Cryptographic Assumptions Research Articles

Limits of Preprocessing

It is a classical result that the inner product function cannot be computed by an AC0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm AC}^0$$\\end{document} circuit. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n+n/(logω(1)n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n + n/(\\log^{\\omega(1)}n)$$\\end{document} bits and obtain a tight correlation bound. Our methods extend to many other functions, including pseudorandom functions, and imply a---weak yet nontrivial---limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the above conjecture with the question of learning AC0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm AC}^0$$\\end{document} under simple input distributions.

Efficient learning of t-doped stabilizer states with single-copy measurements

One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms for states generated from Clifford circuits with at most log⁡(n) non-Clifford gates. However, these algorithms necessitate multi-copy measurements, posing implementation challenges in the near term due to the requisite quantum memory. On the contrary, using solely single-qubit measurements in the computational basis is insufficient in learning even the output distribution of a Clifford circuit with one additional T gate under reasonable post-quantum cryptographic assumptions. In this work, we introduce an efficient quantum algorithm that employs only nonadaptive single-copy measurement to learn states produced by Clifford circuits with a maximum of O(log⁡n) non-Clifford gates, filling a gap between the previous positive and negative results.

StopGuess: A framework for public-key authenticated encryption with keyword search

Public key encryption with keyword search (PEKS) allows users to search on encrypted data without leaking the keyword information from the ciphertexts. But it does not preserve keyword privacy within the trapdoors, because an adversary (e.g., untrusted server) might launch inside keyword-guessing attacks (IKGA) to guess keywords from the trapdoors. In recent years, public key authenticated encryption with keyword search (PAEKS) has become a promising primitive to counter the IKGA. However, existing PAEKS schemes focus on the concrete construction of PAEKS, making them unable to support modular construction, intuitive proof, or flexible extension. In this paper, our proposal called “StopGuess” is the first elegant framework to achieve the above-mentioned features. StopGuess provides a general solution to eliminate IKGA, and we can construct a bundle of PAEKS schemes from different cryptographic assumptions under the framework. To show its feasibility, we present two generic constructions of PAEKS and their (pairing-based and lattice-based) instantiations in a significantly simpler and more modular manner. Besides, without additional costs, we extend PAEKS to achieve anonymity which preserves the identity of users; we integrate it with symmetric encryption to support data retrieval functionality which makes it practical in resource-constrained applications.

Symbolic protocol verification with dice1

Symbolic protocol verification generally abstracts probabilities away, considering computations that succeed only with negligible probability, such as guessing random numbers or breaking an encryption scheme, as impossible. This abstraction, sometimes referred to as the perfect cryptography assumption, has shown very useful as it simplifies automation of the analysis. However, probabilities may also appear in the control flow where they are generally not negligible. In this paper we consider a framework for symbolic protocol analysis with a probabilistic choice operator: the probabilistic applied π-calculus. We define and explore the relationships between several behavioral equivalences. In particular we show the need for randomized schedulers and exhibit a counter-example to a result in a previous work that relied on non-randomized ones. As in other frameworks that mix both non-deterministic and probabilistic choices, schedulers may sometimes be unrealistically powerful. We therefore consider two subclasses of processes that avoid this problem. In particular, when considering purely non-deterministic protocols, as is done in classical symbolic verification, we show that a probabilistic adversary has – maybe surprisingly – a strictly superior distinguishing power for may testing, which, when the number of sessions is bounded, we show to coincide with purely possibilistic similarity.

A Security-Enhanced Certificateless Conditional Privacy-Preserving Authentication Scheme for Vehicular Ad Hoc Networks

By adopting advanced Internet of Things (IoT) technology to sense and collect traffic-related information to improve traffic safety and efficiency, the vehicular ad hoc network (VANET) is becoming a prominent application that changes human driving experiences in the current era. Because frequent data exchange occurs in open environments, VANETs are inherently vulnerable to security and privacy attacks. In history, many certificateless aggregate signature (CLAS) schemes with conditional privacy-preserving (CPP) have been proposed to ensure the authenticity and integrity of the exchanged data and protect users’ privacy. However, we reveal that the state-of-the-art schemes cannot be deployed in practical VANET applications by proposing concrete signature forgery attacks. To this end, we propose a new CLAS-based authentication scheme with CPP for VANETs. The rigorous security proofs based on the standard cryptographic assumption show that the scheme has enhanced security. Moreover, theoretical analysis and experimental evaluation illustrate the practicality of our design.

