Scalable Multiparty Computation with Nearly Optimal Work and Resilience

We present the first general protocol for secure multiparty computation in which the totalamount of work required by nplayers to compute a function fgrows only polylogarithmically with n(ignoring an additive term that depends on nbut not on the complexity of f). Moreover, the protocol is also nearly optimal in terms of resilience, providing computational security against an active, adaptive adversary corrupting a (1/2 i¾? i¾?) fraction of the players, for an arbitrary i¾?> 0.

[1]  A. Maximov,et al.  Fast computation of large distributions and its cryptographic applications , 2005 .

[2]  Yehuda Lindell,et al.  Universally composable two-party and multi-party secure computation , 2002, STOC '02.

[3]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[4]  Matthew K. Franklin,et al.  Communication complexity of secure computation (extended abstract) , 1992, STOC '92.

[5]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.

[6]  Tatsuaki Okamoto Advances in Cryptology — ASIACRYPT 2000 , 2000, Lecture Notes in Computer Science.

[7]  Cynthia Dwork,et al.  Advances in Cryptology – CRYPTO 2020: 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, August 17–21, 2020, Proceedings, Part III , 2020, Annual International Cryptology Conference.

[8]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[9]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[10]  Matthias Fitzi,et al.  Optimally efficient multi-valued byzantine agreement , 2006, PODC '06.

[11]  Gabriel Bracha,et al.  An O(log n) expected rounds randomized byzantine generals protocol , 1987, JACM.

[12]  A. Lubotzky,et al.  Ramanujan graphs , 2017, Comb..

[13]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

[14]  Ivan Damgård,et al.  Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption , 2003, CRYPTO.

[15]  Victor Shoup Advances in Cryptology - CRYPTO 2005: 25th Annual International Cryptology Conference, Santa Barbara, California, USA, August 14-18, 2005, Proceedings , 2005, CRYPTO.

[16]  A. Yao How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[17]  Ivan Damgård,et al.  Efficient Multiparty Computations Secure Against an Adaptive Adversary , 1999, EUROCRYPT.

[18]  Martin Hirt,et al.  Efficient Multi-party Computation with Dispute Control , 2006, TCC.

[19]  Martin Hirt,et al.  Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation , 2005, ASIACRYPT.

[20]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[21]  Martin Hirt,et al.  Robust Multiparty Computation with Linear Communication Complexity , 2006, CRYPTO.

[22]  Ivan Damgård,et al.  Scalable and Unconditionally Secure Multiparty Computation , 2007, CRYPTO.

[23]  Ueli Maurer,et al.  Player Simulation and General Adversary Structures in Perfect Multiparty Computation , 2000, Journal of Cryptology.

[24]  Andrew Chi-Chih Yao,et al.  Theory and Applications of Trapdoor Functions (Extended Abstract) , 1982, FOCS.

[25]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[26]  Matthias Fitzi,et al.  Towards Optimal and Efficient Perfectly Secure Message Transmission , 2007, TCC.

[27]  Dan Boneh,et al.  Advances in Cryptology - CRYPTO 2003 , 2003, Lecture Notes in Computer Science.

[28]  Ueli Maurer,et al.  Efficient Secure Multi-party Computation , 2000, ASIACRYPT.

[29]  Yuval Ishai,et al.  Computationally Private Randomizing Polynomials and Their Applications , 2005, Computational Complexity Conference.

[30]  A. J. Menezes,et al.  Advances in Cryptology - CRYPTO 2007, 27th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2007, Proceedings , 2007, CRYPTO.

[31]  Yuval Ishai,et al.  Scalable Secure Multiparty Computation , 2006, CRYPTO.

[32]  Yuval Ishai,et al.  Constant-Round Multiparty Computation Using a Black-Box Pseudorandom Generator , 2005, CRYPTO.

[33]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.

[34]  Yehuda Lindell,et al.  Information-theoretically secure protocols and security under composition , 2006, STOC '06.

[35]  Matthew K. Franklin,et al.  Joint Encryption and Message-Efficient Secure Computation , 1993, CRYPTO.

[36]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.

[37]  Markus Jakobsson,et al.  Mix and Match: Secure Function Evaluation via Ciphertexts , 2000, ASIACRYPT.

[38]  R. Cramer,et al.  Multiparty Computation from Threshold Homomorphic Encryption , 2000 .

[39]  Martin Hirt,et al.  Perfectly-Secure MPC with Linear Communication Complexity , 2008, TCC.

[40]  Tal Rabin,et al.  Simplified VSS and fast-track multiparty computations with applications to threshold cryptography , 1998, PODC '98.

[41]  Ueli Maurer,et al.  Robustness for Free in Unconditional Multi-party Computation , 2001, CRYPTO.

[42]  Yehuda Lindell Composition of Secure Multi-Party Protocols: A Comprehensive Study , 2003 .

[43]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[44]  Yuval Ishai,et al.  How Many Oblivious Transfers Are Needed for Secure Multiparty Computation? , 2007, CRYPTO.