Abstract
This chapter contains some topics from combinatorics, cryptology and recurring sequences. The material is mainly selected to give a brief indication of some further applications of algebraic concepts, mainly groups and fields, to areas such as the design of experiments, transmission of secret information or communication with satellites. The selected areas and examples of further applications form only a sample. We refer the interested reader to the special literature on these topics, and also to the notes at the end of the chapter. Some additional references on other topics of applications of abstract algebra are given at the end of the bibliography.
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References
Aigner, M. Combinatorial Theory. Springer-Verlag, Berlin-Heidelberg-New York, 1979.
Berman, G. and Fryer, K. D. Introduction to Combinatorics. Academic Press, New York, 1972.
Bogart, K. P. Introductory Combinatorics, Pitman, Boston, 1983.
Cochran, W. G. and Cox, G. M. Experimental Designs. Wiley, New York, 1957.
Denes, J. and Keedwell, A. D. Latin Squares and Their Applications, English Universities Press, London, 1974.
Hall, M. Combinatorial Theory. Blaisdell, Waltham, Mass., 1967.
Hirschfeld, J. W. P. Projective Geometries over Finite Fields. Clarendon Press, Oxford, 1979.
Horadam, A. F. A Guide to Undergraduate Projective Geometry. Pergamon Press (Australia), Rushcutters Bay, 1970.
Hughes, D. R. and Piper, F. C. Projective Planes. Springer-Verlag, New York-Heidelberg-Berlin, 1973.
Mann, H. B. Analysis and Design of Experiments. Dover, New York, 1949.
Pilz, G. Near-Rings, 2nd ed. North-Holland, Amsterdam, 1983.
Raghavarao, D. Constructions and Combinatorial Problems in Design of Experiments. Wiley, New York, 1971.
Ryser, H. J. Combinatorial Mathematics. Mathematical Association of America, New York, 1963.
Vajda, S. The Mathematics of Experimental Design. Hafner, New York, 1967.
Vilenkin, N. Ya. Combinatorics. Academic Press, New York-London, 1971.
Wallis, W. D., Street, A. P. and Wallis, J. S. Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Lecture Notes in Mathematics, 292. Springer-Verlag, Berlin-Heidelberg-New York, 1972.
Welsh, D. J. A. Combinatorial Mathematics and Its Applications. Academic Press, London-New York, 1971.
Wilson, R. J. (ed.) Applications of Combinatorics. Shiva, Nantwich, England; Birkhäuser, Boston-Cambridge, Mass., 1982.
Beker, H. and Piper, F. Cipher Systems, The Protection of Communications. Northwood Books, London, 1982.
Beth, T., Hess, P. and Wirl, K. Kryptographie. B. G. Teubner, Stuttgart, 1983.
Brawley, J. V. and LevinEj, J. Involutory commutants with some applications to algebraic cryptography, I. J. reine angew. Math., 224 (1966), 20–43.
Brawley, J. V. and Levine2, J. Some cryptographic applications of permutation polynomials. Cryptologia, 1 (1977), 76–92.
Davies, D. W., Price, W. L. and Parkin, G. I. An evaluation of public key cryptosystems. NPL Report CTU 1, April 1980.
Deavours, C. A. The Ithaca connection: computer cryptography in the making. Cryptologia, 1 (1977), 312–317.
Denning, D. E. R. Cryptography and Data Security. Addison-Wesley, Reading, Mass., 1983.
Diffie, W. and Hellman, M. E. New directions in cryptography. IEEE Trans. Inf. Theor., 22 (1976), 644–684.
Diffie, W. and Hellman, M. E. Privacy and authentication—an introduction to cryptography. Proc. IEEE, 67 (1979), 397–427.
Galland, J. E. Historical and Analytical Bibliography of the Literature of Cryptology. American Mathematical Society, Providence, R.I., 1970.
Gardner, M. A new kind of cipher that would take millions of years to break. Sci. Amer., 237 (1977), 120–124.
Hellman, M. E. The mathematics of public-key cryptography. Sci. Amer., 241 (1979), 130–139.
Hillj, L. S. Cryptography in an algebraic alphabet. Amer. Math. Mon., 36 (1929), 306–312.
