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On the Amortized Complexity of Zero-Knowledge Protocols

Ronald Cramer, Ivan Damgård, Marcel Keller
2013 Journal of Cryptology  
We propose a general technique that allows improving the complexity of zero-knowledge protocols for a large class of problems where previously the best known solution was a simple cut-and-choose style  ...  protocol, i.e., where the size of a proof for problem instance x and error probability 2 −n was O(|x|n) bits.  ...  techniques that can build zero-knowledge protocols from HVZK ones without significant loss of efficiency.  ... 
doi:10.1007/s00145-013-9145-x fatcat:sborl3in4vhopixi455t2v77ii

On the Amortized Complexity of Zero-Knowledge Protocols [chapter]

Ronald Cramer, Ivan Damgård
2009 Lecture Notes in Computer Science  
We propose a general technique that allows improving the complexity of zero-knowledge protocols for a large class of problems where previously the best known solution was a simple cut-and-choose style  ...  protocol, i.e., where the size of a proof for problem instance x and error probability 2 −n was O(|x|n) bits.  ...  techniques that can build zero-knowledge protocols from HVZK ones without significant loss of efficiency.  ... 
doi:10.1007/978-3-642-03356-8_11 fatcat:5zq5okdxnbg5lnk6fgeuxv7nvi

On the Amortized Complexity of Zero Knowledge Protocols for Multiplicative Relations [chapter]

Ronald Cramer, Ivan Damgård, Valerio Pastro
2012 Lecture Notes in Computer Science  
The idea is then to combine all the proofs into one protocol and try to make the amortized complexity per proof be small.  ...  Our basic protocols are only honest-verifier zero-knowledge, but this can be improved to generalverifier zero-knowledge using standard tools.  ...  On the complexity of the protocol We now examine the complexity of the integer multiplication protocol assuming we want a knowledge error that is exponentially small in l, as in previous sections.  ... 
doi:10.1007/978-3-642-32284-6_4 fatcat:aogwrvixtvftha2gu5dxx55kky

Communication complexity of functions related to set intersection

Ulrich Tamm
2016 2016 Information Theory and Applications Workshop (ITA)  
The amortized communication complexity of functions f : {0, 1, . . . , m − 1} × {0, 1, . . . , m − 1} having an allzero row and and an all-zero column in their function matrix is determined.  ...  For m = 2 this yields the set intersection funtion or Boolean "and", for m = 3 a function mentioned in a problem in [5] arises.  ...  For one input (belonging to the all-zero row or all -zero column) the function value is clear after transmission of just one bit.  ... 
doi:10.1109/ita.2016.7888182 dblp:conf/ita/Tamm16 fatcat:3exyynnpyvgkroqgam6hk3c7da

Compressed $$\varSigma $$-Protocol Theory and Practical Application to Plug & Play Secure Algorithmics [chapter]

Thomas Attema, Ronald Cramer
2020 Lecture Notes in Computer Science  
Second, we reduce the case of general nonlinear relations to blackbox applications of our pivot via a novel variation on arithmetic secret sharing based techniques for Σ-Protocols (Cramer et al., ICITS  ...  ., S&P 2018) have been proposed as a drop-in replacement in case of zero-knowledge (ZK) for arithmetic circuits, achieving logarithmic communication instead of linear.  ...  We are grateful for a comment by Michael Klooß that our exact analysis of knowledge error is only meaningful for a portion of the full parameter space relevant to our application.  ... 
doi:10.1007/978-3-030-56877-1_18 fatcat:khgfqrq6urbjdpillrlaqap35i

Direct sum fails for zero error average communication

Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information cost.  ...  We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost.  ...  [Bra12a, BGPW13] conjecture that in the zero error regime, the amortized communication complexity of a function is exactly captured by its external information complexity.  ... 
doi:10.1145/2554797.2554844 dblp:conf/innovations/KolMSY14 fatcat:kxedaq6lnjbhverqm4zchd2zhm

Direct Sum Fails for Zero-Error Average Communication

Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff
2016 Algorithmica  
Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information cost.  ...  We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost.  ...  [Bra12a, BGPW13] conjecture that in the zero error regime, the amortized communication complexity of a function is exactly captured by its external information complexity.  ... 
doi:10.1007/s00453-016-0144-9 fatcat:epwh4bwgkvcnjepzmopr7ha3bu

Amortization with Fewer Equations for Proving Knowledge of Small Secrets [chapter]

Rafael del Pino, Vadim Lyubashevsky
2017 Lecture Notes in Computer Science  
The cost of this is an increase in the running time of the zero-knowledge proof.  ...  This implies that the communication complexity of the final protocol will be at least a factor of k larger than that of the basic one, where k is the security parameter.  ...  This work is supported by the SNSF ERC Transfer Grant CRETP2-166734 -FELICITY and the H2020 Project SAFEcrypto.  ... 
doi:10.1007/978-3-319-63697-9_13 fatcat:25x34xnharafjahzfxy2u24yvm

