scholarly journals Extracting Witnesses from Proofs of Knowledge in the Random Oracle Model

2001 ◽  
Vol 8 (52) ◽  
Author(s):  
Jens Groth
Keyword(s):  
Random Oracle Model ◽  
Random Oracle ◽  
Proof System ◽  
Interactive Proof ◽  
Proof Of Knowledge ◽  
Proofs Of Knowledge ◽  
Voting Scheme ◽  
Definition Of ◽  
Interactive Proof System ◽  
Threshold Encryption

We prove that a 3-move interactive proof system with the special soundness property made non-interactive by applying the Fiat-Shamir heuristic is almost a non-interactive proof of knowledge in the random oracle model. In an application of the result we demonstrate that the Damgård-Jurik voting scheme based on homomorphic threshold encryption is secure against a nonadaptive adversary according to Canetti's definition of multi-party computation security.

REMARKS ON A QUERY-BASED VARIANT OF THE PARALLEL REPETITION THEOREM

2001 ◽  
Vol 12 (04) ◽  
pp. 517-531
Author(s):  
OLEG VERBITSKY
Keyword(s):  
Strong Correlation ◽  
Error Probability ◽  
Cryptographic Protocols ◽  
Parallel Execution ◽  
Proof System ◽  
Interactive Proof ◽  
Parallel Repetition ◽  
Interactive Proof System

The Parallel Repetition Theorem says that n-fold parallel execution of a two-prover one-round interactive proof system reduces the error probability exponentially in n. The bound on the error probability of the parallelized system depends on the error probability and the answer size of the single proof system. It is still unknown whether the theorem holds true with a bound depending only on the query size. This kind of a bound may be preferable whenever the query size is considerably smaller than the answer size, what really happens in some cryptographic protocols. Such a bound is only known in the case that queries to the provers are independent. The present paper extends this result to some cases of strong correlation between queries. In particular, a query-based variant of the Parallel Repetition Theorem is proven when the graph of dependence between queries to the provers is a tree and, in a bit weaker form, when this graph is a cycle.

scholarly journals Program extraction applied to monadic parsing

2019 ◽  
Vol 29 (4) ◽  
pp. 487-518 ◽  
Author(s):  
Ulrich Berger ◽  
Alison Jones ◽  
Monika Seisenberger
Keyword(s):  
Natural Language ◽  
Case Studies ◽  
Proof System ◽  
Theoretic Approach ◽  
Formal Proofs ◽  
Interactive Proof ◽  
Program Extraction ◽  
Interactive Proof System

Abstract This article outlines a proof-theoretic approach to developing correct and terminating monadic parsers. Using modified realizability, we extract formally verified and terminating programs from formal proofs. By extracting both primitive parsers and parser combinators, it is ensured that all complex parsers built from these are also correct, complete and terminating for any input. We demonstrate the viability of our approach by means of two case studies: we extract (i) a small arithmetic calculator and (ii) a non-deterministic natural language parser. The work is being carried out in the interactive proof system Minlog.

scholarly journals Scalable Revocable Identity-Based Signature Scheme with Signing Key Exposure Resistance from Lattices

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Congge Xie ◽  
Jian Weng ◽  
Jinming Wen
Keyword(s):  
Quantum Computing ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Signature Scheme ◽  
Integer Solutions ◽  
Identity Based ◽  
Definition Of ◽  
Lattice Based Cryptography ◽  
Key Exposure

In 2014, a new security definition of a revocable identity-based signature (RIBS) with signing key exposure resistance was introduced. Based on this new definition, many scalable RIBS schemes with signing key exposure resistance were proposed. However, the security of these schemes is based on traditional complexity assumption, which is not secure against attacks in the quantum era. Lattice-based cryptography has many attractive features, and it is believed to be secure against quantum computing attacks. We reviewed existing lattice-based RIBS schemes and found that all these schemes are vulnerable to signing key exposure. Hence, in this paper, we propose the first lattice-based RIBS scheme with signing key exposure resistance by using the left-right lattices and delegation technology. In addition, we employ a complete subtree revocation method to ensure our construction meeting scalability. Finally, we prove that our RIBS scheme is selective-ID existentially unforgeable against chosen message attacks (EUF-sID-CMA) under the standard short integer solutions (SIS) assumption in the random oracle model.

