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Proofs of Knowledge for Non-monotone Discrete-Log Formulae and Applications
[chapter]

2002
*
Lecture Notes in Computer Science
*

This paper addresses the problem

doi:10.1007/3-540-45811-5_21
fatcat:imiwp5ea3vexph7dm6p2r52d74
*of*defining*and*providing*proofs**of**knowledge**for*a general class*of*exponentiation-based*formulae*. ... We sketch two*applications*by which we enhance group signatures schemes with revocation*of*identity*and*multi-signer features. ... DCR-predicates capture as a particular case*proofs**of**knowledge**of**discrete*logarithms or representations, as well as equality*of**discrete**logs*("*AND*") or*knowledge**of*one*discrete**log*out*of*n (disjunctive ...##
###
Log-concavity for series in reciprocal gamma functions and applications
[article]

2012
*
arXiv
*
pre-print

We demonstrate that the sum is

arXiv:1206.4814v1
fatcat:l372xnu23rd7feb2ylhcxxic6q
*log*-concave if the sequence*of*coefficients times factorial is*log*-concave*and*the sum is*discrete*Wright*log*-concave if the coefficents are*log*-concave. ... Additivity*of*logarithmic convexity implies that the function sum*of*gammas with*non*-negative coefficients is also*log*-convex. ... Hence by Lemma 2 we conclude that λ m > 0 implying*discrete*Wright*log*-concavity*of*µ → g(µ, x)*for*each x ≥ 0*and*absolutely*monotonicity**of*x → λ β,µ (x). ...##
###
Linear Zero-Knowledgde. A Note on Efficient Zero-Knowledge Proofs and Arguments

1996
*
BRICS Report Series
*

<br />Both protocols are also

doi:10.7146/brics.v3i7.19970
fatcat:72ffeyehq5db7j6fcjeik7jjva
*proofs**of**knowledge**of*an NP-witness*of*membership in<br />the language involved. ... <br />Moreover, the constants involved are small enough*for*the protocols to be practical in<br />a realistic situation: both protocols are based on a Boolean*formula*Phi containing*and*-<br />, or-*and*... However, it is currently an open problem to prove anything about the soundness*and*"*discreteness*"*of*the*proofs*from [2] , even assuming hardness*of*factoring or*discrete**log*. ...##
###
Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness

2015
*
Duke mathematical journal
*

We use this to prove convexity type

doi:10.1215/00127094-3164790
fatcat:doadw72e55erbaeajzvhuvufue
*and*propagation*of*smallness results*for*harmonic functions on the lattice. ... In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand*and*absolutely*monotonic*functions on the other hand. ... Our preliminary results in the*discrete*setting in- ...##
###
Rapid Demonstration of Linear Relations Connected by Boolean Operators
[chapter]

1997
*
Lecture Notes in Computer Science
*

Our protocols support many

doi:10.1007/3-540-69053-0_22
fatcat:zr6akke3w5awbhaymccq3jsg3e
*proof*modes,*and*are as secure as the*Discrete*Logarithm assumption or the RSA/factoring assumption. ... Consider a polynomial-time prover holding a set*of*secrets. ... If a*monotone**formula*has m logical connectives, then this technique requires the prover to perform m*proofs**of**knowledge*, one*for*each sub-*formula*. ...##
###
Efficient Zero-Knowledge Proofs of Knowledge without Intractability Assumptions
[chapter]

2000
*
Lecture Notes in Computer Science
*

Instantiations

doi:10.1007/978-3-540-46588-1_24
fatcat:hipqekvb45hyfhmk65nwrwqgyu
*of*our main protocol lead to efficient perfect ZK*proofs**of**knowledge**of**discrete*logarithms*and*RSA-roots, or more generally, q-one-way group homomorphisms. ... In its most general incarnation, our result says that*for*relations that have a particular three-move honest-verifier zero-*knowledge*(HVZK)*proof**of**knowledge*,*and*which admit a particular three-move HVZK ... There are several known protocols*of*this form, e.g., [Sch89]*for**discrete**logs**and*[GQ88]*for*RSA roots. ...##
###
Learning Pseudo-Booleank-DNF and Submodular Functions
[chapter]

2013
*
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Our learning algorithm implies a property tester

doi:10.1137/1.9781611973105.98
dblp:conf/soda/RaskhodnikovaY13
fatcat:psohoyrxz5bltjq2zmo45adzyi
*for*submodularity*of*functions f : {0, 1} n → {0, . . . , k} with query complexity polynomial in n*for*k = O((*log*n/*log**log*n) 1/2 )*and*constant proximity ... We show that an analog*of*Håstad's switching lemma holds*for*pseudo-Boolean k-DNFs if all constants associated with the terms*of*the*formula*are bounded. ... Acknowledgments We are grateful to Jan Vondrak, Vitaly Feldman, Lev Reyzin, Nick Harvey, Paul Beame, Ryan O'Donnell*and*other people*for*their feedback*and*comments on the results in this paper. ...##
###
Strengthening convex relaxations of 0/1-sets using Boolean formulas

