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Algebraic Cryptology from an Historical Viewpoint

Algebraic Cryptology from an Historical Viewpoint. Chris Christensen Northern Kentucky University. Cryptology. Cryptography. Cryptanalysis. Algebraic cryptology. Cryptography Polynomials Finite rings and fields Cryptanalysis Solving systems of multivariate polynomial equations.

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Algebraic Cryptology from an Historical Viewpoint

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  1. Algebraic Cryptology from an Historical Viewpoint Chris Christensen Northern Kentucky University

  2. Cryptology Cryptography Cryptanalysis

  3. Algebraic cryptology Cryptography Polynomials Finite rings and fields Cryptanalysis Solving systems of multivariate polynomial equations

  4. Julius Caesar (100 – 44 BC)

  5. A. A. Albert (1905 – 1972) … we shall see that cryptography is more than a subject permitting mathematical formulation, for indeed it would not be an exaggeration to state that abstract cryptography is identical with abstract mathematics. November 22, 1941

  6. Lester S. Hill (1891 – 1961) Monthly articles: • “Cryptography in an algebraic alphabet.” 1929. • “Concerning certain linear transformations apparatus of cryptography.” 1931.

  7. Hill’s cipher

  8. Hill’s cipher is algebraic

  9. 1986 Fell-Diffie “Analysis of a public key approach based upon polynomial substitution”

  10. Algebraic cryptography • 1983 Matsumoto and Imai • 1999 Tzuong-TsiengMoh Multivariate Public Key Cryptosystems, Ding, Gower, and Schmidt.

  11. Claude Shannon (1916 – 2001) Thus if we could show that solving a certain [crypt0]system requires as least as much work as solving a system of simultaneous equations in a large number of unknowns, of a complex type, then we would have a lower bound of sorts for [its security]. 1949

  12. Hill cipher, again

  13. Algebraic cryptanalysis • 1965 Bruno Buchberger, Grobner basis • 1999 and 2002 Jean-Charles Faugere, F4 and F5 • 1999 Kipnis and Shamir, XL • 2006 Ding, mutant XL Algebraic Cryptanalysis, Gregory V. Bard

  14. LN WQ JW

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