Lattice-based Cryptography Research Articles

FS-IBEKS: Forward secure identity-based encryption with keyword search from lattice

Public Key Encryption with Keyword Search (PEKS) makes it possible for a cloud server (CS) to match a trapdoor and a ciphertext. However, with the upgrowth of quantum techniques, most of the existing PEKS schemes will be broken by quantum computers in the coming future. Moreover, they are also under the threat of potential key exposure. Lattice-based forward secure PEKS scheme (FS-PEKS) overcomes the two problems above by combining the techniques of forward security and lattice-based cryptography. However, FS-PEKS schemes work in public key infrastructure (PKI), which will incur complicated certificate management procedures. In this work, to overcome the key management issue but still guarantee security even when attackers corrupt the keys, we extend the FS-PEKS scheme into the identity-based framework and present a forward secure identity-based encryption with keyword search (FS-IBEKS) scheme from lattice. The proposed scheme is secured under the selective identity against chosen plaintext attack (IND-sID-CPA) in the random oracle model. To further improve the security, we present another FS-IBEKS scheme into the standard model and give concrete security proof under the adaptive identity against chosen plaintext attack (IND-ID-CPA). The comprehensive performance evaluation demonstrates that our FS-IBEKS schemes are feasible for cloud computing.

AC-PM: An Area-Efficient and Configurable Polynomial Multiplier for Lattice Based Cryptography

As the computation bottleneck in lattice-based cryptography (LBC), the polynomial multiplication based on number theoretic transform (NTT) has been continuously studied for flexible hardware implementations with high area-efficiency. This paper presents an area-efficient and configurable NTT-based polynomial multiplier (AC-PM) incorporating algorithmic and architectural level optimization techniques. For the core operation of polynomial multiplication, two low-complexity and fast modular multiplication algorithms are introduced with loose constraints of LBC-friendly primes. Based on the proposed algorithms, a reconfigurable processing element (RPE) is dedicatedly designed to execute all the operations in an NTT-based polynomial multiplication: NTT, inverse NTT (INTT), and coefficient-wise multiplication (CWM). The proposed AC-PM can be configured with different numbers of RPEs and supports various polynomial degrees without recompilation. Additionally, the dataflow complexity is greatly simplified. More importantly, to the best of our knowledge, the twiddle factors are reused, for the first time, to support both NTT and INTT with multiple polynomial degrees, which leads to increased flexibility of AC-PM with small overhead on hardware resource. FPGA implementation results demonstrate that the proposed AC-PM significantly outperforms the prior arts in both flexibility and area efficiency.

Revisiting Higher-Order Masked Comparison for Lattice-Based Cryptography: Algorithms and Bit-Sliced Implementations

Masked comparison is one of the most expensive operations in side-channel secure implementations of lattice-based post-quantum cryptography, especially for higher masking orders. First, we introduce two new masked comparison algorithms, which improve the arithmetic comparison of D’Anvers et al. (2021) and the hybrid comparison method of Coron et al. (2021) respectively. We then look into implementation-specific optimizations, and show that small specific adaptations can have a significant impact on the overall performance. Finally, we implement various state-of-the-art comparison algorithms and benchmark them on the same platform (ARM-Cortex M4) to allow a fair comparison between them. We improve on the arithmetic comparison of D’Anvers et al. with a factor <inline-formula><tex-math notation="LaTeX">$\approx 20\%$</tex-math></inline-formula> by using Galois Field multiplications and the hybrid comparison of Coron et al. with a factor <inline-formula><tex-math notation="LaTeX">$\approx 25\%$</tex-math></inline-formula> by streamlining the design. Our implementation-specific improvements allow a speedup of a straightforward comparison implementation of <inline-formula><tex-math notation="LaTeX">$\approx 33\%$</tex-math></inline-formula> . We discuss the differences between the various algorithms and provide the implementations and a testing framework to ease future research.

