Abstract
In Eurocrypt’98 [1], Okamoto et al. exhibited a new trapdoor function based on the use of a special moduli (p2q) allowing easy discrete logarithm computations. The authors proved that the scheme’s resistance to chosen-plaintext attacks is equivalent to factoring n. Unfortunately, the proposed scheme suffers from not being a permutation (the expansion rate is ~ 3), and hence cannot be used for public-key signatures. In this paper, we show how to refine the function into a trapdoor permutation that can be used for signatures. Interestingly, our variant still remains equivalent to factoring and seems to be the second known trap-door permutation (Rabin-Williams’ scheme [3] being the first) provably as secure as a primitive problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
T. Okamoto and S. Uchiyama, A New Public-Key Cryptosystem as secure as Factoring, LNCS 1403, Advances in Cryptology, Proceedings of Eurocrypt’98, Springer-Verlag, pp. 308–318, 1998.
W. Diffie and M. Hellman, New Directions in Cryptography, IEEE Transaction on Information Theory, IT-22,6, pp. 644–654, 1995.
M. Rabin, Digitalized Signatures and Public-Key Functions as Intractable as Factorization, Technical Report No. 212, MIT Laboratory of Computer Science, Cambridge, pp. 1–16, 1979.
L. Goubin and J. Patarin, Trapdoor One-Way Permutations and Multivariate Polynomials, Proceedings of ICICS’97, LNCS 1334, Springer-Verlag, pp 356–368, 1997.
E. Okamoto and R. Peralta, Faster Factoring of Integers of a Special Form, IEICE Trans. Fundamentals, Vol. E79-A, No 4, pp 489–493, 1996.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Paillier, P. (1999). A Trapdoor Permutation Equivalent to Factoring. In: Public Key Cryptography. PKC 1999. Lecture Notes in Computer Science, vol 1560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49162-7_17
Download citation
DOI: https://doi.org/10.1007/3-540-49162-7_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65644-9
Online ISBN: 978-3-540-49162-0
eBook Packages: Springer Book Archive