Essays about: "Pollard’s Rho"

Found 4 essays containing the words Pollard’s Rho.

  1. 1. Integer factorization algorithms

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Joakim Nilsson; [2020]
    Keywords : ;

    Abstract : The mathematical area of integer factorization has gone a long way since the early days of Pierre de Fermat, and with simpler algorithms developed in the last century such as the Trial division and Pollards rho algorithm to the more complex method of the Quadratic sieve algorithm (QS), we have now arrived at the General Number Field Sieve (GNFS) which has been recognized as the fastest integer factorization algorithm for very large numbers. Today the research of integer factorization has many applications, among others in the security systems of encryption methods like the famous RSA algorithm. READ MORE

  3. 2. On Pollard's rho method for solving the elliptic curve discrete logarithm problem

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Jenny Falk; [2019]
    Keywords : elliptic curves; Pollard s rho method; elliptic curve discrete logarithm problem; cryptography; adding walk; mixed walk; cycle-detecting algorithm; iterating function; random walk;

    Abstract :     Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem. Pollard's rho method is regarded as the best method for attacking the logarithm problem to date, yet it is still not efficient enough to break an elliptic curve cryptosystem. READ MORE

  4. 3. Pollard's rho method

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Ida Bucic; [2019]
    Keywords : Number theory; Factorization; Floyd s cycle finding algorithm;

    Abstract : In this work we are going to investigate a factorization method that was invented by John Pollard. It makes possible to factorize medium large integers into a product of prime numbers. We will run a C++ program and test how do different parameters affect the results. READ MORE

  5. 4. Modelling the Number of Periodic Points of Quadratic Maps Using Random Maps

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Jakob Streipel; [2017]
    Keywords : arithmetic dynamical systems; periodic points; quadratic maps; random maps;

    Abstract : Since the introduction of Pollard's rho method for integer factorisation in 1975 there has been great interest in understanding the dynamics of quadratic maps over finite fields. One avenue for this, and indeed the heuristic on which Pollard bases the proof of the method's efficacy, is the idea that quadratic maps behave roughly like random maps. READ MORE