Zero-knowledge Proofs Of Knowledge Research Articles

Analysis and Construction of Zero-Knowledge Proofs for the MinRank Problem

Abstract The MinRank problem is an NP-complete problem that is prevalent in multivariate cryptography and its goal is to find a non-zero linear combination of given a series of matrices over a ring such that the obtained matrix has a small rank. At Asiacrypt 2001, two Zero-Knowledge Proofs of Knowledge (ZKPoK) for the MinRank problem are proposed, and we call them MRZK and MRZK$^{\dagger }$, respectively. The latter is an improved version of the proof size of the former. However, the efficiency of MRZK$^{\dagger }$ has been open and not analyzed. While the MRZK protocol is secure, it must be repeated many times due to the soundness error $2/3$, which leads to the large proof size. For 128-bit security, the MRZK protocol is executed at least 219 iterations and the proof size is about 32 KB. In this paper, we first show that the efficiency of MRZK$^{\dagger }$ is impractical due to unreasonable parameter size. However, when the parameter size is tuned and the efficiency is improved, an imposter can be efficiently constructed. Then, to alleviate the large proof size of MRZK, inspired by the technique designing ZKPoK (Eurocrypt 2020), we propose a sigma protocol with helper to prove the solution to the MinRank problem. Finally, we transform the sigma protocol with helper into a standard ZKPoK (MRZK$^{\sharp }$) by removing the helper. The MRZK$^{\sharp }$ protocol can achieve any small soundness error and enjoy the proof size of about 15 KB (53% improvement over MRZK).

Location privacy in VANETs: Provably secure anonymous key exchange protocol based on self-blindable signatures

Security and privacy in vehicular ad hoc networks (VANETs) are challenging in terms of Intelligent Transportation Systems (ITS) features. The distribution and decentralisation of vehicles could threaten location privacy and confidentiality in the absence of trusted third parties (TTP)s or if they are otherwise compromised. If the same digital signatures (or the same certificates) are used for different communications, then adversaries could easily apply linking attacks. Unfortunately, most of the existing schemes for VANETs in the literature do not satisfy the required levels of security, location privacy, and efficiency simultaneously. This paper presents a new and efficient end-to-end anonymous key exchange protocol based on Yang et al. 's self-blindable signatures. In our protocol, vehicles first privately blind their own private certificates for each communication outside the mix-zone and then compute an anonymous shared key based on zero-knowledge proof of knowledge (PoK). The efficiency comes from the fact that once the signatures are verified, the ephemeral values in PoK are also used to compute a shared key through an authenticated Diffie-Hellman key exchange protocol. Therefore, the protocol does not require any further external information to generate a shared key. Our protocol also does not require an interference with the Roadside Units or Certificate Authorities, and hence can be securely run outside the mixed-zones. We demonstrate the security of our protocol in an ideal/real simulation paradigm. Hence, our protocol achieves secure authentication, forward unlinkability, and accountability. Furthermore, the performance analysis shows that our protocol is more efficient in terms of computational and communication overheads compared to existing schemes.

ZKASP: ZKP-based attestation of software possession for measuring instruments

Software-controlled measuring instruments used in commercial transactions, such as fuel dispensers and smart meters, are sometimes subject to ‘memory replacement’ attacks. Cybercriminals replace the approved software by a malicious one that then tampers with measurement results, inflicting a financial loss to customers and companies. To mitigate such attacks, legal metrology systems often require regular device attestation, where an auditor checks that the device possesses (‘knows’) the approved software. However, current attestation methods usually require the software to be known by the auditor, thus increasing the risk of inadvertent leakage or malicious theft of proprietary information, besides facilitating its malicious adulteration. We describe how this issue can be addressed in legal metrology systems by using zero-knowledge proofs of knowledge (ZKPoK). These proofs enable attestation of possession of approved software, while ensuring its confidentiality from the auditor. To further provide publicly verifiable evidence of freshness, each such proof can be related to a fresh random value from a public randomness beacon. This article presents the basic conceptual idea, while also discussing pitfalls that should be avoided.

