AN EXPLICIT SIEVE BOUND AND SMALL VALUES OF σ(φ(m)) Kevin Ford Abstract. We prove an explicit sieve upper bound based on the large sieve of Montgomery and Vaughan [MV], and apply it to show that σ(φ(m)) > m/39.4 for

Source URL: www.math.uiuc.edu

TELEDYNE MOLECULAR SIEVE FILTER JUDSON TECHNOLOGIES

Source URL: www.judsontechnologies.com

WHEN THE SIEVE WORKS ¨ ANDREW GRANVILLE, DIMITRIS KOUKOULOPOULOS, AND KAISA MATOMAKI Abstract. We are interested in classifying those sets of primes P such that when we sieve out the integers up to x by the primes in P

Source URL: users.utu.fi

SIMPLE ZEROS OF PRIMITIVE DIRICHLET L-FUNCTIONS AND THE ASYMPTOTIC LARGE SIEVE VORRAPAN CHANDEE, YOONBOK LEE, SHENG-CHI LIU, AND MAKSYM RADZIWILL Abstract. Assuming the Generalized Riemann Hypothesis (GRH), we show using

Source URL: math.rutgers.edu

arXiv:1311.4600v2 [math.NT] 20 NovSMALL GAPS BETWEEN PRIMES JAMES MAYNARD Abstract. We introduce a refinement of the GPY sieve method for studying prime k-tuples

Source URL: arxiv.org

Integer Factorization and Computing Discrete Logarithms in Maple Aaron Bradford∗, Michael Monagan∗, Colin Percival∗ , , Department of Mathematics, Simon Fr

Source URL: www.daemonology.net

• Cryptography
• Integer factorization algorithms
• Mathematics
• Abstract algebra
• Quadratic sieve
• General number field sieve
• Prime number
• Safe prime
• Discrete logarithm
• RSA
• Sieve of Atkin
• Quadratic residue

Square Root Algorithms for the Number Field Sieve E. Thom´e1 1 INRIA/CARAMEL, Nancy.

Source URL: www5.rz.rub.de

New Complexity Trade-Offs for the (Multiple) Number Field Sieve Algorithm in Non-Prime Fields Palash Sarkar and Shashank Singh Applied Statistics Unit Indian Statistical Institute

Source URL: eprint.iacr.org

TELEDYNE MOLECULAR SIEVE FILTER JUDSON TECHNOLOGIES

Source URL: www.teledynejudson.com

Rotations and Translations of Number Field Sieve Polynomials Jason E. Gower? CERIAS and Department of Mathematics, Purdue University West Lafayette, IN, USA,

Source URL: www.iacr.org