Guest Editorial: Guest Editorial on Cryptanalysis of (NIST PQC) post‐quantum proposals

Public-key cryptography is now ubiquitous in our lives, protecting everyday interactions ranging from mobile and wireless communications to banking transactions, over-the-air software updates, electronic voting or digital car keys. However, almost the entirety of currently deployed public-key cryptography implementations rely on the hardness of integer factorisation or computing discrete logarithms, and both problems are known to be easy to solve using large-scale quantum computers. Whether such large-scale computers are years away, decades away or more remains to be seen, but since they would break the security of so many critical systems essentially overnight, preparing the transition from classical cryptography to so-called post-quantum primitives, which are believed to be secure even against quantum computers, is seen as necessary and urgent—particularly as updating existing systems is likely to be a lengthy process, and some systems rely on the security of cryptographic keys over long periods of time. In view of these challenges, starting in 2016, US standards institute NIST has been running a standardisation effort in order to come up with post-quantum encryption and signature schemes ready for deployment. The first four selected primitives have been announced in July 2022, with other schemes undergoing further analysis. Concurrently, other countries, such as the Republic of Korea, have launched similar standardisation processes. One of the difficulties involved in running such standardisation processes and selecting primitives is security estimation: in order to set parameters for candidate schemes and to make apple-to-apple comparisons between them, consistent security levels need to be defined, and evidence that the schemes achieve those levels needs to be provided. This is typically done by estimating the cost of the best attacks (both classical and quantum) against the proposed constructions. Cryptanalysis is thus an essential tool for design and standardisation. Not only does it allow to provide and progressively refine security estimates, it also sometimes eliminates entire schemes, plain and simple, by uncovering serious security flaws. Both applications of cryptanalysis have been extensively represented in the NIST standardisation process in particular. ‘Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post-Quantum Cryptography’, by J.-F. Biasse, X. Bonnetain, E. Martin, E. Kirshanova, A. Schrottenloher and F. Song, on quantum cryptanalysis; ‘Recent Progress in the Security Evaluation of Multivariate Public-Key Cryptography’, by Y. Ikematsu, S. Nakamura and T. Takagi, on multivariate cryptography; ‘Lattice-Based Cryptosystems in Standardization Processes: A Survey’, by A. Wang, D. Xiao and Y. Yu, on lattice-based cryptography; and ‘Torsion point attacks on `SIDH-like' cryptosystems’, by P. Kutas and C. Petit, on isogeny-based cryptography. Since some post-quantum proposals rely on relatively new assumptions that have only received much scrutiny as part of the standardisation processes, their cryptanalysis is a fast-changing landscape. Very recent, dramatic developments include W. Beullens' cryptanalysis of the Rainbow multivariate signature, and W. Castryk and T. Decru's cryptanalysis of the SIKE isogeny-based KEM (along with several follow-ups). Both Rainbow and SIKE were serious contenders for eventual standardisation. Those surprising results, which appeared too late to be captured in this special issue, are thus further testimonies to the utmost importance of cryptanalytic work as part of standardisation efforts. We therefore hope that the contributions included in this special issue will be of great value to the community, insofar as they record, and present in an accessible way, important results towards the goal of obtaining secure and dependable standards for post-quantum cryptography. Data sharing not applicable to this article as no data sets were generated or analysed during the current study. Ayoub Otmani obtained a Ph.D. degree in Mathematics and its Applications from the University of Limoges (France) in 2002. He is currently Professor in Computer Science at University of Rouen Normandie. His research lies in coding theory and cryptography. Christophe Petit obtained a PhD in Cryptography at Université catholique de Louvain. He is now Associate Professor at the University of Birmingham and Université libre de Bruxelles. His research focuses on cryptanalysis and mathematical aspects of cryptography, particularly on isogeny-based cryptography. An alumni of ENS (Paris, France), Mehdi Tibouchi obtained his Ph.D. in computer science from Univ. Paris VII and Univ. Luxembourg in 2011. He is now distinguished researcher at NTT Corporation (Tokyo, Japan) and guest associate professor at Kyoto University (Kyoto, Japan). His research interests cover various mathematical aspects of public-key cryptography and cryptanalysis, particularly related to elliptic curves and Euclidean lattices.