Hill, L. S. Concerning certain linear transformation apparatus of cryptography. Amer. Math. Mon., 38 (1931), 135–154.
Kahn, D. The Codebreakers. Weidenfeld & Nicholson, London, 1967.
Konheim, A. G. Cryptography, A Primer. Wiley, New York, 1981.
Leiss, E. L. Principles of Data Security. Plenum, New York, 1982.
Levine, J. Variable matrix substitution in algebraic cryptology. Amer. Math. Mon., 65 (1958), 170–179.
Merkle, R. C. Secure communications over insecure channels. Commun. ACM, 21 (1978), 294–299.
Merkle, R. C. Secrecy, Authentication, and Public Key Systems. UMI Research Press, Ann Arbor, Mich., 1982.
Myer, C. H. and Matyas, S. M. Cryptography: A New Dimension in Computer Data Security. Wiley, New York, 1982.
Price, W. L. A fourth annotated bibliography of recent publications on data security and cryptography. NPL Report DNACS 33/1980.
Rivest, R., Shamir, A. and Adleman, L. A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM, 21 (1978), 120–126.
Simmons, G. J. Cryptology, the mathematics of secure communication. Math. Intel, 1 (1979), 233–246.
Sinkov, A. Elementary Cryptanalysis, a Mathematical Approach. Random House, New York, 1978.
Sloane, N. J. A. Error-correcting codes and cryptography. In The Mathematical Gardner (D. A. Klarner, ed. ), pp. 346–382.
Prindle, Weber and Schmidt, Boston, 1981.
Stillwell, J. The two faces of coding theory. Function, 4 (1980), 8–15.
Ash, R. Information Theory. Wiley-Interscience, New York, 1965.
Dickson, L. E. History of the Theory of Numbers, 3 vols. Carnegie Institute, Washington, D.C., 1919, 1920, 1923.
Golombi, S. W. Shift Register Sequences. Holden-Day, San Francisco, 1967.
Golomb, S. W. (ed.). Digital Communications with Space Applications. Prentice-Hall, Englewood Cliffs, N.J., 1964.
Lidl, R. and Niederreiter, H. Finite Fields. Addison-Wesley, Reading, Mass., 1983.
Lin, S. An Introduction to Error-Correcting Codes. Prentice-Hall, Englewood Cliffs, N.J., 1970.
Lüneburg, H. Galoisfelder, Kreisteilungskörper und Schieberegisterfolgen. Bibliographisches Institut, Mannheim, 1979.
Mann, H. B. (ed.). Error Correcting Codes. Wiley, New York, 1968.
Selmer, E. S. Linear Recurrence Relations over Finite Fields. University of Bergen, Bergen, 1966.
Zierler, N. Linear recurring sequences. J. SIAM, 7 (1959), 31 - 48.
Aho, A. V., Hopcroft, J. E. and Ullman, J. D. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.
Borodin, A. and Munro, I. The Computational Complexity of Algebraic and Numeric Algorithms. Elsevier, New York, 1975.
Knuth, D. E. The Art of Computer Programming, vol. 2, 2nd ed. Addison-Wesley, Reading, Mass., 1981.
Lipson, J. D. Elements of Algebra and Algebraic Computing. Addison-Wesley, Reading, Mass., 1981.
Liu, C. L. Introduction to Combinatorial Mathematics. McGraw-Hill, New York, 1968.
Szabo, N. S. and Tanaka, R. I. Residue Arithmetic and Its Applications to Computer Technology. McGraw-Hill, New York, 1967.
De Bruijn, N. G. Polya’s theory of counting. In Applied Combinatorial Mathematics (E. F. Beckenbach, ed.), Ch. 5. Robert E. Krieger, Malabar, Florida, 1981.
Stone, H. S. Discrete Mathematical Structures and Their Applications. Scientific Research Association, Chicago, 1973.
Tucker, A. Applied Combinatorics. Wiley, New York, 1980.
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Lidl, R., Pilz, G. (1984). Further Applications of Fields and Groups. In: Applied Abstract Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-6465-2_5
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DOI: https://doi.org/10.1007/978-1-4615-6465-2_5
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