scholarly journals Physical cryptographic verification of nuclear warheads

2016 ◽  
Vol 113 (31) ◽  
pp. 8618-8623 ◽  
Author(s):  
R. Scott Kemp ◽  
Areg Danagoulian ◽  
Ruaridh R. Macdonald ◽  
Jayson R. Vavrek
Keyword(s):  
Nuclear Weapon ◽  
Proof System ◽  
Interactive Proof ◽  
Highly Sensitive ◽  
Tomographic Method ◽  
Nuclear Arms Control ◽  
Arbitrary Precision ◽  
Interactive Proof System ◽  
Nuclear Warhead ◽  
Provably Secure

How does one prove a claim about a highly sensitive object such as a nuclear weapon without revealing information about the object? This paradox has challenged nuclear arms control for more than five decades. We present a mechanism in the form of an interactive proof system that can validate the structure and composition of an object, such as a nuclear warhead, to arbitrary precision without revealing either its structure or composition. We introduce a tomographic method that simultaneously resolves both the geometric and isotopic makeup of an object. We also introduce a method of protecting information using a provably secure cryptographic hash that does not rely on electronics or software. These techniques, when combined with a suitable protocol, constitute an interactive proof system that could reject hoax items and clear authentic warheads with excellent sensitivity in reasonably short measurement times.

Circular Transitivity of a Bidirectional Proxy Re-Encryption Scheme

2013 ◽  
Vol 321-324 ◽  
pp. 2639-2642
Author(s):  
Xiao Jing Hong ◽  
Bin Wang
Keyword(s):  
Random Oracle Model ◽  
Random Oracle ◽  
Formal Definition ◽  
Encryption Scheme ◽  
Cdh Assumption ◽  
Definition Of

The concept of proxy re-encryption (PRE) was first introduced by Blaze et al. Since then several CCA secure PRE schemes have been presented. Weng et al. proposed a non-transitive bidirectional PRE scheme without pairings and proved that their scheme to be PRE-CCA secure in the random oracle model under the CDH assumption. However, we show that Weng et als non-transitive scheme is still transitive under the formal definition of non-transitivity presented in this paper. Moreover, the transitivity of Weng et al.s scheme also implies that it is not PRE-CCA secure.

Novel Identity-Based Hash Proof System with Compact Master Public Key from Lattices in the Standard Model

2019 ◽  
Vol 30 (04) ◽  
pp. 589-606
Author(s):  
Qiqi Lai ◽  
Bo Yang ◽  
Zhe Xia ◽  
Yannan Li ◽  
Yuan Chen ◽  
...  
Keyword(s):  
Standard Model ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Public Key ◽  
Proof System ◽  
Secret Key ◽  
Random Lattice ◽  
The Standard Model ◽  
Identity Based ◽  
Hash Proof System

As the progress of quantum computers, it is desired to propose many more efficient cryptographic constructions with post-quantum security. In the literatures, almost all cryptographic schemes and protocols can be explained and constructed modularly from certain cryptographic primitives, among which an Identity-Based Hash Proof System (IB-HPS) is one of the most basic and important primitives. Therefore, we can utilize IB-HPSs with post-quantum security to present several types of post-quantum secure schemes and protocols. Up until now, all known IB-HPSs with post-quantum security are instantiated based on latticed-based assumptions. However, all these lattice-based IB-HPSs are either in the random oracle model or not efficient enough in the standard model. Hence, it should be of great significance to construct more efficient IB-HPSs from lattices in the standard model. In this paper, we propose a new smooth IB-HPS with anonymity based on the Learning with Errors (LWE) assumption in the standard model. This new construction is mainly inspired by a classical identity-based encryption scheme based on LWE due to Agreawal et al. in Eurocrypt 2010. And our innovation is to employ the algorithm SampleGaussian introduced by Gentry et al. and the property of random lattice to simulate the identity secret key with respect to the challenge identity. Compared with other existing IB-HPSs in the standard model, our master public key is quite compact. As a result, our construction has much lower overheads on computation and storage.

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