An efficient privacy-preserving authentication scheme with enhanced security for IoMT applications

The Internet of Medical Things (IoMT), an essential application of Internet of Things (IoT) technology in the health sector, is of great practical importance in improving healthcare quality and reducing healthcare costs and errors. For years, researchers have designed many cryptographic schemes for securing IoMT applications. However, in this work, we reveal that the state-of-the-art cloud-centric IoMT-based smart healthcare system cannot be deployed in real-world scenarios by proposing a concrete signature forgery attack on their underlying pairing-based homomorphic certificateless signature (CLS) scheme. Then we present a new CLS scheme without pairings and formally prove its security under the standard cryptographic assumption. Based on our design, we put forward a new secure and efficient IoMT-based smart healthcare system. The performance comparison results illustrate the practicality of our construction.

Superpolynomial quantum-classical separation for density modeling

Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for which fault-tolerant quantum computers can offer a super-polynomial advantage over classical learning algorithms, given standard cryptographic assumptions. Along the way, we provide a variety of additional results and insights, of potential interest for proving future distribution learning separations between quantum and classical learning algorithms. Specifically, we (a) provide an overview of the relationships between hardness results in supervised learning and distribution learning, and (b) show that any weak pseudo-random function can be used to construct a classically hard density modelling problem. The latter result opens up the possibility of proving quantum-classical separations for density modelling based on weaker assumptions than those necessary for pseudo-random functions.

The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications

AbstractSequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards pseudorandom functions (PRF) recently, based on the Legendre and power residue symbols, due to their efficiency in the multi-party setting. The security of these PRFs is not known to be reducible to standard cryptographic assumptions. In this work, we show that key-recovery attacks against the Legendre PRF are equivalent to solving a specific family of multivariate quadratic (MQ) equation system over a finite prime field. This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance. We show that the currently known techniques and attacks fall short in solving these sparse quadratic equation systems. Furthermore, we build novel cryptographic applications of the Legendre PRF, e.g., verifiable random function and (verifiable) oblivious (programmable) PRFs.

Secure Marine Environment Communication: A Multiobject Authentication Protocol Based on Secret Sharing

In the field of marine communication, with the rapid development of the Internet of Things, big data, blockchain, and other new-generation information technology, marine information security is gradually being attached to more and more coastal countries, and marine information technology has ushered in epoch-making development opportunities. However, marine communication networks are open, and marine equipment is vulnerable to attacks on communication systems. On the one hand, a malicious adversary can intercept and analyze information, obtain relevant data with high probability, and even obtain the identity information of the equipment. On the other hand, attackers can also maliciously inject false information. At the same time, it is difficult for the existing marine information security technology to guarantee the confidentiality and authenticity of information simultaneously, which will bring substantial potential hidden dangers to the development of the ocean. We propose a multitarget authentication and key exchange protocol for secure communication. Our protocol assigns complex cryptographic operations to servers, thus balancing the system’s security and efficiency. The secret is divided into multiple subsecrets using the secret sharing feature, and the subsecret information is used to manage the identity credentials of resource-constrained devices. Then, after successful authentication, the server reassigns the subsecret information of the device to achieve the dynamic generation of identity credentials. Meanwhile, a multitarget authentication scheme is proposed based on recovering secrets. In addition, device extension measures are provided to replace or increase devices. Finally, well-established cryptographic assumptions are used to prove the protocol’s security. Simulation results verify the effectiveness of the protocol in multiobjective authentication.

Authenticated Data Sharing With Privacy Protection and Batch Verification for Healthcare IoT

The healthcare Internet of Things (IoT) is rapidly becoming an invaluable tool in the healthcare industry. However, sharing data in healthcare IoT raises many security and privacy concerns, such as how to ensure data integrity, source authentication, and data privacy. Redactable signature schemes ( <inline-formula><tex-math notation="LaTeX">${{\sf RSS}}$</tex-math></inline-formula> s) could be a feasible solution to address this question because it allows a signature holder to independently delete the privacy-sensitive part of the authenticated data without invalidating the respective signature. This flexible data sharing mechanism not only protects data privacy but also saves bandwidth. However, the state-of-the-art <inline-formula><tex-math notation="LaTeX">${{\sf RSS}}$</tex-math></inline-formula> s suffer from either the costly public key management problem or the secret key escrow problem. Another drawback of these schemes lies in their computation and communication overheads and hence are quite expensive for constrained devices. To address these challenging issues, in this work, we first propose the notion of certificateless <inline-formula><tex-math notation="LaTeX">${{\sf RSS}}$</tex-math></inline-formula> . We then provide an efficient instantiation of our scheme and prove its security under cryptographic assumptions. Our construction supports batch verification and redaction control, which further saves bandwidth and enhances the security of shared data by preventing the dishonest holder from arbitrarily editing data. Moreover, the comparison analysis of theory and experiment with more recent works shows the practicability of our design.

