# Uniform complexity and digital signatures

Session 16: S. Even, Chairman

First Online:

## Abstract

A concept of uniform complexity is defined and a class of functions is shown to have uniform complexity. A special case of these results is used to develop a new digital signature method, which makes forging signatures as hard as factoring a large number and which allows to sign all messages directly. The signature production involves only one exponentiation modulo a large number and the signature checking the comparison of a fourth and a second power modulo a large number. Therefore this new method is faster than known methods with the same degree of safety.

## Keywords

Chinese Remainder Theorem Quadratic Residue Signature Method Uniformity Result Nontrivial Factor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Download
to read the full conference paper text

## References

- Adleman1977a.L. Adleman and K. Manders, “Reducibility, Randomness and Intractability,”
*Proc. 9th Annual ACM Symposium on Theory of Computing*, pp.151–163 (1977).Google Scholar - Babai1979a.L. Babai, “Monte Carlo algorithms in graph isomorphism testing,”
*Submitted to SIAM J. on Computing*(1979).Google Scholar - Berlekamp1970a.E.R. Berlekamp, “Factoring Polynomials Over Large Finite Fields,”
*Mathematics of Computation***24**(111), pp.713–735 (July 1970).Google Scholar - Diffie1976a.W. Diffie and M. Hellman, “New Directions in Cryptography,”
*IEEE Transactions on Information Theory***IT-22**(6), pp.644–654 (Nov. 1976).Google Scholar - Gill1974a.J. Gill, “Computational Complexity of Probabilistic Turing Machines,”
*Proc. 6th Annual ACM Symposium on Theory of Computing*, pp. 91–95 (1974).Google Scholar - Ireland1972a.K. Ireland and M. Rosen,
*Elements of Number Theory*, Bogden and Quigley, New York (1972).Google Scholar - Knuth1969a.D.E. Knuth,
*The Art of Computer Programming*, Addison-Wesley, Reading, Mass. (1969). Vol. 2Google Scholar - Legendre1798a.A.M. Legendre,
*Theorie des Nombres*, Issuer unknown, Paris (1798).Google Scholar - Lehmer1969a.D. Lehmer, “Computer Technology Applied to the Theory of Numbers,” pp. 117–151 in
*Studies in Number Theory*, Mathematics Association of America (1969).Google Scholar - Lempel1979a.A. Lempel, “Cryptology in Transition,”
*ACM Computing Surveys***11**(4), pp.285–304 (Dec. 1979).Google Scholar - Merkle1978a.R. Merkle and M.E. Hellman, “Hiding Information and Receipts in Trapdoor Knapsacks,”
*IEEE Trans. Inform. Theory IT-24*(Sept. 1978).Google Scholar - Popek1979a.G.J. Popek and C.S. Kline, “Encryption and Secure Computer Networks,”
*ACM computing surveys***11**(4), pp.331–356 (Dec. 1979).Google Scholar - Rabin1977a.M.O. Rabin, “Complexity of Computations,”
*Communications of the ACM***20**, pp.625–633 (1977).Google Scholar - Rabin1978a.M.O. Rabin, “Digitalized Signatures,” in
*Foundations of Secure Computation*, ed. Demillo et al., Academic Press (1978).Google Scholar - Rabin1979a.M. O. Rabin, “Digitalized Signatures and Public-Key Functions as Intractable as Factorization,”
*MIT/LCS/TR-212*, Massachusetts Institute of Technology, Laboratory for Computer Science. (Jan. 1979).Google Scholar - Rabin1980a.M.O. Rabin, “Probabilistic Algorithms in Finite Fields,”
*Siam J. Comput.***9**(2), pp.273–280 (May 1980).Google Scholar - Rivest1978a.R.L. Rivest, A. Shamir, and L. Adleman, “A Method for Obtaining Digital Signatures and Publick-Key Cryptosystems,”
*Comm. ACM***21**(2), pp.120–126 (Feb. 1978).Google Scholar - Saltzer1978a.J. Saltzer, “On digital signatures,”
*ACM Operating Syst. Rev.***12**(2), pp.12–14 (Apr. 1978).Google Scholar - Shamir1978a.A. Shamir, “A Fast Signature Scheme,”
*MIT/LCS/TM-107*(July 1978).Google Scholar - Shamir1979a.A. Shamir, “On the Cryptocomplexity of Knapsack Systems,”
*Proc. 11th Annual ACM Symposium on Theory of Computing*, pp.118–129 (1979).Google Scholar - Shanks1972a.D. Shanks, “Five Number Theoretic Algorithms,”
*Second Manitoba Conference on Numerical Mathematics*, pp.51–70 (1972).Google Scholar - Simmons1979a.G.J. Simmons, “Symmetric and Asymmetric Encryption,”
*ACM Computing Surves*(4), pp.305–330 (Dec. 1979).Google Scholar - Williams1979a.H.C. Williams and B. Schmid, “Some Remarks Concerning The MIT Public-Key Cryptosystem,”
*BIT***19**, pp. 528–538 (1979).Google Scholar - Williams1979b.H.C. Williams, “A modification of the RSA public-key encryption procedure,”
*Report 92*,*Department of Computer Science, University of Manitoba, Winnipeg, Canada*(1979).Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1981