Seiko Arita
ABSTRACT
Constructing multilinear maps has been long-standing open problem, before recently the first construction based on ideal lattices has been proposed by Garg et al. After this breakthrough, various new cryptographic systems have been proposed. They introduce the concept of level into the encodings, and the system has a function that extracts a deterministic value at only a specific level, and the encodings are unable to downgrade to the lower levels. These properties are useful for cryptography. We study how this graded encoding system be applied to cryptosystems, and we propose two protocols, group key exchange and witness encryption. In our group key exchange, we achieve the communication size and the computation costs per party are both O(1) with respect to the number of parties by piling the encodings of passed parties in one encoding. A witness encryption is a new type cryptosystem using NP-complete problem. The first construction is based on EXACT-COVER problem. We construct it based on another NP complete Hamilton Cycle problem, and prove its security under the Generic Cyclic Colored Matrix Model.
- . Bresson, O. Chevassut, D. Pointcheval, and J. J. Quisquater. Provably authenticated group diffie-hellman key exchange. In proceedings of 8th ACM Conference on CCS E., pages 255--264, 2001. Google Scholar
Digital Library
- an Boneh and Alice Silverberg. Applications of multilinear forms to cryptography. In Contemporary Mathematics 324, pages 71--90, 2003.Google Scholar
- ean-Sébastien Coron, Tancrède Lepoint, Mehdi Tibouchi. Practical Multilinear Maps over the Integers. In CRYPTO 2013, pages 476--493.Google ScholarCross Ref
- anjam Garg, Craig Gentry, and Shai Halevi. Candidate multilinear maps from ideal lattices and applications. In EUROCRYPT 2013, Lecture Notes in Computer Science. Springer, 2013. Cryptology ePrint Archive, Report 2012/610.Google Scholar
- anjam Garg, Craig Gentry, Shai Halevi, Mariana Raykova, Amit Sahai, Brent Waters. Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits. In FOCS 2013, pages 40--49. Google ScholarDigital Library
- anjam Garg, Craig Gentry, Shai Halevi, Amit Sahai, and Brent Waters. Attributebased encryption for circuits from multilinear maps. In Cryptology ePrint Archive, Report 2013/128, 2013.Google Scholar
- anjam Garg, Craig Gentry, Amit Sahai and Brent Waters. Witness Encryption and its Applications. In STOC, pages 467--476, 2013. Google ScholarDigital Library
- e Kilian. Founding cryptography on oblivious transfer. In Janos Simon, editor, In STOC, pages 20--31. ACM, 1988. Google ScholarDigital Library
- .Schwartz. Fast probabilistic algorithms for verification of polynomial identities. In Journal of the ACM 27: pages 701--717, 1980. Google ScholarDigital Library
- . Shoup. Sequences of Games: A Tool for Taming Complexity in Security Proofs. In Cryptology ePrint Archive, Report 2004/332, 2004.Google Scholar
- . Steiner, G. Tsudik, and M. Waidner. Diffie-Hellman Key Distribution Extended to Group Communication. In Proceedings of the 3rd ACM Conference on Computer and Communications Security, pages 31--37. ACM Press, 1996. Google ScholarDigital Library
- . Zippel. Probabilistic algorithms for sparse polyno-mials. In Proceedings of EUROSAM, Springer Lecture Notes in Computer Science Vol.72, pages 216--226, 1979. Google ScholarDigital Library
Index Terms
- Two applications of multilinear maps: group key exchange and witness encryption
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