Cryptographic obfuscation for smart contracts: Trustless bitcoin bridge and more

Privacy protection for smart contracts is currently inadequate. Existing solutions for privacy-preserving smart contracts either support only a limited class of smart contracts or rely on noncryptographic assumptions.We propose a cryptographic obfuscation scheme for smart contracts based on existing blockchain mechanisms, standard cryptographic assumptions, and witness encryption. In the proposed scheme, an obfuscated smart contract does not reveal its algorithm and hardcoded secrets and preserves encrypted states. Any user can provide it with encrypted inputs and allow an untrusted third party to execute it. Although multiparty computation (MPC) among dynamically changing users is necessary, its privacy is protected if at least one user is honest. If the MPC does not finish within a period of time, anyone can cancel and restart it. The proposed scheme also supports decentralized obfuscation where even the participants of the obfuscation process cannot learn secrets in the obfuscated smart contract unless all of them are malicious. As its applications, we present a new trustless bitcoin bridge mechanism that exposes no secret key and privacy-preserving anti-money laundering built into smart contracts.

Quantum security and theory of decoherence

We sketch a relation between two crucial, yet independent, fields in quantum information research, viz. quantum decoherence and quantum cryptography. We investigate here how the standard cryptographic assumption of shielded laboratory, stating that data generated by a secure quantum device remain private unless explicitly published, is disturbed by the einselection mechanism of quantum Darwinism explaining the measurement process by interaction with the external environment. We illustrate the idea with a paradigmatic example of a quantum random number generator compromised by a quantum analog of the Van Eck phreaking. In particular, we derive a trade-off relation between the eavesdropper’s guessing probability and the collective decoherence factor Γ of the simple form .

Binary Symmetric Polynomial-Based Protected Fair Secret Sharing and Secure Communication over Satellite Networks

The rapid establishment of the low Earth orbit (LEO) satellite network in orbit has promoted the development of satellite communication technology. However, with the reduction of access conditions of satellite networks, the problems of data protection and secure communication have attracted extensive attention. A secret sharing scheme is a cryptographic technology that can disperse risks and tolerate intrusion by dividing and storing secrets. Using secret sharing technology in satellite communication can realize information security and data confidentiality. However, if there are cheaters among the participants, existing secret sharing schemes cannot prevent cheaters from sharing secrets exclusively, even if they can detect attacks. For this reason, this paper proposes a satellite based on binary symmetric polynomials protected fair secret sharing and secure communication scheme. In satellite secret refactoring, this scheme can produce a shared session key between two participants, no other key agreement processes, and reduce the scheme in the shared secret and the actual communication satellite application complexity. Users use the session key to encrypt communication to improve security and resist external attacks. The safety and fairness of the scheme are proved against the four attack models. Compared with the existing schemes, the scheme has a lower cost of deception identification on the premise of satisfying security and fairness. This scheme does not require any cryptographic assumptions and is unconditionally secure.

Communication complexity of byzantine agreement, revisited

As Byzantine Agreement (BA) protocols find application in large-scale decentralized cryptocurrencies, an increasingly important problem is to design BA protocols with improved communication complexity. A few existing works have shown how to achieve subquadratic BA under an adaptive adversary. Intriguingly, they all make a common relaxation about the adaptivity of the attacker, that is, if an honest node sends a message and then gets corrupted in some round, the adversary cannot erase the message that was already sent—henceforth we say that such an adversary cannot perform “after-the-fact removal”. By contrast, many (super-)quadratic BA protocols in the literature can tolerate after-the-fact removal. In this paper, we first prove that disallowing after-the-fact removal is necessary for achieving subquadratic-communication BA. Next, we show new subquadratic binary BA constructions (of course, assuming no after-the-fact removal) that achieve near-optimal resilience and expected constant rounds under standard cryptographic assumptions and a public-key infrastructure (PKI) in both synchronous and partially synchronous settings. In comparison, all known subquadratic protocols make additional strong assumptions such as random oracles or the ability of honest nodes to erase secrets from memory, and even with these strong assumptions, no prior work can achieve the above properties. Lastly, we show that some setup assumption is necessary for achieving subquadratic multicast-based BA.

Certificate-Based Anonymous Authentication With Efficient Aggregation for Wireless Medical Sensor Networks

Wireless medical sensor networks (WMSNs) have aroused widespread attention in recent years with the development of Internet of Things (IoT) technology. WMSNs offer many new opportunities for healthcare professionals to monitor patients and patient self-monitoring. To overcome the resource (such as memory and power) limitations of sensors and attain data security of patients’ private medical information, researchers have designed plenty of work for securing WMSNs. For years, certificate-based aggregate signature (CBAS) schemes have been put forward for WMSNs to prevent patients’ sensitive medical data from being tampered with and damaged. In this work, we analyze the security flaws of a very recent CBAS scheme proposed by Verma <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2021) by presenting two types of security attacks. We later propose a CBAS scheme with user anonymity protection for WMSNs and prove its security based on the standard cryptographic assumption. The performance comparison results from theory and experiment illustrate the practicality of our design.

