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

Emmanuel Bresson, Jacques Stern
2002 Lecture Notes in Computer Science  
This paper addresses the problem 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  ... 
doi:10.1007/3-540-45811-5_21 fatcat:imiwp5ea3vexph7dm6p2r52d74

Log-concavity for series in reciprocal gamma functions and applications [article]

S. I. Kalmykov, D. B. Karp
2012 arXiv   pre-print
We demonstrate that the sum is 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).  ... 
arXiv:1206.4814v1 fatcat:l372xnu23rd7feb2ylhcxxic6q

Linear Zero-Knowledgde. A Note on Efficient Zero-Knowledge Proofs and Arguments

Ivan B. Damgård, Ronald Cramer
1996 BRICS Report Series  
<br />Both protocols are also 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.  ... 
doi:10.7146/brics.v3i7.19970 fatcat:72ffeyehq5db7j6fcjeik7jjva

Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness

Gabor Lippner, Dan Mangoubi
2015 Duke mathematical journal  
We use this to prove convexity type 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-  ... 
doi:10.1215/00127094-3164790 fatcat:doadw72e55erbaeajzvhuvufue

Rapid Demonstration of Linear Relations Connected by Boolean Operators [chapter]

Stefan Brands
1997 Lecture Notes in Computer Science  
Our protocols support many 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.  ... 
doi:10.1007/3-540-69053-0_22 fatcat:zr6akke3w5awbhaymccq3jsg3e

Efficient Zero-Knowledge Proofs of Knowledge without Intractability Assumptions [chapter]

Ronald Cramer, Ivan Damgård, Philip MacKenzie
2000 Lecture Notes in Computer Science  
Instantiations 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.  ... 
doi:10.1007/978-3-540-46588-1_24 fatcat:hipqekvb45hyfhmk65nwrwqgyu

Learning Pseudo-Booleank-DNF and Submodular Functions [chapter]

Sofya Raskhodnikova, Grigory Yaroslavtsev
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
Our learning algorithm implies a property tester 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.  ... 
doi:10.1137/1.9781611973105.98 dblp:conf/soda/RaskhodnikovaY13 fatcat:psohoyrxz5bltjq2zmo45adzyi

Strengthening convex relaxations of 0/1-sets using Boolean formulas

Samuel Fiorini, Tony Huynh, Stefan Weltge
2020 Mathematical programming  
As one 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.  ... 
doi:10.1007/s10107-020-01542-w pmid:34776534 pmcid:PMC8550646 fatcat:i2qtr3izxzhuta5ahhsobak7am

Effective capacity of a correlated Rayleigh fading channel

Qing Wang, Dapeng Wu, Pingyi Fan
2010 Wireless Communications and Mobile Computing  
In their previous work, Wu 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.  ... 
doi:10.1002/wcm.945 fatcat:csjkcvlgtffenmj2ko333swnqu

Complementarity in atomic and oscillator systems

R. Srikanth, Subhashish Banerjee
2010 Physics Letters A  
We develop a unified, information theoretic interpretation 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.  ... 
doi:10.1016/j.physleta.2010.05.050 fatcat:rngmquseuzbrjnll6qgdmppbim

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  ... 

End-point corrected trapezoidal quadrature rules for singular functions

V. Rokhlin
1990 Computers and Mathematics with Applications  
The algorithm is 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.  ... 
doi:10.1016/0898-1221(90)90348-n fatcat:j4bf6kbfwvg2xdnbt5birixnye

Strengthening Convex Relaxations of 0/1-Sets Using Boolean Formulas [article]

Samuel Fiorini, Tony Huynh, Stefan Weltge
2018 arXiv   pre-print
As one result, 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 .  ...  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.  ... 
arXiv:1711.01358v3 fatcat:p3yvosmvdjef3cob6juvpyb4oy

Learning pseudo-Boolean k-DNF and Submodular Functions [article]

Sofya Raskhodnikova, Grigory Yaroslavtsev
2012 arXiv   pre-print
Our algorithm runs in time polynomial in n, k^O(k k / ϵ), 1/ϵ 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.  ... 
arXiv:1208.2294v1 fatcat:i2jq5s6qgvhm5npjolofegqx7u

An Efficient and Usable Multi-show Non-transferable Anonymous Credential System [chapter]

Giuseppe Persiano, Ivan Visconti
2004 Lecture Notes in Computer Science  
In an anonymous credential system a user can prove anonymously the possession 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.  ... 
doi:10.1007/978-3-540-27809-2_21 fatcat:j4apck3ztbhqta754b6mtwq2i4
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