ZKASP: ZKP-based Attestation of Software Possession for Measuring Instruments

Abstract Software-controlled measuring instruments used in commercial transactions, such as fuel dispensers and smart meters, are sometimes subject to “memory replacement” attacks. Cybercriminals replace the approved software by a malicious one that then tampers with measurement results, inflicting a financial loss to customers and companies. To mitigate such attacks, legal metrology systems often require regular device attestation, where an auditor checks that the device possesses (“knows”) the approved software. However, current attestation methods usually require the software to be known by the auditor, thus increasing the risk of inadvertent leakage or malicious theft of proprietary information, besides facilitating its malicious adulteration. We describe how this issue can be addressed in legal metrology systems by using zero-knowledge proofs of knowledge (ZKPoK). These proofs enable attestation of possession of approved software, while ensuring its confidentiality from the auditor. To further provide publicly verifiable evidence of freshness, each such proof can be related to a fresh random value from a public randomness beacon. This article presents the basic conceptual idea, while also discussing pitfalls that should be avoided.

Comments on biometric-based non-transferable credentials and their application in blockchain-based identity management

In IT-ecosystems, access to unauthorized parties is prevented with credential-based access control techniques (locks, RFID cards, biometrics, etc.). Some of these methods are ineffective against malicious users who lend their credentials to other users. To obtain non-transferability, Adams proposed a combination of biometrics encapsulated in Pedersen commitment with Brands digital credential. However, Adams’ work does not consider the Zero Knowledge Proof-of Knowledge (ZKPoK) system for Double Discrete Logarithm Representation of the credential. Besides, biometrics is used directly, without employing any biometric cryptosystem to guarantee biometric privacy, thus Adams’ work cannot be GDPR-compliant. In this paper, we construct the missing ZKPoK protocol for Adam’s work and show its inefficiency. To overcome this limitation, we present a new biometric-based non-transferable credential scheme that maintains the efficiency of the underlying Brands credential. Secondly, we show the insecurity of the first biometric-based anonymous credential scheme designed by Blanton et al.. In this context, we present a brute-force attack against Blanton’s biometric key generation algorithm implemented for fuzzy vault. Next, we integrate an Oblivious PRF (OPRF) protocol to solve the open problem in Blanton’s work and improve its efficiency by replacing the underlying signature scheme with PS-signatures. Finally, we evaluate application scenarios for non-transferable digital/anonymous credentials in the context of Blockchain-based Identity Management (BBIM). We show that our modified constructions preserve biometric privacy and efficiency, and can easily be integrated into current BBIM systems built upon efficient Brands and PS-credentials.

Secure Automated Valet Parking: A Privacy-Preserving Reservation Scheme for Autonomous Vehicles

It is believed that automated valet parking (AVP) system has great potential to mitigate the parking headache for the future smart city, as it can provide on-demand parking services, bringing immense benefits from energy saving for vehicles to time saving for drivers. For an AVP system, parking reservation is an indispensable part so that vehicles can accomplish automated parking in accordance with the reserved parking information. However, the reservation requests may not only reveal the driver identity, but also disclose his/her sensitive locations, e.g., the most visited places, which are of great concerns to users. To deal with this challenge, the anonymous techniques can be naturally applied during parking reservation, but directly applying the anonymous techniques in AVP will introduce a new security issue, i.e., the anonymous user may maliciously crash the AVP system by repetitively sending the reservation requests, which is called “double-reservation attack.” In this paper, we propose a new privacy-preserving reservation scheme for securing AVP system. Specifically, each anonymous user must have only one valid reservation token at any moment, and the token can only be used for booking one vacant parking space once. The proposed scheme does not only preserve the user's identity privacy and location privacy but also prevents the “double-reservation attack” based on several elegant building blocks, i.e., zero-knowledge proofs of knowledge and proxy resignature. Detailed security analysis confirms the security properties of our proposed scheme. In addition, extensive simulations are conducted to compare our proposed scheme with three previous schemes, and the experiment results demonstrate that our scheme is also much efficient in a WiFi-based testbed.

PrivBioMTAuth: Privacy Preserving Biometrics-Based and User Centric Protocol for User Authentication From Mobile Phones

We introduce a privacy preserving biometrics-based authentication solution by which users can authenticate to different service providers from mobile phones without involving identity providers in the transactions. Authentication is performed via zero-knowledge proof of knowledge, based on a cryptographic identity token that encodes the biometric identifier of the user and a secret provided by the user, making it three-factor authentication. Our approach for generating a unique, repeatable, and revocable biometric identifier from the user’s biometric image is based on a machine learning-based classification technique, which involves the features extracted from the user’s biometric image. We have implemented a prototype of the proposed authentication solution and evaluated our solution with respect to its performance, security, and privacy. The evaluation has been performed on a public data set of face images.

