Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7194 LNCS, Issue , 2012, Pages 169-189

  Lipmaa, Helger ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

Additive combinatorics; bilinear pairings; circuit satisfiability; non interactive zero knowledge; progression free sets

Indexed keywords

BILINEAR PAIRING; CIRCUIT SATISFIABILITY; COMBINATORICS; NON-INTERACTIVE; PROGRESSION-FREE SETS;

FORMAL LOGIC;

CRYPTOGRAPHY;

EID: 84858312040     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-28914-9_10     Document Type: Conference Paper

References (25)

1. Abe, M., Fehr, S.: Perfect NIZK with Adaptive Soundness. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 118-136. Springer, Heidelberg (2007)
2. Barreto, P.S.L.M., Naehrig, M.: Pairing-Friendly Elliptic Curves of Prime Order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319-331. Springer, Heidelberg (2006) (Pubitemid 43986803)
3. Behrend, F.A.: On the Sets of Integers Which Contain No Three in Arithmetic Progression. Proceedings of the National Academy of Sciences 32(12), 331-332 (1946)
4. Blum, M., Feldman, P., Micali, S.: Non-Interactive Zero-Knowledge and Its Applications. In: STOC 1988, pp. 103-112. ACM Press (1988)
5. Bourgain, J.: On Triples in Arithmetic Progression. Geom. Funct. Anal. 9(5), 968-984 (1998)
6. Chaabouni, R., Lipmaa, H., Shelat, A.: Additive Combinatorics and Discrete Logarithm Based Range Protocols. In: Steinfeld, R., Hawkes, P. (eds.) ACISP 2010. LNCS, vol. 6168, pp. 336-351. Springer, Heidelberg (2010)
7. Chaabouni, R., Lipmaa, H., Zhang, B.: A Non-Interactive Range Proof with Constant Communication. In: Keromytis, A. (ed.) FC 2012. LNCS, Springer, Heidelberg (2012)
8. Cheon, J.H.: Security Analysis of the Strong Diffie-Hellman Problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1-11. Springer, Heidelberg (2006)
9. Elkin, M.: An Improved Construction of Progression-Free Sets. Israeli J. Math. 184, 93-128 (2011)
10. Gentry, C.: Fully Homomorphic Encryption Using Ideal Lattices. In: Mitzenmacher, M. (ed.) STOC 2009, pp. 169-178. ACM Press (2009)
11. Gentry, C., Wichs, D.: Separating Succinct Non-Interactive Arguments from All Falsifiable Assumptions. In: Vadhan, S. (ed.) STOC 2011, pp. 99-108. ACM Press (2011)
12. Golle, P., Jarecki, S., Mironov, I.: Cryptographic Primitives Enforcing Communication and Storage Complexity. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357, pp. 120-135. Springer, Heidelberg (2003) (Pubitemid 36316775)
13. Green, B., Wolf, J.: A Note on Elkin's Improvement of Behrend's Construction. In: Chudnovsky, D., Chudnovsky, G. (eds.) Additive Number Theory, pp. 141-144. Springer, New York (2010)
14. 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)
15. Groth, J.: Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321-340. Springer, Heidelberg (2010)
16. Groth, J.: Minimizing Non-interactive Zero-Knowledge Proofs Using Fully Homomorphic Encryption. Tech. Rep. 2011/012, IACR (2011)
17. Groth, J., Sahai, A.: Efficient Non-interactive Proof Systems for Bilinear Groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415-432. Springer, Heidelberg (2008) (Pubitemid 351762842)
18. Hess, F., Smart, N.P., Vercauteren, F.: The Eta Pairing Revisited. IEEE Trans. Inf. Theory 52(10), 4595-4602 (2006)
19. van Hoeij, M., Novocin, A.: Gradual Sub-lattice Reduction and a New Complexity for Factoring Polynomials. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 539-553. Springer, Heidelberg (2010)
20. Lipmaa, H.: Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments. Tech. Rep. 2011/009, IACR (2011)
21. Lipmaa, H., Zhang, B.: A More Efficient Computationally Sound Non-Interactive Zero-Knowledge Shuffle Argument. Tech. Rep. 2011/394, IACR (2011)
22. Micali, S.: CS Proofs. In: Goldwasser, S. (ed.) FOCS 1994, pp. 436-453. IEEE (1994)
23. Moser, L.: An Application of Generating Series. Mathematics Magazine 35(1), 37-38 (1962)
24. Sanders, T.: On Roth's Theorem on Progressions. Ann. Math. 174(1), 619-636 (2011)
25. Tao, T., Vu, V.: Additive Combinatorics. Cambridge Studies in Advanced Mathematics. Cambridge University Press (2006)