Public Key Cryptography: Number Theory

• Algebraic Number Theory Archives
• www.mersenne.org
• Primes
  • Prime Number (Definition from mathworld)
  • The Prime Page
  • 48565...29443 (First known illegal prime)
• Sloane's On-Line Encyclopedia of Integer Sequences (Neil Sloane)
• Books
  • Reciprocity Laws
  • Suitable books (not only) for high-schoolers (?)
    • Number Theory and its History (Oystein Ore (Dover))
    • The Higher Arithmetic (Harold Davenport)
    • A Friendly Introduction to Number Theory (Joe Silverman)
    • Elementary Number Theory and Its Applications ( Kenneth Rosen)
• Journal of Number Theory
• @Factoring
• @Primality tests
• Finding solutions to polynomials
  • Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities ( Don Coppersmith, JoC 1997)
• Finite fields
  • Introductions
    • ABSTRACT ALGEBRA ON LINE: finite fields
    • Introduction to Finite Fields (Bill Cherowitzo)
    • Course 373 (% Finite Fields)
    • PascGalois Triangles & Hexagons and other Group-related Cellular Automata (Kathleen M. Shannon & Michael J. Bardzell)
  • Algorithms
    • Fast Arithmetic Operations over $F_{2^n}$ for Software Implementation (Kazumaro Aoki, Kazuo Ohta, SAC 97)
    • Algorithms for exponentiation in finite fields (Gao, von zur Gathen, Shoup, Panario, 1999)
• Software
  • GNU GMP
  • Pari GP
  • GMP (GNU Multiprecision)
  • MAGMA
    • Magma for Cryptographic Applications (Scott Contini)
  • LiDIA
  • FFTW
  • KANT/KASH
• Lecture Notes and Courses
  • Introduction to Analytic Number Theory (Noam Elkies, 1998)
  • An Introduction to Analytic Number Theory (Ilan Vardi)
  • Number Theory and its Applications (HUT)
• Theses
  • On the Difficulty of Prime Root Computation in Certain Finite Cyclic Groups (Anna M. Johnston, Royal Holloway, PhD thesis, 2006)
• Archives of NMBRTHRY@LISTSERV.NODAK.EDU
• Implementation techniques
  • Fast multiplication
    • Montgomery multiplication
      • Explanation
        (Paul Crowley)
• Workshops (not complete)
  • Extensions of Hilbert's Tenth Problem (21-25.03.2005, Palo Alto, CA, USA)
• Does the proof of the Riemann hypothesis really bring the whole e-commerce to its knees? (UCL Crypto)

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Cryptology Pointers by Helger Lipmaa
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(C) Helger Lipmaa 1997-2009.