Verifiable shuffles: A formal model and a Paillier-based three-round construction with provable security

International Journal of Information Security

Volumn 5, Issue 4, 2006, Pages 241-255

  Nguyen, Lan ^a   Safavi Naini, Rei ^a   Kurosawa, Kaoru ^b  

^a UNIVERSITY OF WOLLONGONG   (Australia)

^b IBARAKI UNIVERSITY   (Japan)

Author keywords

Formal security model; Mix nets; Paillier public key system; Privacy; Verifiable shuffles

Indexed keywords

EID: 33749003104     PISSN: 16155262     EISSN: 16155270     Source Type: Journal    
DOI: 10.1007/s10207-006-0004-8     Document Type: Article

References (52)

1. Abe, M.: Universally verifiable mix-net with verification work independent of the number of mix-servers. EUROCRYPT 1998, LNCS 1403, pp. 437-447. Springer-Verlag, Berlin (1998)
2. Abe, M.: Mix-networks on permutation networks. ASIACRYPT 1999, LNCS 1716, pp. 258-273. Springer-Verlag, Berlin (1999)
3. Abe, M., Hoshino, F.: Remarks on mix-network based on permutation networks. PKC 2001, LNCS, pp. 317-324. Springer-Verlag, Berlin (2001)
4. Abe, M., Imai, H.: Flaws in some robust optimistic mix-nets. ACISP 2003, LNCS 2727, pp. 39-50. Springer-Verlag, Berlin (2003)
5. Abe, M.: Combining encryption and proof of knowledge in the random oracle model. Comput. J. 47 (1) (2004)
6. Agrawal, M., Kayal, N., Saxena, N.: PRIMES is in P. Annal. Math. 160 (2), 781-793 (2004)
7. Boneh, D., Golle, P.: Almost Entirely Correct Mixing With Application to Voting. ACM CCS 2002, ACM Press, New York (2002)
8. Brands, S.: An efficient off-line electronic cash system based on the representation problem. CWI Technical Report CS-R9323 (1993)
9. Chaum, D.: Untraceable electronic mail, return addresses, and digital pseudonyms. Commun. ACM 24 (2), 84-88 (1981)
10. Choi, S., Kim, K.: Authentication and payment protocol preserving location privacy in mobile IP. GLOBECOM 2003 (2003)
11. Desmedt, Y., Kurosawa, K.: How to break a practical mix and design a new one. EUROCRYPT 2000, LNCS 1807, pp. 557-572. Springer-Verlag, Berlin (2000)
12. Fouque, P., Pointcheval, D.: Threshold cryptosystems secure against chosen-ciphertext attacks. ASIACRYPT 2001, LNCS 2248, pp. 351-368. Springer-Verlag, Berlin (2001)
13. Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. CRYPTO 2001, LNCS 2139, pp. 368-389. Springer-Verlag, Berlin (2001)
14. Furukawa, J., Miyauchi, H., Mori, K., Obana, S., Sako, K.: An implementation of a universally verifiable electronic voting scheme based on shuffling. Financial Cryptography 2002, LNCS 2357, Springer-Verlag, Berlin (2002)
15. Furukawa, J.: Efficient, verifiable shuffle decryption and its requirement of unlinkability. PKC 2004, LNCS 2947, pp. 319-332. Springer-Verlag, Berlin (2004)
16. Gabber, E., Gibbons, P., Matias, Y., Mayer, A.: How to make personalized Web browsing simple, secure, and anonymous. Financial Cryptography 1997, LNCS 1318, pp. 17-31. Springer-Verlag, Berlin (1997)
17. Goldreich, O.: Foundations of Cryptography Basic Tools. Cambridge University Press, Cambridge (2001)
18. Goldreich, O.: Foundations of Cryptography, Basic Applications. Cambridge University Press, Cambridge (2004)
19. Golle, P., Zhong, S., Boneh, D., Jakobsson, M., Juels, A.: Optimistic mixing for exit-polls. ASIACRYPT 2002, LNCS 2501, pp. 451-465. Springer-Verlag, Berlin (2002)
20. Groth, J.: A verifiable secret shuffle of homomorphic encryptions. PKC 2003, LNCS 2567, pp. 145-160. Springer-Verlag, Berlin (2003)
21. Jakobsson, M.: A practical mix. EUROCRYPT 1998, LNCS 1403, pp. 448-461. Springer-Verlag, Berlin (1998)
22. Jakobsson, M., M'Raihi, D.: Mix-based electronic payments. SAC 1993, LNCS 1505, pp. 457-473. Springer-Verlag, Berlin (1998)
23. Jakobsson, M.: Flash mixing. PODC 1999, pp. 83-89. ACM Press, New York (1999)
24. Jakobsson, M., Juels, A.: Millimix: Mixing in small batches. DIMACS Technical Report, 99-33 (1999)
