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IEEE Transactions on Consumer Electronics

Cryptanalysis of Post-Quantum Security Schemes Based on the Hardness of the Inhomogeneous Small Integer Solution (ISIS) Problem

An Braeken, Awaneesh Kumar Yadav

Published Nov 17, 2025• 1 citation
Publisher

Abstract

With the rise of new advancements in quantum computing, more attention is given to the development of post-quantum security primitives and protocols. Recently, several authentication, key agreement and signature schemes relying on the hardness of the Inhomogeneous Small Inter Solution (ISIS) and its variants have been defined in literature. The advantage of these schemes is that they are simple, easy to implement and possess a reasonable communication and computation cost, compared to other post-quantum alternatives. Unfortunately, we show serious attacks on six different categories of these schemes, corresponding with more than ten publications in recent highly reputed journals. These vulnerabilities pose serious risks to consumer electronics, including IoT devices, smart home systems, and wearable technologies, where secure communication and authentication are vital. Exploitation of these vulnerabilities could lead to unauthorized access, device tampering, and data breaches, significantly impacting user trust and device functionality. Finally, we discuss the feasibility of defining post-quantum secure key exchange protocols, based on the ISIS problem and propose a high level approach to derive secure post-quantum protocols.

DOI
10.1109/tce.2025.3633324

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With the rise of new advancements in quantum computing, more attention is given to the development of post-quantum security primitives and protocols. Recently, several authentication, key agreement and signature schemes relying on the hardness of the Inhomogeneous Small Inter Solution (ISIS) and its variants have been defined in literature. The advantage of these schemes is that they are simple, easy to implement and possess a reasonable communication and computation cost, compared to other post-quantum alternatives. Unfortunately, we show serious attacks on six different categories of these schemes, corresponding with more than ten publications in recent highly reputed journals. These vulnerabilities pose serious risks to consumer electronics, including IoT devices, smart home systems, and wearable technologies, where secure communication and authentication are vital. Exploitation of these vulnerabilities could lead to unauthorized access, device tampering, and data breaches, significantly impacting user trust and device functionality. Finally, we discuss the feasibility of defining post-quantum secure key exchange protocols, based on the ISIS problem and propose a high level approach to derive secure post-quantum protocols.
We are surrounded by many smart applications that make human life efficient. The general concept of IoT applications involves communication between devices. To make our smart environment secure, authentication is the most important requirement to be achieved to avoid unwanted attacks. Cryptographic schemes used currently in such IoT devices are public-key cryptographic primitives that are vulnerable to future quantum attacks. Quantum approaches derived by Shor and Grover will break the public-key primitives with square root and cube root speedups. Hence, there is a need to develop a successful and efficient signature scheme to authenticate such devices. Post-quantum cryptographic approaches are based on hard mathematical problems which are difficult to break by future attacks. Amongst all these post-quantum signature approaches, hash-based post-quantum signatures incorporate existing hash algorithms to achieve the required security level. This paper summarises stateful hash-based post-quantum signature schemes that can be implemented on constrained devices for IoT applications.
We are surrounded by many smart applications that make human life efficient. The general concept of IoT applications involves communication between devices. To make our smart environment secure, authentication is the most important requirement to be achieved to avoid unwanted attacks. Cryptographic schemes used currently in such IoT devices are public-key cryptographic primitives that are vulnerable to future quantum attacks. Quantum approaches derived by Shor and Grover will break the public-key primitives with square root and cube root speedups. Hence, there is a need to develop a successful and efficient signature scheme to authenticate such devices. Post-quantum cryptographic approaches are based on hard mathematical problems which are difficult to break by future attacks. Amongst all these post-quantum signature approaches, hash-based post-quantum signatures incorporate existing hash algorithms to achieve the required security level. This paper summarises stateful hash-based post-quantum signature schemes that can be implemented on constrained devices for IoT applications.
Quantum computing advancements create threat to encryption systems which protect modern digital communication networks. The integer factorization and discrete logarithm problems which RSA and ECC algorithms depend on become vulnerable to Shor's algorithm when large-scale quantum computers achieve operational status. Billions of small IoT devices operating in resource-constrained environments face a major security risk because their lightweight encryption methods lack protection against quantum-level attacks. The research investigates Post-Quantum Cryptography(PQC) as a new cryptographic framework which protects against both quantum and classical attacks. The proposed system integrates three advanced elements that work together to provide lattice-based encryption for mathematical security and hash-based signature schemes for authentication and an intelligent threat detection system. The hybrid framework provides complete security protection while maintaining high performance and low processing requirements which makes it suitable for protecting IoT networks.
