Abstract
Differential uniformity is an important property of cryptographic building blocks used in the design of symmetric ciphers. In this paper it is proved that certain canonical mappings on elliptic curves are differentially uniform. The main observation of this paper is that the impersonation attack against the implicit certificate scheme of Ateniese and de Medeiros does not work if a differentially uniform mapping is used in the scheme. This phenomenon is analyzed in the slightly more general context of a partially blind signature scheme, which is a new cryptographic primitive that seems to gain security properties from differentially uniform mappings.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rijmen, V., Daemen, J.: The Design of Rijndael. AES – The Advanced Encryption Standard. Springer, Heidelberg (2002)
Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, Springer, Heidelberg (1994)
Granboulan, L., Levieil, É., Piret, G.: Pseudorandom permutation families over abelian groups. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 57–77. Springer, Heidelberg (2006)
Ateniese, G., de Medeiros, B.: A provably secure Nyberg-Rueppel signature variant with applications. Cryptology ePrint Archive, Report 2004/093 (2004), http://eprint.iacr.org/2004/093
Nyberg, K., Rueppel, R.A.: A new signature scheme based on the DSA giving message recovery. In: CCS 1993. Proceedings of the 1st ACM conference on Computer and communications security, pp. 58–61. ACM Press, New York (1993)
Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)
Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48, 203–209 (1987)
FIPS: Digital signature standard (DSS). FIPS PUB 186-2 (+ Change Notice). Technical report, U.S. DEPARTMENT OF COMMERCE/National Institute of Standards and Technology (January 2000)
Brown, D.R.L., Gallant, R., Vanstone, S.A.: Provably secure implicit certificate schemes. In: Syverson, P.F. (ed.) FC 2001. LNCS, vol. 2339, pp. 147–156. Springer, Heidelberg (2002)
Pintsov, L.A., Vanstone, S.A.: Postal revenue collection in the digital age. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 105–120. Springer, Heidelberg (2001)
Granboulan, L.: PECDSA. how to build a dl-based digital signature scheme with the best proven security. NESSIE Technical Report NES/DOC/ENS/WP5/022/1 (2002), http://eprint.iacr.org/2002/172
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brumley, B.B., Nyberg, K. (2007). Differential Properties of Elliptic Curves and Blind Signatures. In: Garay, J.A., Lenstra, A.K., Mambo, M., Peralta, R. (eds) Information Security. ISC 2007. Lecture Notes in Computer Science, vol 4779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75496-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-75496-1_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75495-4
Online ISBN: 978-3-540-75496-1
eBook Packages: Computer ScienceComputer Science (R0)