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

Locality-Preserving Hashing for Shifts with Connections to Cryptography

Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function $h:\{0,1\}^n\to \mathbb{Z}_n$ is a $(d,\delta)$ {\em locality-preserving hash function for shifts} (LPHS) if: (1) $h$ can be computed by (adaptively) querying $d$ bits of its input, and (2) $\Pr [ h(x) \neq h(x \ll 1) + 1 ] \leq \delta$, where $x$ is random and $\ll 1$ denotes a cyclic shift by one bit to the left. We make the following contributions. * Near-optimal LPHS via Distributed Discrete Log: We establish a general two-way connection between LPHS and algorithms for distributed discrete logarithm in the generic group model. Using such an algorithm of Dinur et al. (Crypto 2018), we get LPHS with near-optimal error of $\delta=\tilde O(1/d^2)$. This gives an unusual example for the usefulness of group-based cryptography in a post-quantum world. We extend the positive result to non-cyclic and worst-case variants of LPHS. * Multidimensional LPHS: We obtain positive and negative results for a multidimensional extension of LPHS, making progress towards an optimal 2-dimensional LPHS. * Applications: We demonstrate the usefulness of LPHS by presenting cryptographic and algorithmic applications. In particular, we apply multidimensional LPHS to obtain an efficient "packed" implementation of homomorphic secret sharing and a sublinear-time implementation of location-sensitive encryption whose decryption requires a significantly overlapping view

EXPLORING CONFIDENTIALITY AND PRIVACY OF IMAGE IN CLOUD COMPUTING

With the increasing popularity of cloud computing, clients are storing their data in cloud servers and are using “software as a service” for computing services. However, clients’ data may be sensitive, critical, and private, and processing such data with cloud servers may result in losing data privacy or compromising data confidentiality. Some cloud servers may be dishonest, while malicious entities may compromise others. In order to protect data privacy and confidentiality, clients need to be able to hide their actual data values and send the obfuscated values to cloud servers. This thesis deals with the outsourcing of computing to cloud servers, in which clients’ images can be computed and stored. This thesis proposes a technique that obfuscates images before sending them to servers, so these servers can perform computations on images without knowing the actual images. The proposed technique is expected to ensure data privacy and confidentiality. Servers will not be able to identify an individual whose images are stored and manipulated by the server. In addition, our approach employs an obfuscating technique to maintain the confidentiality of images, allowing cloud servers to compute obfuscated data accurately without knowing the actual data value, thus supporting privacy and confidentiality. The proposed approach is based on the Rabin block cipher technique, which has some weaknesses, however. The main drawback is its decryption technique, which results in four values, and only one of these values represents the actual value of plain data. Another issue is that the blocking technique requires a private key for each block that requires a high-computing effort; requiring one private key for each block of data demands that a great number of keys be stored by the client. As a result, it decreases the robustness of the Rabin block cipher. This thesis proposes additional techniques to overcome some of the weaknesses of the Rabin block cipher by introducing some new features, such as tokenization, a digit counter, and a set of blocks. The new technique increases the privacy of data and decreases the computational complexity by requiring fewer private keys. The new features have been implemented in image processing in order to demonstrate their applicability. However, in order to apply our approach to images, we must first apply some preprocessing techniques on images to make them applicable to being obfuscated by our proposed obfuscating system

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

ReSolveD: Shorter Signatures from Regular Syndrome Decoding and VOLE-in-the-Head

We present ReSolveD, a new candidate post-quantum signature scheme under the regular syndrome decoding (RSD) assumption for random linear codes, which is a well-established variant of the well-known syndrome decoding (SD) assumption. Our signature scheme is obtained by designing a new zero-knowledge proof for proving knowledge of a solution to the RSD problem in the recent VOLE-in-the-head framework using a sketching scheme to verify that a vector has weight exactly one. We achieve a signature size of 3.99 KB with a signing time of 27.3 ms and a verification time of 23.1 ms on a single core of a standard desktop for a 128-bit security level. Compared to the state-of-the-art code-based signature schemes, our signature scheme achieves $1.5\times \sim 2\times$ improvement in terms of the common signature size + public-key size metric, while keeping the computational efficiency competitive