Bit commitment using pseudorandomness

Moni Naor
1991 Journal of Cryptology  
Thus we can conclude that if any computational complexity based cryptography is possible, then bit commitment protocols exist, and so do the protocols that rely on bit commitment, such as zero-knowledge  ...  Furthermore, Kilian, Micali and Ostrovsky KMO] have shown that many of the known protocols for zero knowledge can be converted to ones that have this property.  ...  Thus, various Zero-Knowledge protocols can be implemented with low complexity under the sole assumption. that one-way functions exist.  ... 
doi:10.1007/bf00196774 fatcat:g7gchwuq7ff2zbb3anhhmbtqby

Ligero

Scott Ames, Carmit Hazay, Yuval Ishai, Muthuramakrishnan Venkitasubramaniam
2017 Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security - CCS '17  
We design and implement a simple zero-knowledge argument protocol for NP whose communication complexity is proportional to the square-root of the veri cation circuit size.  ...  The communication complexity of our protocol is independent of the circuit structure and depends only on the number of gates.  ...  with the NTL library.  ... 
doi:10.1145/3133956.3134104 dblp:conf/ccs/AmesHIV17 fatcat:fe7vy5gt3zhofpsckw65l6hiqi

Zero-Knowledge Proofs with Low Amortized Communication from Lattice Assumptions [chapter]

Ivan Damgård, Adriana López-Alt
2012 Lecture Notes in Computer Science  
We construct zero-knowledge proofs of plaintext knowledge (PoPK) and correct multiplication (PoPC) for the Regev encryption scheme with low amortized communication complexity.  ...  Thus, we improve the amortized communication cost of each proof by a factor linear in the lattice dimension.  ...  Finally, using general zero-knowledge techniques, it is possible to convert the honest-verifier zero-knowledge proof protocol Π R,I,t obtained from Theorem 2.4 into a full zero-knowledge protocol, while  ... 
doi:10.1007/978-3-642-32928-9_3 fatcat:l2tt6y2sxvhhdfz3w7paduvm6m

Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography [chapter]

Ivan Damgård, Yuval Ishai, Mikkel Krøigaard
2010 Lecture Notes in Computer Science  
Concretely, under standard cryptographic assumptions, we obtain zero-knowledge proofs for circuit satisfiability with 2 −k soundness error in which the amortized computational overhead per gate is only  ...  -What are the minimal resources required for two-party primitives such as zero-knowledge proofs and general secure two-party computation?  ...  The efficiency of the zero-knowledge protocol is essentially the same as that of the MPC protocol, excluding the cost of n commitments to strings whose total size is roughly the communication complexity  ... 
doi:10.1007/978-3-642-13190-5_23 fatcat:fwuhrsowirfmdli5726lvixrqi

Moderately Hard Functions: From Complexity to Spam Fighting [chapter]

Moni Naor
2003 Lecture Notes in Computer Science  
The theory of hard functions (e.g. one-way functions) has been a great success story, and the community has developed a fairly strong understanding of what types of cryptographic primitives can be achieved  ...  We suggest several research directions and (re)call for the development of a theory of such functions.  ...  Furthermore, the discussion above on future directions of research is the result of joint work with Cynthia and Dan. I thank them for many years of fruitful collaboration.  ... 
doi:10.1007/978-3-540-24597-1_37 fatcat:joxlbgqm7jcvzbzrilgjx4a2mu

Coding for interactive computation: Progress and challenges

Mark Braverman
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We highlight some recent progress and challenges in the area of interactive coding and information complexity. * Partially supported by an Alfred P.  ...  I would like to thank Omri Weinstein for his comments on earlier drafts of this paper.  ...  Recall that the characterization of information complexity as the amortized communication complexity of F only worked for non-zero error ε > 0.  ... 
doi:10.1109/allerton.2012.6483456 dblp:conf/allerton/Braverman12 fatcat:diltfli64jcq7hrshj66m7un2u

New Separations Results for External Information [article]

Mark Braverman, Dor Minzer
2021 arXiv   pre-print
We prove a near-quadratic separation between amortized zero-error communication complexity and external information complexity for total functions, disproving a conjecture of . 3.  ...  The external information complexity of a function f(x,y) is the minimum amount of information a two-party protocol computing f must reveal to an outside observer about the input.  ...  The zero-error protocol In this section, we show a zero-error protocol of low amortized communication complexity as asserted in Theorem 1.3.  ... 
arXiv:2103.04049v1 fatcat:p2wnklzhjjep7fwyloaaa2z6bu
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