Abstract
A proof of a shuffle is a zero-knowledge proof that one list of ciphertexts is a permutation and re-encryption of another list of ciphertexts. We call a shuffle restricted if the permutation is chosen from a public subset of all permutations. In this paper, we introduce a general technique for constructing proofs of shuffles which restrict the permutation to a group that is characterized by a public polynomial. This generalizes previous work by Reiter and Wang [22], and de Hoogh et al. [7].
Our approach also gives a new efficient proof of an unrestricted shuffle that we think is conceptually simpler and allow a simpler analysis than all previous proofs of shuffles.
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References
Abe, M., Imai, H.: Flaws in some robust optimistic mix-nets. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 39–50. Springer, Heidelberg (2003)
Adida, B., Wikström, D.: How to shuffle in public. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 555–574. Springer, Heidelberg (2007)
Adida, B., Wikström, D.: Offline/online mixing. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 484–495. Springer, Heidelberg (2007)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd IEEE Symposium on Foundations of Computer Science (FOCS), pp. 136–145. IEEE Computer Society Press, Los Alamitos (2001); Full version at Cryptology ePrint Archive, Report 2000/067 (October 2001), http://eprint.iacr.org
Chaum, D.: Untraceable electronic mail, return addresses and digital pseudo-nyms. Communications of the ACM 24(2), 84–88 (1981)
Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)
de Hoogh, S., Schoenmakers, B., Skoric, B., Villegas, J.: Verifiable rotation of homomorphic encryptions. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 393–410. Springer, Heidelberg (2009)
El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory 31(4), 469–472 (1985)
Furukawa, J.: Efficient and verifiable shuffling and shuffle-decryption. IEICE Transactions 88-A(1), 172–188 (2005)
Furukawa, J., Miyauchi, H., Mori, K., Obana, S., Sako, K.: An implementation of a universally verifiable electronic voting scheme based on shuffling. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357, pp. 16–30. Springer, Heidelberg (2003)
Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer, Heidelberg (2001)
Furukawa, J., Sako, K.: An efficient publicly verifiable mix-net for long inputs. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 111–125. Springer, Heidelberg (2006)
Groth, J.: A verifiable secret shuffle of homomorphic encryptions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2002)
Groth, J.: Linear algebra with sub-linear zero-knowledge arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192–208. Springer, Heidelberg (2009)
Groth, J., Ishai, Y.: Sub-linear zero-knowledge argument for correctness of a shuffle. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 379–396. Springer, Heidelberg (2008)
Jakobsson, M., Juels, A.: Mix and match: Secure function evaluation via ciphertexts. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 162–177. Springer, Heidelberg (2000)
Neff, A.: A verifiable secret shuffle and its application to e-voting. In: 8th ACM Conference on Computer and Communications Security (CCS), pp. 116–125. ACM Press, New York (2001)
Park, C., Itoh, K., Kurosawa, K.: Efficient anonymous channel and all/nothing election scheme. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 248–259. Springer, Heidelberg (1994)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Pfitzmann, B.: Breaking an efficient anonymous channel. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 332–340. Springer, Heidelberg (1995)
Reistad, T.I., Toft, T.: Secret sharing comparison by transformation and rotation. In: Desmedt, Y. (ed.) ICITS 2007. LNCS, vol. 4883, pp. 169–180. Springer, Heidelberg (2009)
Reiter, M.K., Wang, X.: Fragile mixing. In: 11th ACM Conference on Computer and Communications Security (CCS), pp. 227–235. ACM Press, New York (2004)
Ryan, P.Y.A., Schneider, S.A.: Prêt à voter with re-encryption mixes. In: Gollmann, D., Meier, J., Sabelfeld, A. (eds.) ESORICS 2006. LNCS, vol. 4189, pp. 313–326. Springer, Heidelberg (2006)
Sako, K., Killian, J.: Reciept-free mix-type voting scheme. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 393–403. Springer, Heidelberg (1995)
Wikström, D.: A universally composable mix-net. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 317–335. Springer, Heidelberg (2004)
Wikström, D.: A sender verifiable mix-net and a new proof of a shuffle. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 273–292. Springer, Heidelberg (2005)
Wikström, D.: A commitment-consistent proof of a shuffle. In: Boyd, C., González Nieto, J. (eds.) ACISP 2009. LNCS, vol. 5594, pp. 407–421. Springer, Heidelberg (2009)
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Terelius, B., Wikström, D. (2010). Proofs of Restricted Shuffles. 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_7
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