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(Nearly) Round-Optimal Black-Box Constructions of Commitments Secure against Selective Opening Attacks [chapter]

David Xiao
2011 Lecture Notes in Computer Science  
We prove the following black-box constructions and black-box lower bounds for commitments secure against selective opening attacks: 1.  ...  Our lower bounds improve upon the parameters obtained by the impossibility results of Bellare et al.  ...  Optimality of constructions We now define our main tool for proving lower bounds, equivocal senders.  ... 
doi:10.1007/978-3-642-19571-6_33 fatcat:3ary7bor3zh5paq6lxqrgvh65a

Public-Key Cryptography (Dagstuhl Seminar 16371)

Marc Fischlin, Alexander May, David Pointcheval, Tal Rabin, Marc Herbstritt
2017 Dagstuhl Reports  
This report documents the program and results of Dagstuhl seminar 16731 "Public-Key Cryptography" which took place September 11-16, 2016.  ...  The goal of the seminar was to bring together different subareas from public-key cryptography and to promote research among these areas.  ...  For this function we prove a lower bound of N 2 < O(S 2 • T ).  ... 
doi:10.4230/dagrep.6.9.46 dblp:journals/dagstuhl-reports/Fischlin0PR16 fatcat:figv27hq4feibl5nzb7snrtm2i

SIA: Secure information aggregation in sensor networks

Haowen Chan, Adrian Perrig, Bartosz Przydatek, Dawn Song, Peng Ning, Wenliang Du
2007 Journal of Computer Security  
In particular, we present efficient protocols for secure computation of the median and the average of the measurements, for the estimation of the network size, and for finding the minimum and maximum sensor  ...  By constructing efficient random sampling mechanisms and interactive proofs, we enable the user to verify that the answer given by the aggregator is a good approximation of the true value even when the  ...  Acknowledgments The authors would like to thank anonymous referees and shepherd Philippe Bonnet for their valuable comments and feedback.  ... 
doi:10.3233/jcs-2007-15104 fatcat:ilanfbwlm5dltcgbxstlewazlu

Efficiency Limitations of Σ-Protocols for Group Homomorphisms Revisited [chapter]

Björn Terelius, Douglas Wikström
2012 Lecture Notes in Computer Science  
., we prove lower bounds on both the soundness error and the knowledge error of such protocols.  ...  We study the problem of constructing efficient proofs of knowledge of preimages of general group homomorphisms. We simplify and extend the recent negative results of Bangerter et al.  ...  They proved a lower bound on the knowledge error in the generic group model for such protocols and gave concrete examples of protocols where the bounds hold in the plain model.  ... 
doi:10.1007/978-3-642-32928-9_26 fatcat:jb6eoat3hbfylb2xdvfrlowrja

On the power of nonuniformity in proofs of security

Kai-Min Chung, Huijia Lin, Mohammad Mahmoody, Rafael Pass
2013 Proceedings of the 4th conference on Innovations in Theoretical Computer Science - ITCS '13  
We prove our results by providing general techniques for extending certain types of black-box separations to handle nonuniformity.  ...  In this paper, we initiate a formal study of the power and limits of nonuniform black-box proofs of security.  ...  Our proof proceeds by proving a nonuniform hardness lower bound for families of collision-resistant hash functions, and next relying on the above proof template sketched for the case of one-way permutations  ... 
doi:10.1145/2422436.2422480 dblp:conf/innovations/ChungLMP13 fatcat:z5un4rarmjghdlbijfuryzzt6a

Space Complexity in Polynomial Calculus

Yuval Filmus, Massimo Lauria, Jakob Nordström, Noga Ron-Zewi, Neil Thapen
2015 SIAM journal on computing (Print)  
principle that has constant width, and prove an Ω(n) space lower bound in PCR for these formulas as well. 3) We prove an Ω(n) space lower bound in PC for the canonical 3-CNF version of the pigeonhole  ...  space lower bound for a bitwise encoding of the functional pigeonhole principle with m pigeons and n holes.  ...  semester on Logic and Complexity at the Charles University in in Prague in the au-  ... 
doi:10.1137/120895950 fatcat:vzsfnttcf5gnppg7vz2ij3hmvm

Bounds on the Efficiency of "Black-Box" Commitment Schemes [chapter]

Omer Horvitz, Jonathan Katz
2005 Lecture Notes in Computer Science  
Here, we present bounds on the efficiency of statistically-binding commitment schemes constructed using black-box access to one-way permutations; our bounds are tight for the case of perfectly-binding  ...  commitment scheme could be constructed "from scratch").  ...  Lower bounding the efficiency of commitment Let (S (·) , R (·) ) be an (S p , S h , ε h , ε b )-secure construction of a commitment scheme for m-bit messages (based on one-way permutations).  ... 
doi:10.1007/11523468_11 fatcat:o2kh4umihjhvtbjxstxibzqx5u