2020
*
Mathematical programming
*

As one

doi:10.1007/s10107-020-01542-w
pmid:34776534
pmcid:PMC8550646
fatcat:i2qtr3izxzhuta5ahhsobak7am
*application*, interpreting an iterated*application**of*our procedure as a hierarchy, our findings simplify, improve,*and*extend previous results by Bienstock*and*Zuckerberg on covering problems. ... Namely, the required extra information will be in the form*of*a Boolean*formula*ϕ defining the target set S. The new relaxation is obtained by "feeding" the convex set into the*formula*ϕ . ... This work was done while Samuel Fiorini was visiting the Simons Institute*for*the Theory*of*Computing. ...##
###
Effective capacity of a correlated Rayleigh fading channel

2010
*
Wireless Communications and Mobile Computing
*

In their previous work, Wu

doi:10.1002/wcm.945
fatcat:csjkcvlgtffenmj2ko333swnqu
*and*Negi derived a*formula**for*effective capacity*of*a Rayleigh fading channel with arbitrary Doppler spectrum. ... To address this difficulty, we develop a verification methodology based on a new*discrete*-frequency EC*formula*; different from the EC*formula*developed by Wu*and*Negi, our new*discrete*-frequency EC*formula*... Since S(f i ) ≥ 0*andŜ*(f i ) ≥ 0, we only need to prove v*log*( a+v b+v ) is a*monotonically*increasing function*of*v*for*v > 0*and*a ≥ 0, b ≥ 0. Now we prove this. ...##
###
Complementarity in atomic and oscillator systems

2010
*
Physics Letters A
*

We develop a unified, information theoretic interpretation

doi:10.1016/j.physleta.2010.05.050
fatcat:rngmquseuzbrjnll6qgdmppbim
*of*the number-phase complementarity that is*applicable*both to finite-dimensional (atomic)*and*infinite-dimensional (oscillator) systems. ... The relevant uncertainty principle is obtained as a lower bound on entropy excess, the difference between number entropy*and*phase*knowledge*, the latter defined as the relative entropy with respect to ... to use a combination*of*entropy*and**knowledge*, in particular, the difference between entropy*of*the*discrete*, infinite observable*and*between phase*knowledge*. ...##
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Page 10247 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

*of*the class

*of*all

*non*-

*monotonic*

*knowledge*bases. ... SLPs constitute also a special case

*of*the powerful

*non*-

*monotonic*formalism called 68N Software 2004m:68019 Autoepistemic Logic

*of*

*Knowledge*

*and*Belief (AELB), intro- duced by Teodor Przymusinski (1994 ...

##
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End-point corrected trapezoidal quadrature rules for singular functions

1990
*
Computers and Mathematics with Applications
*

The algorithm is

doi:10.1016/0898-1221(90)90348-n
fatcat:j4bf6kbfwvg2xdnbt5birixnye
*applicable*to a wide class*of**monotonic*singularities*and*does not require that an analytical expression*for*the singularity be known; only the*knowledge**of*its first several moments*and*... Abatract--A group*of*quadrature*formulae**for*end-point singular functions is presented generalizing classical end-point corrected trapezoidal quadrature rules. ... Then*for*Sufficiently large n, the matrix A ~*of*the system (6), (7) is*non*-singular,*and*the convergence rate*of*T~: at least k.*Proof*. ...##
###
Strengthening Convex Relaxations of 0/1-Sets Using Boolean Formulas
[article]

2018
*
arXiv
*
pre-print

As one result, interpreting an iterated

arXiv:1711.01358v3
fatcat:p3yvosmvdjef3cob6juvpyb4oy
*application**of*our procedure as a hierarchy, our findings simplify, improve,*and*extend previous results by Bienstock*and*Zuckerberg on covering problems. ... Namely, the required extra information will be in the form*of*a Boolean*formula*ϕ defining the target set S . ...*Applications*In this section, we present several*applications**of*our procedure, in which we repeatedly make use*of*Theorems 4*and*5. 5.1.*Monotone**formulas**for*matching. ...##
###
Learning pseudo-Boolean k-DNF and Submodular Functions
[article]

2012
*
arXiv
*
pre-print

Our algorithm runs in time polynomial in n, k^O(k k / ϵ), 1/ϵ

arXiv:1208.2294v1
fatcat:i2jq5s6qgvhm5npjolofegqx7u
*and**log*(1/δ)*and*works even in the agnostic setting. ... We show that an analog*of*Hastad's switching lemma holds*for*pseudo-Boolean k-DNFs if all constants associated with the terms*of*the*formula*are bounded. ... Acknowledgments We are grateful to Jan Vondrak, Vitaly Feldman, Lev Reyzin, Nick Harvey, Paul Beame, Ryan O'Donnell*and*other people*for*their feedback*and*comments on the results in this paper. ...##
###
An Efficient and Usable Multi-show Non-transferable Anonymous Credential System
[chapter]

2004
*
Lecture Notes in Computer Science
*

In an anonymous credential system a user can prove anonymously the possession

doi:10.1007/978-3-540-27809-2_21
fatcat:j4apck3ztbhqta754b6mtwq2i4
*of*credentials to a service provider. Multi-show*and**non*-transferability are two important properties*of*such systems. ... In this paper we give a construction*for*multi-show*non*-transferable credentials*for*which the owner can prove that the credentials satisfy access control policies expressed by means*of*linear boolean ... constant) due to a*proof**of**knowledge**of*an RSA representation that is very efficient*and*a constant factor due to one*proof**of**knowledge**of*a double*discrete**log*. ...
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