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A Note on Addition Chains and some Related Conjectures

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Abstract

Addition chains are finite increasing sequences of positive integers, useful for the efficient evaluation of powers over rings. Many features of addition chains are considered, and some results related to the still open Scholz- Brauer conjecture are presented.

This work was financially supported in part by the United States Army through its European Research Office, under grant n. DAJA45-86-C-0044.

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References

  1. D. E. Knuth, The Art of Computer Programming, vol. II, Addison-Wesley, Reading Massachusetts, 1981, pp. 441–466.

    MATH  Google Scholar 

  2. A. Borodin, I. Munro, The Computational Complexity of Algebraic and Numeric Problems, American Elsevier Pub., New York, 1975.

    MATH  Google Scholar 

  3. R. Rivest, A. Shamir, L. Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Comm. of ACM, vol. 21, Feb. 1978, pp. 120–126.

    Article  MathSciNet  MATH  Google Scholar 

  4. R.J. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer Academic Pub., Boston, 1987.

    Book  MATH  Google Scholar 

  5. M. Elia, F. Neri, Generation of Pseudorandom Independent Sequences, Proceedings of the IASTED International Symposium MIC ’86, Innsbruck (Austria), Feb. 18–21, 1986, M. H. Hanza ed., Acta Press, pp. 25–28.

    Google Scholar 

  6. A. Chi-Chili Yao, On the Evaluation of Powers, SIAM J. Comput, Vol. 5, No. 1, Mar. 1976, pp. 100–103.

    Article  MathSciNet  Google Scholar 

  7. A. Brauer, Bull. Amer. Math. Soc., 45 (1939), pp. 736–739.

    Article  MathSciNet  Google Scholar 

  8. P. Erdos, Remarks on Number Theory, III: On Addition Chains, Acta Arithm., 6 (1960), pp. 77 - 81.

    Google Scholar 

  9. A. Schonhage, Theoretical Comp. Sci., 1 (1975), pp. 1–12.

    Article  MathSciNet  Google Scholar 

  10. A. Scholz, Jahresbericht der Deutschen Mathematiker-Vereinigung, (II), 47 (1937), pp. 41–42.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Elettronica Politecnico di Torino I, 10129, Torino, Italy

    M. Elia & F. Neri

Authors
  1. M. Elia
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  2. F. Neri
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “La Sapienza”, I-00185, Rome, Italy

    Renato M. Capocelli

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© 1990 Springer-Verlag New York Inc.

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Elia, M., Neri, F. (1990). A Note on Addition Chains and some Related Conjectures. In: Capocelli, R.M. (eds) Sequences. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3352-7_13

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  • DOI: https://doi.org/10.1007/978-1-4612-3352-7_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7977-8

  • Online ISBN: 978-1-4612-3352-7

  • eBook Packages: Springer Book Archive

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