Application of Discrete Pruned Enumeration in Solving BDD

The bounded distance decoding (BDD) is a fundamental problem in lattice-based cryptography which is derived from the closest vector problem (CVP). In this paper, we adapt the lattice enumeration with discrete pruning, a burgeoning method for the shortest lattice vector problem (SVP), to solve BDD in various cryptanalysis scenarios using direct method. We first transfer the basic definition involved in discrete pruning technique from SVP to CVP, prove corresponding properties and give the specific procedures of the algorithm. Additionally, we use the discrete pruning technique to interpret the classical CVP algorithms, including Babai’s nearest plane and Lindner–Peikert nearest planes, which can be regarded as discrete pruned enumeration on some special pruning sets. We propose three probability models in the runtime analysis to accurately estimate the cost of our algorithm in different application scenarios. We study the application of discrete pruned enumeration for BDD mainly on LWE-based cryptosystem and DSA with partially known nonces. The experimental results show that our new algorithm has higher efficiency than the previous algorithms which directly solve BDD, including the nearest plane(s) algorithms and the lattice enumeration with classical pruning strategies, and we are able to recover the DSA secret with less leaked information than the previous works.

A survey of quantum secure group signature schemes: Lattice-based approach

The group signatures allow any member to sign the message on behalf of the group. While anyone who does not need to be a group member can verify the signature, they do not know who the signer is. The first examples are constructed using classical techniques such as the discrete logarithm and the integer factorization problem. The fact that the cryptosystems using classical techniques will be broken in polynomial time with quantum computing power increases the interest in post-quantum cryptography. Lattice-based cryptography is a good alternative for the post-quantum world due to its simple structures, efficient implementations, and worst-case hardness. Therefore, the lattice-based group signature schemes have been proposed for quantum era. In this paper, our aim is to review group signature schemes over lattices. We classify the schemes into four groups according to the fact that they allow adding and revoking members: static, group signature schemes with revocation mechanism, partially dynamic and fully dynamic. Firstly, we define the algorithms needed to construct the schemes. We give the development process and requirements for constructing group signatures before we review all group signature schemes over lattices. In addition, we compare all proposed lattice-based group signature schemes in view of underlying lattice problems, security requirements, the sizes of group public and secret signing key, signature size and security model. The main contribution of this study is that it is the first study examining lattice-based group signature schemes in detail.

Work in Lattice-Based Cryptography: Key Exchange Protocols under RLWE-Based Problems and Ding Reconciliation Technique

Lattice-based cryptography stands at the forefront of contemporary cryptographic research, offering robust security guarantees that withstand the challenges posed by quantum computing. This research paper undertakes a comprehensive exploration of lattice-based key exchange protocols, with a specific and meticulous focus on the Ring Learning with Errors (RLWE) problem—a cornerstone in the lattice-based paradigm. In addition, the paper delves deeply into the innovative ding reconciliation technique, strategically employed to amplify the efficiency and effectiveness of RLWE-based key exchange protocols.Within this paper's purview lies a holistic examination of key concepts, intricacies, and recent developments in the field of lattice-based cryptography. The paper rigorously analyzes the theoretical foundations that underpin the security assurances of lattice-based protocols, particularly in the context of post-quantum cryptography. The RLWE problem, as a central tenet, is dissected to unveil its significance as a building block for cryptographic constructions, especially in the realm of key exchange.The integration of the ding reconciliation technique introduces an added layer of depth to the research. By elucidating the mechanics of this method, the paper showcases its role in streamlining the error correction process inherent in RLWE-based protocols. The reconciliation technique's contribution to efficiency is examined through both theoretical analysis and empirical validation, presenting a compelling case for its adoption in practical scenarios.Moreover, this paper critically surveys the landscape of recent developments in lattice-based cryptography, elucidating novel protocol designs, algorithmic optimizations, and real-world applications. The inherent challenges, ranging from computational complexity to practical implementation considerations, are scrutinized, providing a balanced perspective on the field's ongoing evolution.As the paper concludes, it consolidates the insights garnered from its comprehensive review, offering a panoramic understanding of lattice-based cryptography's inner workings. It outlines the broader implications of these cryptographic protocols in safeguarding digital communications and securing data transmission in a quantum-advantaged era. By synthesizing a comprehensive overview, this research paper aims to provide researchers, practitioners, and enthusiasts with a nuanced understanding of lattice-based cryptography, RLWE-based key exchange protocols, and the innovative ding reconciliation technique.