Signing with Codes

Code-based cryptography is an area of classical cryptography in which cryptographic primitives rely on hard problems and trapdoor functions related to linear error-correcting codes. Since its inception in 1978, the area has produced the McEliece and the Niederreiter cryptosystems, multiple digital signature schemes, identification schemes and code-based hash functions. All of these are believed to be resistant to attacks by quantum computers. Hence, code-based cryptography represents a post-quantum alternative to the widespread number-theoretic systems. This thesis summarizes recent developments in the field of code-based cryptography, with a particular emphasis on code-based signature schemes. After a brief introduction and analysis of the McEliece and the Niederreiter cryptosystems, we discuss the currently unresolved issue of constructing a practical, yet provably secure signature scheme. A detailed analysis is provided for the Courtois, Finiasz and Sendrier signature scheme, along with the mCFS and parallel CFS variations. Finally, we discuss a recent proposal by Preetha et al. that attempts to solve the issue of provable security, currently failing in the CFS scheme case, by randomizing the public key construct. We conclude that, while the proposal is not yet practical, it represents an important advancement in the search for an ideal code-based signature scheme

Quantum Resistant Authenticated Key Exchange for OPC UA using Hybrid X.509 Certificates

While the current progress in quantum computing opens new opportunities in a wide range of scientific fields, it poses a serious threat to today?s asymmetric cryptography. New quantum resistant primitives are already available but under active investigation. To avoid the risk of deploying immature schemes we combine them with well-established classical primitives to hybrid schemes, thus hedging our bets. Because quantum resistant primitives have higher resource requirements, the transition to them will affect resource constrained IoT devices in particular. We propose two modifications for the authenticated key establishment process of the industrial machine-to-machine communication protocol OPC UA to make it quantum resistant. Our first variant is based on Kyber for the establishment of shared secrets and uses either Falcon or Dilithium for digital signatures in combination with classical RSA. The second variant is solely based on Kyber in combination with classical RSA. We modify existing opensource software (open62541, mbedTLS) to integrate our two proposed variants and perform various performance measurement

Measures of Nonclassical Correlations and Quantum-Enhanced Interferometry

In the first part of this dissertation a framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of nonclassical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented. To demonstrate how these measures differ from entanglement we move to the set of Bell-diagonal states for two qubits, which can be depicted as a tetrahedron in three dimensions. We consider the level surfaces of entanglement and of the correlation measures from our framework for Bell-diagonal states. This provides a complete picture of the structure of entanglement and discord for this simple case and, in particular, of their nonanalytic behavior under decoherence. The pictorial approach also indicates how to show that all of the proposed correlation measures are neither convex nor concave. In the second part we look at two practical interferometric setups that use nonclassical states of light to enhance their performance. First we consider an interferometer powered by laser light (a coherent state) into one input port and ask the following question: what is the best state to inject into the second input port, given a constraint on the mean number of photons this state can carry, in order to optimize the interferometer\u27s phase sensitivity? This question is the practical question for high-sensitivity interferometry. We answer the question by considering the quantum Cram\\u27er-Rao bound for such a setup. The answer is squeezed vacuum. Then we analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint that the state input to the interferometer\u27s initial 50:50 beam splitter B is a product state of the two input modes. Requiring a product state is a natural restriction: if one were allowed to input an arbitrary, entangled two-mode state $|\Xi \rangle$ to the beam splitter, one could generally just as easily input the state $B|\Xi \rangle$ directly into the two modes after the beam splitter, thus rendering the beam splitter unnecessary. We find optimal states for a fixed photon number and for a fixed mean photon number. Our results indicate that entanglement is not a crucial resource for quantum-enhanced interferometry. Initially the analysis for both of these setups is performed for the idealized case of a lossless interferometer. Then the analysis is extended to the more realistic scenario where the interferometer suffers from photon losses