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On the Amortized Complexity of Zero-Knowledge Protocols

2013
*
Journal of Cryptology
*

We propose a general technique that allows improving

doi:10.1007/s00145-013-9145-x
fatcat:sborl3in4vhopixi455t2v77ii
*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. ...##
###
On the Amortized Complexity of Zero-Knowledge Protocols
[chapter]

2009
*
Lecture Notes in Computer Science
*

We propose a general technique that allows improving

doi:10.1007/978-3-642-03356-8_11
fatcat:5zq5okdxnbg5lnk6fgeuxv7nvi
*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. ...##
###
On the Amortized Complexity of Zero Knowledge Protocols for Multiplicative Relations
[chapter]

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. ...

##
###
Communication complexity of functions related to set intersection

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. ...

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

2020
*
Lecture Notes in Computer Science
*

Second, we reduce

doi:10.1007/978-3-030-56877-1_18
fatcat:khgfqrq6urbjdpillrlaqap35i
*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. ...##
###
Direct sum fails for zero error average communication

2014
*
Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14
*

Our example also refutes a version

doi:10.1145/2554797.2554844
dblp:conf/innovations/KolMSY14
fatcat:kxedaq6lnjbhverqm4zchd2zhm
*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*. ...##
###
Direct Sum Fails for Zero-Error Average Communication

2016
*
Algorithmica
*

Our example also refutes a version

doi:10.1007/s00453-016-0144-9
fatcat:epwh4bwgkvcnjepzmopr7ha3bu
*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*. ...##
###
Amortization with Fewer Equations for Proving Knowledge of Small Secrets
[chapter]

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. ...

##
###
Bit commitment using pseudorandomness

1991
*
Journal of Cryptology
*

Thus we can conclude that if any computational

doi:10.1007/bf00196774
fatcat:g7gchwuq7ff2zbb3anhhmbtqby
*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. ...##
###
Ligero

2017
*
Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security - CCS '17
*

We design and implement a simple

doi:10.1145/3133956.3134104
dblp:conf/ccs/AmesHIV17
fatcat:fe7vy5gt3zhofpsckw65l6hiqi
*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. ...##
###
Zero-Knowledge Proofs with Low Amortized Communication from Lattice Assumptions
[chapter]

2012
*
Lecture Notes in Computer Science
*

We construct

doi:10.1007/978-3-642-32928-9_3
fatcat:l2tt6y2sxvhhdfz3w7paduvm6m
*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 ...##
###
Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography
[chapter]

2010
*
Lecture Notes in Computer Science
*

Concretely, under standard cryptographic assumptions, we obtain

doi:10.1007/978-3-642-13190-5_23
fatcat:fwuhrsowirfmdli5726lvixrqi
*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*...##
###
Moderately Hard Functions: From Complexity to Spam Fighting
[chapter]

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. ...

##
###
Coding for interactive computation: Progress and challenges

2012
*
2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
*

We highlight some recent progress and challenges in

doi:10.1109/allerton.2012.6483456
dblp:conf/allerton/Braverman12
fatcat:diltfli64jcq7hrshj66m7un2u
*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. ...##
###
New Separations Results for External Information
[article]

2021
*
arXiv
*
pre-print

We prove a near-quadratic separation between

arXiv:2103.04049v1
fatcat:p2wnklzhjjep7fwyloaaa2z6bu
*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. ...
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