Zero Knowledge with Rubik’s Cubes and Non-abelian Groups

2013 ◽  
pp. 74-91 ◽  
Author(s):  
Emmanuel Volte ◽  
Jacques Patarin ◽  
Valérie Nachef
Keyword(s):  
Abelian Groups ◽  
Zero Knowledge

Publicly auditable conditional blind signatures

2021 ◽  
Vol 29 (2) ◽  
pp. 229-271
Author(s):  
Panagiotis Grontas ◽  
Aris Pagourtzis ◽  
Alexandros Zacharakis ◽  
Bingsheng Zhang
Keyword(s):  
Proof Of Concept ◽  
Equivalence Test ◽  
Zero Knowledge ◽  
Private Key ◽  
Blind Signatures ◽  
Cryptographic Primitive ◽  
Security Properties ◽  
Designated Verifier

This work formalizes Publicly Auditable Conditional Blind Signatures (PACBS), a new cryptographic primitive that allows the verifiable issuance of blind signatures, the validity of which is contingent upon a predicate and decided by a designated verifier. In particular, when a user requests the signing of a message, blinded to protect her privacy, the signer embeds data in the signature that makes it valid if and only if a condition holds. A verifier, identified by a private key, can check the signature and learn the value of the predicate. Auditability mechanisms in the form of non-interactive zero-knowledge proofs are provided, so that a cheating signer cannot issue arbitrary signatures and a cheating verifier cannot ignore the embedded condition. The security properties of this new primitive are defined using cryptographic games. A proof-of-concept construction, based on the Okamoto–Schnorr blind signatures infused with a plaintext equivalence test is presented and its security is analyzed.

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

scholarly journals An access control model for the Internet of Things based on zero-knowledge token and blockchain

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lihua Song ◽  
Xinran Ju ◽  
Zongke Zhu ◽  
Mengchen Li
Keyword(s):  
Internet Of Things ◽  
Access Control ◽  
Single Point ◽  
Control Model ◽  
Third Party ◽  
Security Level ◽  
Zero Knowledge ◽  
Access Control Model ◽  
Test Analysis ◽  
Zero Knowledge Proof

AbstractInformation security has become a hot topic in Internet of Things (IoT), and traditional centralized access control models are faced with threats such as single point failure, internal attack, and central leak. In this paper, we propose a model to improve the access control security of the IoT, which is based on zero-knowledge proof and smart contract technology in the blockchain. Firstly, we deploy attribute information of access control in the blockchain, which relieves the pressure and credibility problem brought by the third-party information concentration. Secondly, encrypted access control token is used to gain the access permission of the resources, which makes the user's identity invisible and effectively avoids attribute ownership exposure problem. Besides, the use of smart contracts solves the problem of low computing efficiency of IoT devices and the waste of blockchain computing power resources. Finally, a prototype of IoT access control system based on blockchain and zero-knowledge proof technology is implemented. The test analysis results show that the model achieves effective attribute privacy protection, compared with the Attribute-Based Access Control model of the same security level, the access efficiency increases linearly with the increase of access scale.

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