Supersingular Isogeny-Based Ring Signature

A ring signature is a digital signature scheme that allows identifying a group of possible signers without revealing the identity of the actual signer. In this paper, we first present a post-quantum sigma protocol for a ring that relies on the supersingular isogeny-based interactive zero-knowledge identification scheme proposed by De Feo, Jao, and Plût in 2014. Then, we construct a ring signature from the proposed sigma protocol for a ring by applying the Fiat-Shamir transform. In order to reduce the size of exchanges, we use Merkle trees and show that the signature size increases logarithmically in the size of the ring. The security proofs and complexity analyses of the proposed protocols are also provided

A Survey on Exotic Signatures for Post-quantum Blockchain: Challenges and Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this article, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and that are crucial cryptographic tools used in the blockchain ecosystem for (1) account management, (2) consensus efficiency, (3) empowering scriptless blockchain, and (4) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind, and ring signatures. Herein the term "exotic"refers to signatures with properties that are not just beyond the norm for signatures, e.g., unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats

A Survey on Exotic Signatures for Post-Quantum Blockchain: Challenges & Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this paper, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and which are crucial cryptographic tools used in the blockchain ecosystem for (i) account management, (ii) consensus efficiency, (iii) empowering scriptless blockchain, and (iv) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind and ring signatures. Herein the term exotic refers to signatures with properties which are not just beyond the norm for signatures e.g. unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats

Post-Quantum Zero-Knowledge Proofs for Accumulators with Applications to Ring Signatures from Symmetric-Key Primitives

In this paper we address the construction of privacy-friendly cryptographic primitives for the post-quantum era and in particular accumulators with zero-knowledge membership proofs and ring signatures. This is an important topic as it helps to protect the privacy of users in online authentication or emerging technologies such as cryptocurrencies. Recently, we have seen first such constructions, mostly based on assumptions related to codes and lattices. We, however, ask whether it is possible to construct such primitives without relying on structured hardness assumptions, but solely based on symmetric-key primitives such as hash functions or block ciphers. This is interesting because the resistance of latter primitives to quantum attacks is quite well understood. In doing so, we choose a modular approach and firstly construct an accumulator (with one-way domain) that allows to efficiently prove knowledge of (a pre-image of) an accumulated value in zero-knowledge. We, thereby, take care that our construction can be instantiated solely from symmetric-key primitives and that our proofs are of sublinear size. Latter is non trivial to achieve in the symmetric setting due to the absence of algebraic structures which are typically used in other settings to make these efficiency gains. Regarding efficient instantiations of our proof system, we rely on recent results for constructing efficient non-interactive zero-knowledge proofs for general circuits. Based on this building block, we then show how to construct logarithmic size ring signatures solely from symmetric-key primitives. As constructing more advanced primitives only from symmetric-key primitives is a very recent field, we discuss some interesting open problems and future research directions. Finally, we want to stress that our work also indirectly impacts other fields: for the first time it raises the requirement for collision resistant hash functions with particularly low AND count

Post-Quantum Era Privacy Protection for Intelligent Infrastructures

As we move into a new decade, the global world of Intelligent Infrastructure (II) services integrated into the Internet of Things (IoT) are at the forefront of technological advancements. With billions of connected devices spanning continents through interconnected networks, security and privacy protection techniques for the emerging II services become a paramount concern. In this paper, an up-to-date privacy method mapping and relevant use cases are surveyed for II services. Particularly, we emphasize on post-quantum cryptography techniques that may (or must when quantum computers become a reality) be used in the future through concrete products, pilots, and projects. The topics presented in this paper are of utmost importance as (1) several recent regulations such as Europe's General Data Protection Regulation (GDPR) have given privacy a significant place in digital society, and (2) the increase of IoT/II applications and digital services with growing data collection capabilities are introducing new threats and risks on citizens' privacy. This in-depth survey begins with an overview of security and privacy threats in IoT/IIs. Next, we summarize some selected Privacy-Enhancing Technologies (PETs) suitable for privacy-concerned II services, and then map recent PET schemes based on post-quantum cryptographic primitives which are capable of withstanding quantum computing attacks. This paper also overviews how PETs can be deployed in practical use cases in the scope of IoT/IIs, and maps some current projects, pilots, and products that deal with PETs. A practical case study on the Internet of Vehicles (IoV) is presented to demonstrate how PETs can be applied in reality. Finally, we discuss the main challenges with respect to current PETs and highlight some future directions for developing their post-quantum counterparts