Abstract
A batch proof and verification technique by Chida and Yamamoto is extended to work in a more general scenario. The new batch proof and verification technique is more useful and can save more cost than the original technique. An application of the new batch proof and verification technique is range proof, which proves that a secret integer is in an interval range. Like the most resent and advanced range proof protocol by Camenisch, Chaabouni and Shelat in Asiacrypt2008, the new range proof technique is especially suitable for practical small ranges, but more efficient and stronger in security than the former. The new range proof technique is very efficient and more efficient than the existing solutions in practical small ranges. Moreover, it achieves stronger security and stronger privacy (perfect honest-verifier zero knowledge) than most of the existing range proof schemes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abe, M., Suzuki, K.: M+1-st price auction using homomorphic encryption. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 115–124. Springer, Heidelberg (2002)
Aditya, R., Peng, K., Boyd, C., Dawson, E.: Batch verification for equality of discrete logarithms and threshold decryptions. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 494–508. Springer, Heidelberg (2004)
Bellare, M., Garay, J.A., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)
Boudot, F.: Efficient proofs that a committed number lies in an interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)
Camenisch, J., Chaabouni, R., Shelat, A.: Efficient protocols for set membership and range proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234–252. Springer, Heidelberg (2008)
Chaabouni, R., Lipmaa, H., Shelat, A.: Additive combinatorics and discrete logarithm based range protocols (2009), http://eprint.iacr.org/2009/469
Chida, K., Yamamoto, G.: Batch processing for proofs of partial knowledge and its applications. IEICE Trans. Fundamentals E91CA(1), 150–159 (2008)
Chida, K., Kobayashi, K., Morita, H.: Efficient sealed-bid auctions for massive numbers of bidders with lump comparison. In: Davida, G.I., Frankel, Y. (eds.) ISC 2001. LNCS, vol. 2200, pp. 408–419. Springer, Heidelberg (2001)
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)
Fujisaki, E., Okamoto, T.: Statistical zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997)
Gennaro, R., Leigh, D., Sundaram, R., Yerazunis, W.S.: Batching schnorr identification scheme with applications to privacy-preserving authorization and low-bandwidth communication devices. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 276–292. Springer, Heidelberg (2004)
Groth, J.: Non-interactive zero-knowledge arguments for voting. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 467–482. Springer, Heidelberg (2005)
Kikuchi, H.: (m+1)st-price auction. In: Syverson, P.F. (ed.) FC 2001. LNCS, vol. 2339, p. 341. Springer, Heidelberg (2002)
Lee, B., Kim, K.: Receipt-free electronic voting scheme with a tamper-resistant randomizer. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 389–406. Springer, Heidelberg (2003)
Lipmaa, H.: On diophantine complexity and statistical zero-knowledge arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003)
Omote, K., Miyaji, A.: A second-price sealed-bid auction with the discriminant of the p-th root. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357, pp. 57–71. Springer, Heidelberg (2003)
Peng, K., Bao, F.: Batch zk proof and verification of or logic. In: Yung, M., Liu, P., Lin, D. (eds.) Inscrypt 2008. LNCS, vol. 5487, pp. 141–156. Springer, Heidelberg (2009)
Peng, K., Boyd, C.: Batch zero knowledge proof and verification and its applications. ACM TISSEC 10(2), Article No. 6 (May 2007)
Schnorr, C.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peng, K., Bao, F. (2010). Batch Range Proof for Practical Small Ranges. In: Bernstein, D.J., Lange, T. (eds) Progress in Cryptology – AFRICACRYPT 2010. AFRICACRYPT 2010. Lecture Notes in Computer Science, vol 6055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12678-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-12678-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12677-2
Online ISBN: 978-3-642-12678-9
eBook Packages: Computer ScienceComputer Science (R0)