Towards a Formal Treatment of Logic Locking

Logic locking aims to protect the intellectual property of a circuit from a fabricator by modifying the original logic of the circuit into a new “locked” circuit such that an entity without the key should not be able to learn anything about the original circuit. While logic locking provides a promising solution to outsourcing the fabrication of chips, unfortunately, several of the proposed logic locking systems have been broken. The lack of established secure techniques stems in part from the absence of a rigorous treatment toward a notion of security for logic locking, and the disconnection between practice and formalisms. We seek to address this gap by introducing formal definitions to capture the desired security of logic locking schemes. In doing so, we investigate prior definitional efforts in this space, and show that these notions either incorrectly model the desired security goals or fail to capture a natural “compositional” property that would be desirable in a logic locking system. Finally we move to constructions. First, we show that universal circuits satisfy our security notions. Second, we show that, in order to do better than universal circuits, cryptographic assumptions are necessary.

An Approach to the Construction of a Recursive Argument of Polynomial Evaluation in the Discrete Log Setting

Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications. Polynomial commitment schemes are important building blocks for the construction of SNARks. Polynomial commitment schemes enable the prover to commit to a secret polynomial of the prover and convince the verifier that the evaluation of the committed polynomial is correct at a public point later. Bünz et al. recently presented a novel polynomial commitment scheme with no trusted setup in Eurocrypt’20. To provide a transparent setup, their scheme is built over an ideal class group of imaginary quadratic fields (or briefly, class group). However, cryptographic assumptions on a class group are relatively new and have, thus far, not been well-analyzed. In this paper, we study an approach to transpose Bünz et al.’s techniques in the discrete log setting because the discrete log setting brings a significant improvement in efficiency and security compared to class groups. We show that the transposition to the discrete log setting can be obtained by employing a proof system for the equality of discrete logarithms over multiple bases. Theoretical analysis shows that the transposition preserves security requirements for a polynomial commitment scheme.

Extending On-chain Trust to Off-chain -- Trustworthy Blockchain Data Collection using Trusted Execution Environment (TEE)

Blockchain creates a secure environment on top of strict cryptographic assumptions and rigorous security proofs. It permits on-chain interactions to achieve trustworthy properties such as traceability, transparency, and accountability. However, current blockchain trustworthiness is only confined to on-chain, creating a “trust gap” to the physical, off-chain environment. This is due to the lack of a scheme that can truthfully reflect the physical world in a real-time and consistent manner. Such an absence hinders further blockchain applications in the physical world, especially for the security-sensitive ones. In this paper, we propose a framework to extend blockchain trust from on-chain to off-chain, and take trustworthy vaccine tracing as an example scheme. Our scheme consists of 1) a Trusted Execution Environment (TEE)-enabled trusted environment monitoring system built with the Arm Cortex-M33 microcontroller that continuously senses the inside of a vaccine box through trusted sensors and generates anti-forgery data; and 2) a consistency protocol to upload the environment status data from the TEE system to blockchain in a truthful, real-time consistent, continuous and fault-tolerant fashion. Our security analysis indicates that no adversary can tamper with the vaccine in any way without being captured. We carry out an experiment to record the internal status of a vaccine shipping box during transportation, and the results indicate that the proposed system incurs an average latency of 84 ms in local sensing and processing followed by an average latency of 130 ms to have the sensed data transmitted to and been available in the blockchain.

Secure Information Transfer Using Two Keyless Cryptography Methods

In the current paper, some methods of information security protocols based on physical layer security are considered. It is proved that well known Shamir’s protocol can be applied to RSA cryptosystem but not to Rabin, Mac-Ellice and trellis based cryptosystems.The main stream of this paper is a description of key sharing protocol on constant public and noiseless channels (like Internet). It is shown that it is able to provide a high reliability and control of security in terms of Shannon’s information providing nothing-additional requirements to communication channels and without any cryptographic assumptions.

Computationally Secure Quantum Oblivious Transfer

AbstractOblivious transfer (OT) is one of the cornerstones of secure multiparty computation. It is clear that unconditionally secure OT is impossible. Any protocol for OT requires computational assumptions, such as number‐theoretic cryptographic assumptions or the assumptions of existence of one‐way functions. On the other hand, it is broadly believed that one‐way functions alone do not promise secure OT. However, in this paper, a novel computationally secure quantum oblivious transfer (QOT) protocol is proposed with the help of quantum channels under the minimum assumption requirements: the existence of one‐way functions.