ABE based Access Control with Authenticated Dynamic Policy Updating in Clouds

Attribute-Based Encryption (ABE) is a promising cryptographic primitive to implement access control for secure data storage in the cloud. Since the data owner may frequently change the access policies defined in the ciphertext, it is significant to provide the capacity for dynamic policy updating. However the cloud should also authenticate the owner because the adversary may modify the access policies of the files in the cloud to prevent the legal users from accessing them. In this paper, we focus on the owner’s authentication in the ABE systems and propose a novel scheme which enables access control with authenticated dynamic policy updating in the cloud. We adapt the Pedersen commitment and Zero Knowledge Proof of Knowledge (ZKPK) to realize the anonymous authentication of the owner’s policy updating key without increasing any secret information to the owner side. The analysis shows that our scheme is authentic and efficient as well as adaptive to different types of access policies.

Constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP

Barak and Lindell showed that there exist constant-round zero-knowledge arguments of knowledge with strict polynomial-time extractors. This leaves the open problem of whether it is possible to obtain an analogous result regarding constant-round zero-knowledge proofs of knowledge for NP. This paper focuses on this problem and gives a positive answer by presenting a construction of constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP.

Fully anonymous multi-service subscription system without random oracles

Lately,Canard et al.(CANARD S,JAMBERT A.Untraceability and profiling are not mutually exclusive [C]// TrustBus 2010:Proceedings of the 7th International Conference on Trust,Privacy and Security in Digital Business,LNCS 6264.Berlin:Springer-Verlag,2010:117-128) introduced the notion of multi-service subscription and proposed several instantiations.Unfortunately,their systems only satisfied a weaker variant of anonymity called revocable-anonymity and they were not fit for "pay-per-use" services.To this end,a revised multi-service subscription system was put forward to extending Canard et al's system.The new system achieved pay-per-use subscriptions by incorporating the anonymous payment system raised by Liu et al.(LIU J K,AU M H,SUSILO W,et al.Enhancing location privacy for electric vehicles(at the right time).[2012-08-01].http://eprint.iacr.org/2012/342).To allow users to prove in zero-knowledge that their account balance is enough for making a payment for the required access,it also utilized the Peng-Bao range proof for small ranges.Furthermore,it was constructed on several 4-round perfect zero-knowledge proofs of knowledge,which were obtained by applying a technique by Cramer et al.to the underlying Sigma-protocols.Compared with typical systems in the literature,the new solution gains advantages in terms of security.Concretely,it can be proved secure in the standard model.Moreover,it matches the strongest level of three crucial security notions,such as inseparability for spendable tokens,anonymity for users,and zero-knowledge for underlying proof systems.

Multifactor Identity Verification Using Aggregated Proof of Knowledge

The problem of identity theft, that is, the act of impersonating others' identities by presenting stolen identifiers or proofs of identities, has been receiving increasing attention because of its high financial and social costs. In this paper, we address the problem of verification of such identifiers and proofs of identity. Our approach is based on the concept of privacy preserving multifactor verification of such identifiers and proofs achieved by the development of a new cryptographic primitive, which uses aggregate signatures on commitments that are then used for aggregate zero-knowledge proof of knowledge (ZKPK) protocols. The resultant signatures are very short and the ZKPs are succinct and efficient. We prove the security of our scheme under the co-gap Diffie-Hellman (co-GDH) assumption for groups with bilinear maps. Our cryptographic scheme is an improvement in terms of the performance, flexibility, and storage requirements than the existing efficient ZKPK techniques that may be used to prove under zero knowledge and the knowledge of multiple secrets.

