Summatory functions of digital sums occurring in cryptography

Periodica Mathematica Hungarica

Volumn 38, Issue 1-2, 1999, Pages 111-130

  Thuswaldner, Jörg M ^a  

^a UNIVERSITY OF LEOBEN   (Austria)

Author keywords

Cryptosystem; Digital sum; Dirichlet series

Indexed keywords

EID: 0004730216     PISSN: 00315303     EISSN: 15882829     Source Type: Journal    
DOI: 10.1023/a:1004715619287     Document Type: Article

References (17)

1. P. FLAJOLET, M. REGNIER and R. SEDGEWICK, Some uses of the Mellin integral transform in the analysis of algorithms, in: Combinatorial algorithms on words, 241-254, A. Apostolico and Z. Galil, 12, ASI Series. Series F: Computer and Systems Sciences, Springer, Berlin, 1985.
2. H. MÜLLER, Über Werte polynomialer Dirichlet-Reihen im Nullpunkt, Arch. Math. 66 (1996), 30-34.
3. D. E. KNUTH, The Art of Computer Programming, Vol 2: Seminumerical Algorithms, Addison Wesley, London, 1981.
4. H. MÜLLER., Über die Meromorphe Fortsetzung einer Klasse verallgemeinerter Zeta-funktionen, Arch. Math. 58 (1992), 265-275.
5. F. MORAIN and J. OLIVOS, Speeding up the Computations on an Elliptic Curve Using Addition-Subtraction Chains, Inform Theory Appl 24 (1990), 531-543.
6. H. MÜLLER. On Generalized Zeta-Functions at Negative Integers, Illinois J. Math. 32 (1988), 222-229.
7. H. DELANGE, Sur la fonction sommatoire de la fonction "Somme des Chiffres", Enseign. Math. 21 (1975), 31-47.
8. R. RIVEST, A. SHAMIR and L. M. ADLEMAN, A Method for Obtaining Digital Signatures and Public Key Cryptosystems, Communications of the ACM 21 (1978), 120-126
9. P. FLAJOLET, P. J. GRABNER, P. KIRSCHENHOFER, H. PRODINGER and R. F. TICHY, Mellin Transform and Asymptotics: Digital Sums, Theoret. Comput. Sci 123 (1994), 291-314
10. W. DIFFLE and M. E. HELLMAN, New Directions in Cryptography, IEEE Trans. Inform. Theory 22 1976, 644-654.
11. D. M. GORDON, A Survey of Fast Exponentiation Methods, J. Algorithms 27 (1998), 129-146.
12. E. C. TITCHMARSH, The Theory of Functions, 2nd. ed., Oxford University Press, London, 1975.
13. P. J. GRABNER. and J. M. THUSWALDNER, Analytic Continouation of a Class of Dirichlet Series, Abh. d. Math. Sem. Univ. Hamburg 66 (1996), 241-247.
14. E. T. WHITTAKER and G. N. WATSON, A Course in Modern Analysis, Cambridge University Press, Cambridge, 1927.
15. P. ERDOS, Remarks on Number Theory. III: Addition Chains, Acta Arith. 6 (1960), 77-81.
16. J. L. MAUCLAIRE and L. MURATA, On q-additive functions. I, Proc. Jap. Acad., Ser. A 59 (1983), 274-276.
17. J. L. MAUCLAIRE and L. MURATA, On q-additive functions. II, Proc. Jap. Acad., Ser. A 59 (1983), 441-444.