Bounds on the efficiency of black-box commitment schemes

Omer Horvitz, Jonathan Katz
2010 Theoretical Computer Science  
Here, we present bounds on the efficiency of statistically-binding commitment schemes constructed using black-box access to one-way permutations; our bounds are tight for the case of perfectly-binding  ...  commitment scheme could be constructed "from scratch").  ...  Lower bounding the efficiency of commitment Let (S (·) , R (·) ) be an (S p , S h , ε h , ε b )-secure construction of a commitment scheme for m-bit messages (based on one-way permutations).  ... 
doi:10.1016/j.tcs.2009.10.021 fatcat:nyeq5zhkanbqxb763w5f67oyk4

Space Complexity in Polynomial Calculus

Yuval Filmus, Massimo Lauria, Jakob Nordstrom, Neil Thapen, Noga Ron-Zewi
2012 2012 IEEE 27th Conference on Computational Complexity  
principle that has constant width, and prove an Ω(n) space lower bound in PCR for these formulas as well. 3) We prove an Ω(n) space lower bound in PC for the canonical 3-CNF version of the pigeonhole  ...  space lower bound for a bitwise encoding of the functional pigeonhole principle with m pigeons and n holes.  ...  semester on Logic and Complexity at the Charles University in in Prague in the au-  ... 
doi:10.1109/ccc.2012.27 dblp:conf/coco/FilmusLNTR12 fatcat:qmcbbck3fbgqhjoe5h4re3k6sm

Page 6758 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
Summary: “We prove the first general and non-trivial lower bound for the number of times a |-out-of-n oblivious transfer of strings of length / should be invoked so as to obtain, by an information- theoretically  ...  We also prove the first non-trivial lower bound for the number of random bits needed to implement such a reduction whenever the receiver sends no messages to the sender.  ... 

SIA

Bartosz Przydatek, Dawn Song, Adrian Perrig
2003 Proceedings of the first international conference on Embedded networked sensor systems - SenSys '03  
In particular, we present efficient protocols for secure computation of the median and the average of the measurements, for the estimation of the network size, and for finding the minimum and maximum sensor  ...  By constructing efficient random sampling mechanisms and interactive proofs, we enable the user to verify that the answer given by the aggregator is a good approximation of the true value even when the  ...  Acknowledgments The authors would like to thank anonymous referees and shepherd Philippe Bonnet for their valuable comments and feedback.  ... 
doi:10.1145/958491.958521 dblp:conf/sensys/PrzydatekSP03 fatcat:gbxb7svt3zbwrkyqem3cvm7vpy

Finding Collisions in Interactive Protocols---Tight Lower Bounds on the Round and Communication Complexities of Statistically Hiding Commitments

Iftach Haitner, Jonathan J. Hoch, Omer Reingold, Gil Segev
2015 SIAM journal on computing (Print)  
We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations, and from trapdoor permutations  ...  As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees  ...  Acknowledgment We thank Mohammad Mahmoody and Rafael Pass for useful discussions. References [1] W. Aiello, Y. Ishai, and O. Reingold  ... 
doi:10.1137/130938438 fatcat:5iw3bhicbvegvh6fy7jyachs4i

Finding Collisions in Interactive Protocols – Tight Lower Bounds on the Round and Communication Complexities of Statistically Hiding Commitments [article]

Iftach Haitner and Jonathan J. Hoch and Omer Reingold and Gil Segev
2021 arXiv   pre-print
We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations, and from trapdoor permutations  ...  As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees  ...  Acknowledgment We thank Mohammad Mahmoody and Rafael Pass for useful discussions. References [1] W. Aiello, Y. Ishai, and O. Reingold  ... 
arXiv:2105.01417v1 fatcat:a5c7aaa4pngefa4yofjepxd5om

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments [chapter]

Rafael Pass
2013 Lecture Notes in Computer Science  
We present barriers to provable security of two fundamental (and well-studied) cryptographic primitives perfect non-interactive zero knowledge (NIZK), and non-malleable commitments: • Black-box reductions  ...  perfect) NIZK for N P based on any "standard" intractability assumptions. • Black-box reductions cannot be used to demonstrate non-malleability of non-interactive, or even 2-message, commitment schemes  ...  Since we are proving a lower-bound we simply state the weaker definition.  ... 
doi:10.1007/978-3-642-36594-2_19 fatcat:vogdn6q7dfdeld6gst6enntmea

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments

Rafael Pass
2016 Computational Complexity  
We present barriers to provable security of two fundamental (and well-studied) cryptographic primitives perfect non-interactive zero knowledge (NIZK), and non-malleable commitments: • Black-box reductions  ...  perfect) NIZK for N P based on any "standard" intractability assumptions. • Black-box reductions cannot be used to demonstrate non-malleability of non-interactive, or even 2-message, commitment schemes  ...  Since we are proving a lower-bound we simply state the weaker definition.  ... 
doi:10.1007/s00037-016-0122-2 fatcat:b4bkyiddbzhbzcgo5l7jaeqcve
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