Key exchange protocol under Ding reconciliation scheme in Lattice-based cryptography

The Ding Reconciliation Scheme is dissected in detail in this study. A recently proposed method within the lattice-based cryptography framework. The study delves into the mathematical foundations and principles of the scheme, its role in secure key exchange, and its in-depth examination of the key exchange protocol that leverages it. It discusses theoretical security guarantees, vulnerabilities, and mitigation strategies. The paper also provides insights into the practical implementation of the scheme, highlighting its computational efficiency and performance evaluations. It also conducts a comparative analysis with other prominent lattice-based key exchange protocols to assess its strengths and weaknesses, highlighting potential advantages and areas for further research. The paper serves as a reference for researchers, cryptographers, and practitioners interested in the Ding Reconciliation Scheme and its applications in lattice-based cryptography, contributing to the ongoing dialogue in the field and promoting advancements in secure communication solutions.

An Extensive Study on Lattice-Based Cryptography and its Applications for RLWE-Based Problems

Lattice-based cryptography has emerged as a powerful paradigm for constructing secure cryptographic primitives, offering resistance to quantum attacks and providing a versatile framework for building post-quantum cryptographic systems. This research paper provides an in-depth exploration of lattice-based cryptography, focusing specifically on its applications for problems based on Ring Learning with Errors (RLWE). We analyze the fundamental concepts of lattice theory, delve into the RLWE problem, and highlight the security properties and challenges associated with lattice-based schemes. Furthermore, we discuss various real-world applications of lattice-based cryptography, demonstrating its potential for secure communication, privacy-preserving protocols, and post-quantum cryptography.

Low-Cost Shuffling Countermeasures Against Side-Channel Attacks for NTT-Based Post-Quantum Cryptography

Lattice-based cryptography (LBC) schemes are promising candidates in the post-quantum cryptography (PQC) standardization process. Number theoretic transform (NTT), as a crucial technique, is widely used to accelerate LBC implementations on computer systems. However, existing side-channel attacks can recover the secret key in real-world cryptographic devices bypassing mathematical problems. The motivation of this work is to provide a low-cost security-enhanced architecture for NTT-based PQC processors. We convert the nested loops in NTT to a hardware-friendly single-level loop. The corresponding architecture instantiates a unified shuffling controller to schedule the order of independent basic operations. We propose the coefficient index randomization and the NTT network randomization schemes against existing power attacks and template attacks. We further achieve high performance and efficiency on the off-the-shelf FPGAs. The shuffling schemes have a negligible impact on performance, and the resource overhead is only 9%.

Efficient Partially-parallel NTT Processor for Lattice-based Post-quantum Cryptography

This paper presents a partially-parallel number theoretic transform (NTT) processor design for polynomial multipliers, which is a key component of a lattice-based cryptography. Since the data flow of NTT is similar to that of FFT, studies have been conducted to apply the FFT structure to fit the NTT structure. However, the previous architectures suffer from high hardware complexity and low throughput. Thus, we propose a new partially-parallel design that models the data reordering process and derives a generalized data reordering circuit. The proposed partially parallel design solved the problem of the previous architectures. Moreover, it provides improved performance through efficient data reordering. Synthesis results shows that the proposed 8-parallel 512-point NTT processor achieves 15% to 76% improvements in terms of hardware efficiency compared to the previous architectures. As a result, the proposed NTT processor is a good solution in a more diversified lattice-based crypto-processor with constrained usage conditions.

