Abstract
We propose new schemes for Certificates of Recoverability (CRs). These consist of a user’s public key and attributes, its private key encrypted in such a way that it is recoverable by one or more Key Recovery Agents (KRAs), plus a publicly verifiable proof of this (the actual CR). In the original schemes, the level of cryptographic security employed by the KRA and the users is necessarily the same. In our schemes the level of cryptographic security employed by the KRA can be set higher, in a scalable fashion, than that being employed by the users. Among the other improvements of our schemes are its applicability to create CRs for cryptosystems based on the Discrete Log problem in small subgroups, most notably the Digital Signature Standard and Elliptic Curve Crypto systems. Also, the size of the constructed proofs of knowledge can be taken smaller than in the original schemes. We additionally show several ways to support secret sharing in our scheme. Finally we present several new constructions and results on the hardness of “small parts”, in the setting of Diffie-Hellman keys in extension fields.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Adleman, M., DeMarrais, J.: A subexponentional algorithm over all finite fields. In: CRYPTO 1993 Proc., pp. 147–158. Springer, Heidelberg (1993)
Asokan, N., Shoup, V., Waidner, M.: Optimistic Fair Exchange of Digital Signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 591–606. Springer, Heidelberg (1998)
Bellare, M., Rogaway, P.: Random Oracles are Practical: A paradigm for Designing Efficient Protocols. In: 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)
Boneh, D., Venkatesan, R.: Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 129–142. Springer, Heidelberg (1996)
Brouwer, A.E., Pellikaan, R., Verheul, E.R.: Doing More with Fewer Bits. In: Asiacrypt 1999 Proc. Springer, Heidelberg (1999)
Coppersmith, D.: Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. on IT 30, 587–594 (1984)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. on IT 22, 644–654 (1976)
ElGamal, T.: A Public Key Cryptosystem and a Signature scheme Based on Discrete Logarithms. IEEE Trans. on IT 31(4), 469–472 (1985)
Fiat, A., Shamir, A.: How to prove yourselve: Practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Gordon, D.M.: Discrete Logarithms in GF(p) using the number field sieve. SIAM J. of Discrete Math. 6, 124–138
Håstad, J.: On Using RSA with Low Exponent in a Public Key Network. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 403–408. Springer, Heidelberg (1986)
Kilian, J., Leighton, F.T.: Fair Cryptosystems Revisited. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 208–221. Springer, Heidelberg (1995)
Lenstra, A.K.: Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems over Finite Fields. In: Mu, Y., Pieprzyk, J.P., Varadharajan, V. (eds.) ACISP 1997. LNCS, vol. 1270, pp. 127–138. Springer, Heidelberg (1997)
Lenstra, A.K., Verheul, E.R.: Selecting Cryptographic Key Sizes, these proceedings.
Lenstra, H.W.: Finding isomorphisms between two finite fields. Math. of Comp. 56, 329–347 (1991)
Lidl, R., Niederreiter, H.: Finite Fields. Addison-Wesley, Reading (1983)
Pohlig, S.C., Hellman, M.E.: An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Trans. on IT 24, 106–110 (1978)
Pollard, J.M.: Monte Carlo methods for index computation (mod p). Math. of Comp. 32, 918–924 (1978)
Naor, M., Yung, M.: Universal one-way functions and their cryptographic applications. In: 21st Annual ACM Symposium on Theory of Computer Science (1997)
Pedersen, T.P.: Distributed Provers with Applications to Undeniable Signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 221–242. Springer, Heidelberg (1991)
Pedersen, T.P.: A Threshold Cryptosystem Without a Trusted Party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)
Schoenmakers, B.: A Simple Publicly Verifiable Secret Sharing Scheme and Its Application to Electronic Voting. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 148–164. Springer, Heidelberg (1999)
Schnorr, C.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)
Stadler, M.: Publicly Verifiable Secret Sharing. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 190–199. Springer, Heidelberg (1996)
Stadler, M., Piveteau, J.-M., Camenisch, J.: Fair Blind Signatures. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 209–219. Springer, Heidelberg (1995)
Stinson, D.R.: Cryptography: theory and practice. CRC press, Boca Raton (1995)
Young, A., Yung, M.: Auto-Recoverable Auto-Certifiable Cryptosystems. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 16–31. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Verheul, E.R. (2000). Certificates of Recoverability with Scalable Recovery Agent Security. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 2000. Lecture Notes in Computer Science, vol 1751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46588-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-46588-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66967-8
Online ISBN: 978-3-540-46588-1
eBook Packages: Springer Book Archive