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Compact Zero-Knowledge Proofs of Small Hamming Weight
[chapter]

2018
*
Lecture Notes in Computer Science
*

We introduce a new technique that allows to give a zeroknowledge

doi:10.1007/978-3-319-76581-5_18
fatcat:x5ubojvqyjefdax4nhi3bhnrqy
*proof*that a committed vector has*Hamming**weight*bounded by a given constant. ... The*proof*has unconditional soundness and is very*compact*: It has size independent*of*the length*of*the committed string, and for large fields, it has size corresponding to a constant number*of*commitments ... We now show how to realise n d -OT k using this commitment scheme, and applying the*zero*-*knowledge**proof**of**Hamming**weight*from Sect. 3. ...##
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A lattice-based batch identification scheme

2011
*
2011 IEEE Information Theory Workshop
*

We use the hardness

doi:10.1109/itw.2011.6089381
dblp:conf/itw/SilvaCL11
fatcat:ot5zcjzxfracdm3bcn6vregzkq
*of*a lattice problem, namely the Inhomogeneous*Small*Integer Solution problem (I-SIS), as security assumption. ... Our version consists*of*a method for allowing a user to authenticate himself with different levels*of*clearance upon the choice*of*a subset*of*keys in his possession. ... As the identification protocol was kept the same (which varies is an indication*of*which key to use), the*proofs**of*security and*zero*-*knowledge*properties are inherited (from both Stern's and Cayrel's ...##
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Fault tolerance in systems design in VLSI using data compression under constraints of failure probabilities

2001
*
IEEE Transactions on Instrumentation and Measurement
*

, sequence

doi:10.1109/19.982974
fatcat:lqwteu23qzbbdpfzzn5f5wnw5i
*weights*, space*compaction*, time*compaction*. ... The*compaction*techniques utilize the concepts*of**Hamming*distance, sequence*weights*, and derived sequences in conjunction with the probabilities*of*error occurrence in the selection*of*specific gates ... ACKNOWLEDGMENT The authors are extremely grateful to the anonymous reviewers for their many valuable suggestions that immensely helped in the preparation*of*the revised version*of*the manuscript. ...##
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An Application of p-Fibonacci Error-Correcting Codes to Cryptography

2021
*
Mathematics
*

In this manuscript, we explored the possibility

doi:10.3390/math9070789
fatcat:3o54uyxm5vd45burqrmzzk4sv4
*of*using the error-correcting codes proposed by Stakhov in 2006 to design an identification protocol based on*zero*-*knowledge**proofs*. ... In addition to their usefulness in proving one's identity electronically, identification protocols based on*zero*-*knowledge**proofs*allow designing secure cryptographic signature schemes by means*of*the ...*proof*systems and*zero*-*knowledge**proofs*. ...##
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Maximal compact tori in the Hamiltonian groups of 4-dimensional symplectic manifolds
[article]

2006
*
arXiv
*
pre-print

We prove that the group

arXiv:math/0612565v1
fatcat:bpfxkgmugbbd3evpsqmatyivwa
*of*Hamiltonian automorphisms*of*a symplectic 4-manifold contains only finitely many conjugacy classes*of*maximal*compact*tori with respect to the action*of*the full symplectomorphism ... We also extend to rational and ruled manifolds a result*of*Kedra which asserts that, if M is a simply connected symplectic 4-manifold with b_2≥ 3, and if M_δ denotes a blow-up*of*M*of**small*enough capacity ... Assuming Theorem 4.1, the*proof**of*Theorem 1.4 reduces to showing that on any*compact*simply connected 4-manifold with b 2 (M ) ≥ 3, and for*small*enough δ, the exceptional divisor Σ ⊂ ( M δ , ω δ ) is ...##
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Improved Zero-Knowledge Identification with Lattices

2012
*
Tatra Mountains Mathematical Publications
*

It relies on the syndrome decoding problem and uses

doi:10.2478/v10127-012-0038-4
fatcat:xt42dbd7dvg4lhycgdg7slux3e
*of*a 3-pass*zero*-*knowledge**proof**of**knowledge*(ZK-PoK) with a soundness error*of*2/3 and perfect completeness. ... In contrast to typical*zero*-*knowledge*schemes, Lyubashevsky's construction is based on a witness-indistinguishable (not*zero*-*knowledge*)*proof**of**knowledge*. Furthermore, it has no soundness error. ... In the security*proofs*along this text we use the concept*of**zero*-*knowledge*interactive*proof**of**knowledge*system. ...##
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Sequence compaction for power estimation: theory and practice

1999
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

As the experimental results show, large

doi:10.1109/43.771179
fatcat:xaspgb2yhva65mjrfxvrdkhrye
*compaction*ratios*of*orders*of*magnitude can be obtained without significant loss in accuracy (less than 5% on average) for power estimates. . ... The goal*of*this paper is to present an effective and robust technique for*compacting*large sequences*of*input vectors into much smaller ones such that the power estimates are as accurate as possible and ...*Proof*: Let be the*weight**of*the initial sequence. ...##
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p-Adic estimates of hamming weights in abelian codes over galois rings