A novel hybrid authentication protocol utilizing lattice-based cryptography for IoT devices in fog networks

The Internet of Things (IoT) has taken the interconnected world by storm. Due to their immense applicability, IoT devices are being scaled at exponential proportions worldwide. But, very little focus has been given to securing such devices. As these devices are constrained in numerous aspects, it leaves network designers and administrators with no choice but to deploy them with minimal or no security at all. We have seen distributed denial-of-service attacks being raised using such devices during the infamous Mirai botnet attack in 2016. Therefore we propose a lightweight authentication protocol to provide proper access to such devices. We have considered several aspects while designing our authentication protocol, such as scalability, movement, user registration, device registration, etc. To define the architecture we used a three-layered model consisting of cloud, fog, and edge devices. We have also proposed several pre-existing cipher suites based on post-quantum cryptography for evaluation and usage. We also provide a fail-safe mechanism for a situation where an authenticating server might fail, and the deployed IoT devices can self-organize to keep providing services with no human intervention. We find that our protocol works the fastest when using ring learning with errors. We prove the safety of our authentication protocol using the automated validation of Internet security protocols and applications tool. In conclusion, we propose a safe, hybrid, and fast authentication protocol for authenticating IoT devices in a fog computing environment.

Shaping Postquantum Cryptography: The Hidden Subgroup and Shift Problems

The security of popular public key-cryptographic protocols, such as RSA, Diffie-Hellman key exchange and the Digital Signature Algorithm (DSA), is endangered by the advent of quantum computers. Shor brought a big breakthrough with his quantum algorithm that can be used to factor an arbitrarily large integer into the product of its prime factors, hence jeopardizing the security of RSA, and that at the same time also solves the Discrete Logarithm Problem, which raises issues for certain Diffie-Hellman based cryptosystems and digital signatures. It is hence crucial to upgrade our current tools for post-quantum cryptography: it should be infeasible, even using quantum algorithms, to break the new cryptosystems. Popular candidates include for example elliptic curve or lattice-based cryptography, but they share something in common: they are specific cases of the more general Hidden Subgroup and connected Hidden Shift Problem.

Area-Time-Efficient Scalable Schoolbook Polynomial Multiplier for Lattice-Based Cryptography

Lattice-based cryptography (LBC) stands out as one of the most viable classes of quantum-resistant schemes. This brief explores a time-sharing approach, with different parallelism levels, for a crucial operation in LBC cryptosystems, i.e., polynomial multiplication. We also employ an innovative coefficient ordering method in our time-shared schoolbook polynomial multiplication (SPM) to combine the best of two worlds: design compactness and lower processing latency. Thus, our work offers a choice of design points with performance vs. resource trade-offs. Our fastest proposed design exhibits 80% and 57% reductions in LUTs and throughput, respectively, compared to the existing fully parallel SPM architecture (on Xilinx Ultrascale+), which lead to a 53% improvement in the area-time-product efficiency. Our smallest proposed design is more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.2\times $ </tex-math></inline-formula> faster than the existing low-cost parallel SPM architecture (on Xilinx Kintex-7) at the expense of 85% additional area resources.

Efficient Medical Big Data Management With Keyword-Searchable Encryption in Healthchain

Along with applying blockchain technology in the health care service system (HSS), many distributed solutions have been proposed to solve the centralized, data island problems. Although blockchain-enabled HSS has significantly changed the traditional management mode of medical Big Data [e.g., electronic medical records (EMRs)], some new problems such as ledger corpulence, data searchable security, and quantum attack threat are exposed. In this article, we first introduce an efficient EMRs management model called on-chain ledger and off-chain storage (OLOS), in which the indexes of EMRs are uploaded on public blockchain and the real EMRs data are stored in native server. This model can relieve the public ledger and save the public cloud space. Meanwhile, it can protect data security by keeping off the direct operation on real EMRs data. Then, to protect the cross-institutional EMRs sharing security and improve the quantum-resist ability, we proposed a secure keyword-searchable attribute-based encryption (KS-ABE) scheme based on lattice cryptography. Moreover, the scheme can prove to be secure against adaptive chosen-keyword attack and adaptive chosen-policy attack in the random oracle model. Besides, comparison analysis and experimental results show that our KS-ABE scheme has fewer communication costs and smaller key sizes than similar literary works.