25. Jakobsson, M., Juels, A.: Mix and match: Secure function evaluation via ciphertexts. ASIACRYPT 2000, LNCS 1976, pp. 162-177. Springer-Verlag, Berlin (2000)
26. Jakobsson, M., Juels, A.: An Optimally Robust Hybrid Mix Network. PODC 2001, ACM Press, New York (2001)
27. Jakobsson, M., Juels, A., Rivest, R.: Making mix nets robust for electronic voting by randomized partial checking. USENIX Security (2002)
28. Juels, A.: Targeted advertising and privacy too. CT-RSA 2001, LNCS 2020, pp. 408-425. Springer-Verlag, Berlin (2001)
29. Koblitz, N., Menezes, A.: Another look at "provable security". Journal of Cryptology. DOI 10.1007/s00145-005-0432-z, URL http://dx.doi.org/10.1007/s00145-005-0432-z, Springer-Verlag, Berlin (2006)
30. Kong, J., Hong, X.: ANODR: ANonymous on demand routing with untraceable routes for mobile ad-hoc networks. In: Fourth ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc 2003), pp. 291-302 (2003)
31. Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton, Florida (1996)
32. Mitomo, M., Kurosawa, K.: Attack for flash mix. ASIACRYPT 2000, LNCS 1976, pp. 192-204. Springer-Verlag (2000)
33. Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertexts attacks. STOC 1990, pp. 427-437. ACM Press, New York (1990)
34. Neff, A.: A Verifiable Secret Shuffle and its Application to e-Voting. ACM CCS 2001, pp. 116-125. ACM Press, New York (2001)
35. Neff, A.: Verifiable Mixing (Shuffling) of ElGamal Pairs. Available online: http://www.votehere.org/vhti/documentation/egshuf.pdf (2003)
36. Nguyen, L., Safavi-Naini, R.: Breaking and Mending Resilient Mix-nets. PET 2003, LNCS 2760, pp. 66-80. Springer-Verlag, Berlin (2003)
37. Nguyen, L., Safavi-Naini, R., Kurosawa, K.: Verifiable shuffles: A formal model and a Paillier-based efficient construction with provable security. ACNS 2004, LNCS 3089, pp. 61-75. Springer-Verlag, Berlin (2004)
38. Nguyen, L., Safavi-Naini, R.: An efficient verifiable shuffle with perfect zero-knowledge proof system. Cryptographic Algorithms and Their Uses, pp. 40-56 (2004)
39. Ogata, W., Kurosawa, K., Sako, K., Takatani, K.: Fault tolerant anonymous channel. ICICS '97, LNCS 1334, pp. 440-444. Springer-Verlag, Berlin (1997)
40. Ohkubo, M., Abe, M.: A length-invariant hybrid mix. ASIACRYPT 2000, LNCS 1976, pp. 178-191. Springer-Verlag, Berlin (2000)
41. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. EUROCRYPT 1999, LNCS 1592, pp. 223-239. Springer-Verlag, Berlin (1999)
42. Park, C., Itoh, K., Kurosawa, K.: Efficient anonymous channel and all/ nothing election scheme. EUROCRYPT 1993, LNCS 765, pp. 248-259. Springer-Verlag, Berlin (1993)
43. Pfitzmann, B.: Breaking an efficient anonymous channel. EUROCRYPT 1994, LNCS 950, pp. 332-340. Springer-Verlag, Berlin (1994)
44. Schnorr, P., Jakobsson, M.: Security of signed El Gamal encryption. ASIACRYPT 2000, LNCS 1976, pp. 73-89. Springer-Verlag, Berlin (2000)
45. Shamir, A.: How to share a secret. Commun. ACM 22, 612-613 (1979)
46. Tsiounis, Y., Yung, M.: On the security of El Gamal based encryption. PKC 1998, LNCS 1431, pp. 117-134. Springer-Verlag, Berlin (1998)
47. Wang, X., Lai, X., Feng, D., Chen, H., Yu, X.: Cryptanalysis of the Hash Functions MD4 and RIPEMD. EUROCRYPT 2005, LNCS 3494, pp. 1-18. Springer-Verlag, Berlin (2005)
48. Wang, X., Yu, H.: How to Break MD5 and other hash functions. EUROCRYPT 2005, LNCS 3494, pp. 19-35. Springer-Verlag, Berlin (2005)
49. Wang, X., Yu, H., Yin, Y.: Efficient collision search attacks on SHA-0. CRYPTO 2005, LNCS 3621, pp. 1-16. Springer-Verlag, Berlin (2005)
50. Wang, X., Yin, Y., Yu, H.: Finding Collisions in the Full SHA-1. CRYPTO 2005, LNCS 3621, pp. 17-36. Springer-Verlag, Berlin (2005)
51. Wikstrom, D.: The security of a mix-center based on a semantically secure cryptosystem. Indocrypt 2002, LNCS 2551, pp. 368-381. Springer-Verlag, Berlin (2002)
52. Wikstrom, D.: Five practical attacks for "Optimistic Mixing for Exit-Polls." SAC 2003, LNCS 3006 (2003)