2006
*
IEEE Transactions on Information Theory
*

A generalization

doi:10.1109/tit.2005.864428
fatcat:3pd5om7wv5gybpxhjvf64e7myi
*of*McEliece's theorem on the -adic valuation*of**Hamming**weights**of*words in cyclic codes is proved in this paper by means*of*counting polynomial techniques introduced by Wilson along with ... It is natural to ask whether there is a single analogue*of*McEliece's theorem which correctly captures the behavior*of*codes over all finite fields and all rings*of*integers modulo prime powers. ...*Hamming**weight*. ...##
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On the hardness of the decoding and the minimum distance problems for rank codes
[article]

2014
*
arXiv
*
pre-print

Our results are based on an embedding from linear codes equipped with

arXiv:1404.3482v1
fatcat:xt74dmiqlrfubilplovelx3ww4
*Hamming*distance unto linear codes over an extension field equipped with the rank metric. ... . , α n are linearly independent, then any codeword*of*C(C, α)*of**Hamming**weight*w is also*of*rank*weight*w.*Proof*. Let W ⊂ {1, 2, . . . , n} be a set*of*w coordinates. ... the rank*weight**of*x being not more than the*Hamming**weight**of*x. ...##
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Cycle-Based Decomposition of Markov Chains With Applications to Low-Power Synthesis and Sequence Compaction for Finite State Machines

2006
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

The key idea is based on the fact that a Markov process can be decomposed into a collection

doi:10.1109/tcad.2006.882478
fatcat:gxznaybiibbdxchbznllveqcpi
*of*directed cycles with positive*weights*, which are proportional to the probability*of*the cycle traversals in ... The proposed encoding algorithm reduces power consumption by an average*of*15%. The second application is sequence*compaction*for improving the efficiency*of*dynamic power simulators. ... probability*of*the minimum-*weight*edge becomes*zero*. ...##
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A New Path to Code-based Signatures via Identification Schemes with Restricted Errors
[article]

2021
*
arXiv
*
pre-print

As a concrete application, we describe how

arXiv:2008.06403v3
fatcat:cbrrlayonfdjnltu6cav6slb74
*Zero*-*Knowledge*Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to*compact*public keys as well as significantly ... In this paper we introduce a variant*of*the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries*of*the searched vector are defined over a subset*of*the underlying ... ., three-pass*proofs**of**knowledge*for a certain relation. ...##
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A Circuit-Based Approach to Efficient Enumeration

2017
*
International Colloquium on Automata, Languages and Programming
*

Moreover, valuations

doi:10.4230/lipics.icalp.2017.111
dblp:conf/icalp/AmarilliBJM17
fatcat:2pzmzkghbzhmznn24eovmavp4e
*of*constant*Hamming**weight*can be enumerated with linear preprocessing and constant delay. ... We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the*Hamming**weight**of*each valuation. ... ., computing the i-th valuation [6, 9] ; managing updates [28] ; or enumerating in order*of**weight*, or in lexicographic order: this latter problem is open for MSO [33, Section 6.1] but results are known ...##
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Geometric variants of the Hofer norm
[article]

2006
*
arXiv
*
pre-print

The main step in the

arXiv:math/0103089v3
fatcat:5niq4su2srcdnlhb6r4qmhpegi
*proof*is to show that a "*weighted*" version*of*the nonsqueezing theorem holds for all fibrations over S^2 generated by sufficiently short loops.Further, an example is given showing ... that the Hofer norm may differ from the sum*of*the one sided seminorms. ...*Proof**of*Claim: We first show that M J is*compact*for all fibered J. ...##
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A New Simulation Approach to Performance Evaluation of Binary Linear Codes in the Extremely Low Error Rate Region
[article]

2016
*
arXiv
*
pre-print

*of*those conditions, which involve SNRs and can be calculated numerically. ... Interestingly and importantly, the derivation

*of*the SB based on nested Gallager regions suggests us a new simulation approach to performance evaluation

*of*binary linear codes over additive white Gaussian ... In contrast to the

*proof*by setting the derivative to be

*zero*, the above

*proof*is more insightful, which actually suggests a more

*compact*form

*of*the GFBT based on nested regions R(r), as given by Pr{E ...

##
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Loops in the Hamiltonian group: a survey
[article]

2009
*
arXiv
*
pre-print

We describe conditions under which a circle action does not contract in the Hamiltonian group, and construct an example

arXiv:0711.4086v2
fatcat:lkxszza5hvetrine6johir4p7e
*of*a loop*of*diffeomorphisms*of*a symplectic manifold M with the property that none ...*of*the loops smoothly isotopic to preserve any symplectic form on M. ... All mistakes are*of*course the responsibility*of*the author. ...
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