Basic security requirements such as confidentiality, user authentication and data integrity, are assured by using public-key cryptography (PKC). In particular, public-key signature schemes provide non-repudiation, integrity of transmitted messages and authentication. The presence of a large scale quantum computer would be a real threat to break the most widely used public-key cryptographic algorithms in practice, RSA, DSA, ECDSA signature schemes and Diffie-Hellman key exchange. Thus, all security protocols and applications where these public-key cryptographic algorithms are used are vulnerable to quantum-computer attacks. There are five directions of cryptographic primitives secure against a quantum computer: multivariate quadratic equation-based, hash-based, lattice-based, code-based and supersingular isogeny-based cryptography. These primitives could serve as replacements for current public-key cryptographic algorithms to prepare for post-quantum era. It is important to prioritize the fields to be replaced by post-quantum cryptography (PQC) since it is hard to replace the currently deployed PKC with PQC at the same time. The fields directly connected to human life such as vehicular communications should be the primary targets of PQC applications. This survey is dedicated to providing guidelines for adapting the most suitable post-quantum candidates to the requirements of various devices and suggesting efficient and physically secure implementations that can be built into existing embedded applications as easily as traditional PKC. It focuses on the five types of post-quantum signature schemes and investigates their theoretical backgrounds, structures, state-of-the-art constructions and implementation aspects on various platforms raging from resource constrained IoT devices to powerful servers connected to the devices for secure communications in post-quantum era. It offers appropriate solutions to find tradeoffs between key sizes, signature lengths, performance, and security for practical applications.
Recent advances in quantum technology and the potential that practical quantum computers may become a reality in the future have led to renewed interest in developing cryptographic technologies that are secure against conventional and quantum attacks. Currently, virtually all asymmetric cryptographic schemes in use are threatened by the potential development of powerful quantum computers. Post-quantum cryptography is one of main the ways to combat this threat. Its security is based on the complexity of mathematical problems that are currently considered unsolvable efficiently, even with the help of quantum computers. The security of information systems is ensured through protection against various threats that use system vulnerabilities. Security protocols are the building blocks of secure communication. They implement security mechanisms to provide security services. Security protocols are considered abstract when analyzed, but may have additional vulnerabilities in implementation. This work contains a holistic study of security protocols. Basics of security protocols, taxonomy of attacks on security protocols and their implementation are considered, as well as various methods and models of protocol security analysis. In particular, the differences between information-theoretic and computational security, computational and symbolic models are specified. In addition, an overview of the computational security models for Authenticated Key Exchange (AKE) and Password Authentication Key Exchange (PAKE) protocols is provided. The most important security models for the AKE and PAKE protocols were also described. With the emergence of new technologies that may have different security requirements, as well as with increased opportunities for competition, there is always a need to develop new protocols. Thus, the purpose of this article is to review, classify, analyze, and research the vulnerabilities of information systems from classical, quantum, and special attacks, performed taking into account the forecast regarding the possibilities of attacks on post-quantum cryptographic transformations; studying security assessment models for existing cryptographic protocols, as well as reviewing and benchmarking security models and providing suggestions for protection against existing potential attacks.
Widely used communication and messaging protocols, e.g., TLS 1.3 and Signal, are insecure against an adversary with a quantum computer. We expect that post-quantum security will become mandatory for a new generation of cryptographic protocols in the nearest 10-15 years. The analysis of existing post-quantum secure cryptographic tools for key exchange, encryption and message authentication based on hard problems in codes, lattices, ring learning with errors and elliptic curve isogenies revealed their advantages and drawbacks. In particular, we conclude, that the main threat to communication and messaging protocols is only pre-quantum security of currently used Diffie-Hellman key exchange protocols. We summarize efficiency and safety results for each class of post-quantum cryptographic schemes and present an experimental implementation of isogeny-based Diffie-Hellman-like key exchange protocol as an illustration of their applicability.