbach partitions for a key exchange protocol.Computer Scienc

Correspondence of Leonhard Euler with Christian Goldbach

When Leonhard Euler first arrived at the Russian Academy of Sciences, at the age of 20, his career was supported and promoted by the Academy’s secretary, the Prussian jurist and amateur mathematician Christian Goldbach (1690-1764). Their encounter would grow into a lifelong friendship, as evinced by nearly 200 letters sent over 35 years. This exchange – Euler’s most substantial long-term correspondence – has now been edited for the first time with an English translation, ample commentary and documentary indices. These present an overview of 18th-century number theory, its sources and repercussions, many details of the protagonists’ biographies, and a wealth of insights into academic life in St. Petersburg and Berlin between 1725 and 1765. Part I includes an introduction and the original texts of the Euler-Goldbach letters, while Part II presents the English translations and documentary indices

A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic

In the ?rst section of this opening chapter we review two different proofs of the PythagoreanTheorem,oneduetoEuclidandtheotheroneduetoaformerpresident oftheUnitedStates,JamesGar?eld.Inthesamesectionwealsoreviewsomehigher dimensional analogues of the Pythagorean Theorem. Later in the chapter we de?ne Pythagorean triples; explain what it means for a Pythagorean triple to be primitive; and clarify the relationship between Pythagorean triples and points with rational coordinates on the unit circle. At the end we list the problems that we will be interested in studying in the book. In the notes at the end of the chapter we talk about Pythagoreans and their, sometimes strange, beliefs. We will also brie?y review the history of Pythagorean triples

Topics in analytic number theory

We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average nonvanishing of Dirichlet L-functions at the central point. Finally, in joint work with Siegfred Baluyot, we build on work of Soundararajan and synthesize our studies of primes and L-functions by examining Dirichlet L-functions of quadratic characters of prime conductor