scholarly journals Statically Aggregate Verifiable Random Functions and Application to E-Lottery

Cryptography ◽  
2020 ◽  
Vol 4 (4) ◽  
pp. 37
Author(s):  
Bei Liang ◽  
Gustavo Banegas ◽  
Aikaterini Mitrokotsa
Keyword(s):  
Random Function ◽  
Random Functions ◽  
Large Sets ◽  
Diffie Hellman ◽  
Winning Number ◽  
Verifiable Random Functions

Cohen, Goldwasser, and Vaikuntanathan (TCC’15) introduced the concept of aggregate pseudo-random functions (PRFs), which allow efficiently computing the aggregate of PRF values over exponential-sized sets. In this paper, we explore the aggregation augmentation on verifiable random function (VRFs), introduced by Micali, Rabin and Vadhan (FOCS’99), as well as its application to e-lottery schemes. We introduce the notion of static aggregate verifiable random functions (Agg-VRFs), which perform aggregation for VRFs in a static setting. Our contributions can be summarized as follows: (1) we define static aggregate VRFs, which allow the efficient aggregation of VRF values and the corresponding proofs over super-polynomially large sets; (2) we present a static Agg-VRF construction over bit-fixing sets with respect to product aggregation based on the q-decisional Diffie–Hellman exponent assumption; (3) we test the performance of our static Agg-VRFs instantiation in comparison to a standard (non-aggregate) VRF in terms of costing time for the aggregation and verification processes, which shows that Agg-VRFs lower considerably the timing of verification of big sets; and (4) by employing Agg-VRFs, we propose an improved e-lottery scheme based on the framework of Chow et al.’s VRF-based e-lottery proposal (ICCSA’05). We evaluate the performance of Chow et al.’s e-lottery scheme and our improved scheme, and the latter shows a significant improvement in the efficiency of generating the winning number and the player verification.

scholarly journals A Novel Construction of Constrained Verifiable Random Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Muhua Liu ◽  
Ping Zhang ◽  
Qingtao Wu
Keyword(s):  
Random Function ◽  
Secret Key ◽  
Bilinear Maps ◽  
Random Functions ◽  
Compute Function ◽  
Multilinear Maps ◽  
Verifiable Random Functions ◽  
Selective Security

Constrained verifiable random functions (VRFs) were introduced by Fuchsbauer. In a constrained VRF, one can drive a constrained key skS from the master secret key sk, where S is a subset of the domain. Using the constrained key skS, one can compute function values at points which are not in the set S. The security of constrained VRFs requires that the VRFs’ output should be indistinguishable from a random value in the range. They showed how to construct constrained VRFs for the bit-fixing class and the circuit constrained class based on multilinear maps. Their construction can only achieve selective security where an attacker must declare which point he will attack at the beginning of experiment. In this work, we propose a novel construction for constrained verifiable random function from bilinear maps and prove that it satisfies a new security definition which is stronger than the selective security. We call it semiadaptive security where the attacker is allowed to make the evaluation queries before it outputs the challenge point. It can immediately get that if a scheme satisfied semiadaptive security, and it must satisfy selective security.

Fonctions Certaines Admettant des Répartitions Asymptotiques et Fonctions Aléatoires Stationnaires

1975 ◽  
Vol 12 (S1) ◽  
pp. 177-185
Author(s):  
A. Blanc-Lapierre
Keyword(s):  
Harmonic Analysis ◽  
Random Function ◽  
Random Variables ◽  
Random Variable ◽  
Type A ◽  
Asymptotic Distributions ◽  
Random Functions ◽  
Stationary Random Function ◽  
Translation Parameter ◽  
Character Independence

In the article below, we consider sets of non-random functions of time t admitting certain asymptotic distributions. Purely temporal and deterministic considerations lead us to associate to a set , say, of functions H(t) of this type, a space Ω of samples ω.To each function H(t) ⊂ , there corresponds a random variable h (ω). To the set of translated functions H(t + λ) of a function H(t) ⊂ , there corresponds a stationary random function of the translation parameter λ, say, h(λ, ω). We study the transposition to the set of non-random functions H(t) of such properties as moments, gaussian character, independence, harmonic analysis, and others, of the random variables h (ω) and of the random functions h (λ, ω).Some remarks are made concerning the links between ergodicity and the above problems.

scholarly journals A Stone-Weierstrass theorem for random functions

1970 ◽  
Vol 2 (2) ◽  
pp. 233-236 ◽  
Author(s):  
A. Mukherjea
Keyword(s):  
Random Function ◽  
Random Variables ◽  
Compact Set ◽  
Mean Square ◽  
Weierstrass Theorem ◽  
Random Functions ◽  
The Given ◽  
Uniformly Bounded

It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.

VECTOR RANDOM FIELDS WITH LONG-RANGE DEPENDENCE

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 249-258 ◽  
Author(s):  
CHUNSHENG MA
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Random Function ◽  
Short Range ◽  
Diagonal Entry ◽  
Random Functions ◽  
Cross Covariance ◽  
Direct Covariance ◽  
Crucial Ingredient ◽  
Special Case

It is well-known that the crucial ingredient for a vector Gaussian random function is its covariance matrix, where a diagonal entry termed a direct covariance is simply the covariance function of a component but it seems no simple interpretation for an off-diagonal entry termed a cross covariance, which often make it hard to specify. In this paper we employ three approaches to derive vector random functions in space and/or time, which are not homogeneous (stationary) in general but contain the stationary case as a special case, and have long-range or short-range dependence.

scholarly journals Feller chains and random functions

2015 ◽  
Vol 56 ◽  
Author(s):  
Vytautas Kazakevičius
Keyword(s):  
Random Function ◽  
Transition Probability ◽  
The Other ◽  
One Dimensional ◽  
Random Functions ◽  
Other Hand ◽  
Dimensional Distribution ◽  
The One

We prove that each Feller transition probability is the one-dimensional distribution of some stochastically continuous random function. We also introduce the notion of a regular random function and show, on one hand, that every random  function has a regular modification, and on the other hand, that the composition of independent regular stochastically continuous random functions is stochastically continuous as well.

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