An Overview of VeryIDX - A Privacy-Preserving Digital Identity Management System for Mobile Devices

Users increasingly use their mobile devices to communicate, to conduct business transaction and access resources and services. In such a scenario, digital identity management (DIM) technology is fundamental in customizing user experience, protecting privacy, underpinning accountability in business transactions, and in complying with regulatory controls. Users identity consists of data, referred to as identity attributes , that encode relevant-security properties of the clients. However, identity attributes can be target of several attacks: the loss or theft of mobile devices results in a exposure of identity attributes; identity attributes that are send over WI-FI or 3G networks can be easily intercepted; identity attributes can also be captured via Bluetooth connections without the user’s consent; and mobile viruses, worms and Trojan horses can access the identity attributes stored on mobile devices if this information is not protected by passwords or PIN numbers. Therefore, assuring privacy and security of identity attributes, as well as of any sensitive information stored on mobile devices is crucial. In this paper we address such problems by proposing an approach to manage user identity attributes by assuring their privacypreserving usage. The approach is based on the concept of privacy preserving multi-factor authentication achieved by a new cryptographic primitive which uses aggregate signatures on commitments that are then used for aggregate zero-knowledge proof of knowledge (ZKPK) protocols. We present the implementation of such approach on Nokia NFC cellular phones and report performance evaluation results.

A New \mathcal{NP} -Complete Problem and Public-Key Identification

The appearance of the theory of zero-knowledge, presented by Goldwasser, Micali and Rackoff in 1985, opened a way to secure identification schemes. The first application was the famous Fiat-Shamir scheme based on the problem of modular square roots extraction. In the following years, many other schemes have been proposed, some Fiat-Shamir extensions but also new discrete logarithm based schemes. Therefore, all of them were based on problems from number theory. Their main common drawback is high computational load because of arithmetical operations modulo large integers. Implementation on low-cost smart cards was made difficult and inefficient. With the Permuted Kernels Problem (PKP), Shamir proposed the first efficient scheme allowing for an implementation on such low-cost smart cards, but very few others have afterwards been suggested. In this paper, we present an efficient identification scheme based on a combinatorial \mathcal{NP}-complete problem: the Permuted Perceptrons Problem (PPP). This problem seems hard enough to be unsolvable even with very small parameters, and some recent cryptanalysis studies confirm that position. Furthermore, it admits efficient zero-knowledge proofs of knowledge and so it is well-suited for cryptographic purposes. An actual implementation completes the optimistic opinion about efficiency and practicability on low-cost smart cards, and namely with less than 2KB of EEPROM and just 100 Bytes of RAM and 6.4 KB of communication.

Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes

<p>This paper presents the first efficient statistical zero-knowledge protocols to prove statements such as:<br />A committed number is a pseudo-prime.<br />A committed (or revealed) number is the product of two safe primes, i.e., primes p and q such that (p - 1)=2 and (q - 1)=2 are primes as well.<br />A given value is of large order modulo a composite number that consists of two safe prime factors.</p><p>So far, no methods other than inefficient circuit-based proofs are known for proving such properties. Proving the second property is for instance necessary in many recent cryptographic schemes that rely on both the hardness of computing discrete logarithms and of difficulty computing roots modulo a composite.<br />The main building blocks of our protocols are statistical zero-knowledge proofs that are of independent interest. Mainly, we show how to prove the correct computation of a modular addition, a modular multiplication, or a modular exponentiation, where all values including the modulus are committed but not<br />publicly known. Apart from the validity of the computation, no other information about the modulus (e.g., a generator which order equals the modulus) or any other operand is given. Our technique can be generalized to prove in zeroknowledge<br />that any multivariate polynomial equation modulo a certain modulus is satisfied, where only commitments to the variables of the polynomial and a commitment to the modulus must be known. This improves previous results,<br />where the modulus is publicly known.<br />We show how a prover can use these building blocks to convince a verifier that a committed number is prime. This finally leads to efficient protocols for proving that a committed (or revealed) number is the product of two safe primes. As a consequence, it can be shown that a given value is of large order modulo a<br />given number that is a product of two safe primes.</p><p> </p><p>Keywords. RSA-based protocols, zero-knowledge proofs of knowledge, primality tests.</p>

The power of preprocessing in zero-knowledge proofs of knowledge

We show that, after a constant-round preprocessing stage, it is possible for a prover to prove knowledge of a witness for any polynomial-time relation without any further interaction. The number of proofs that can be given is not bounded by any fixed polynomial in the size of the preprocessing. Our construction is based on the sole assumption that one-way functions and noninteractive zero-knowledge proof systems of membership exist.

The Power of Preprocessing in Zero-Knowledge Proofs of Knowledge

The Power of Preprocessing in Zero-Knowledge Proofs of Knowledge