On Advances of Lattice-Based Cryptographic Schemes and Their Implementations

Lattice-based cryptography is centered around the hardness of problems on lattices. A lattice is a grid of points that stretches to infinity. With the development of quantum computers, existing cryptographic schemes are at risk because the underlying mathematical problems can, in theory, be easily solved by quantum computers. Since lattice-based mathematical problems are hard to be solved even by quantum computers, lattice-based cryptography is a promising foundation for future cryptographic schemes. In this paper, we focus on lattice-based public-key encryption schemes. This survey presents the current status of the lattice-based public-key encryption schemes and discusses the existing implementations. Our main focus is the learning with errors problem (LWE problem) and its implementations. In this paper, the plain lattice implementations and variants with special algebraic structures such as ring-based variants are discussed. Additionally, we describe a class of lattice-based functions called lattice trapdoors and their applications.

Smooth Projective Hash Function From Codes and its Applications

Nowadays, Smooth Projective Hash Functions (SPHFs) play an important role in constructing cryptographic tools such as secure Password-based Authenticated Key Exchange (PAKE) protocol in the standard model, oblivious transfer, and zero-knowledge proofs. Specifically, in this article, we focus on constructing PAKE protocol; that is, a kind of key exchange protocol which needs only a low entropy password to produce a cryptographically strong shared session key. In spite of relatively good progress of SPHFs in applications, it seems there has been little effort to build them upon quantum-resistant assumptions such as lattice-based cryptography and code-based cryptography to make them secure against quantum computer attacks. More precisely, there are two proposals based on lattice assumptions that utilize the SPHFs to construct PAKE secured in standard model. Considering quantum-resistant assumptions is less than straightforward and needs some relaxations. In this article, we introduce two new Approximate SPHF (ASPHFs) from error-correcting codes. Upon designing ASPHF, we can construct two efficient PAKE protocols. The security of our protocols could be proved based on the hardness of bounded decoding (BD) problem and learning with parity (LPN) problem in the standard model.

Bounds on quantum evolution complexity via lattice cryptography

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal’ operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to \sim 10^4∼104.

Ultra High-Speed Polynomial Multiplications for Lattice-Based Cryptography on FPGAs

Lattice-based cryptography (LBC) has emerged as the most viable substitutes to the classical cryptographic schemes as 5 out of 7 finalist schemes in the 3rd round of the NIST post-quantum cryptography (PQC) standardization process are lattice based in construction. This work explores novel architectural optimizations in the FPGA-based hardware implementation of polynomial multiplication, which is a bottleneck in every LBC construction. To target ultra-high throughput, both schoolbook polynomial multiplication (SPM) and number theoretic transform (NTT) are explored: a completely parallel architecture of an SPM is undertaken while for NTT, radix-2 and radix- <inline-formula><tex-math notation="LaTeX">$2^2$</tex-math></inline-formula> multi-path delay commutator (MDC) based pipelined architectures are adopted. Our proposed high-speed SPM (HSPM) structure on latest Xilinx UltraScale+ FPGA is 5× faster than the state-of-the-art LBC designs. Whereas, the proposed high-speed NTT (HNTT) structure (i.e., R <inline-formula><tex-math notation="LaTeX">$2^2$</tex-math></inline-formula> MDC) takes only 0.63 <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> s for the encryption, hence achieving the highest throughput of 408 Mbps. Moreover, all of the proposed designs achieve highest design efficiencies (i.e., throughput per slice (TPS)) in comparison to available LBC designs.

An extendable key space integer image-cipher using 4-bit piece-wise linear cat map

This paper presents a multiplierless image-cipher, with extendable 2048-bit key-space, based on a 4-dimensional (4D) quantized piece-wise linear cat map (PWLCM). The quantized PWLCM exhibits limit-cycles of 4-bit encoded integers with periods greater than 107. The synthesis of the PWLCM in a finite state space allows to eliminate the undesirable finite precision effect due to the hardware realization. The proposed image-cipher combines chaos, modular arithmetic, and lattice-based cryptography to encrypt a color image by performing pixel permutation and diffusion in a single operation. Further, an image-dependent confusion operation based on an 8-bit 2D-PWLCM is performed on the whole image to enhance security. In order to increase the key-space without key duplication, 16 × 16 sub-images are modified using sub-keys of different lattice length vectors generated from the external key. Both simulations and security analyses confirm that the proposed algorithm can resist common cipher attacks, in addition to its advantages such as simplicity, ease of implementation on low-end processors and extensibility of key-space that allows it to easily adapt even for future post-quantum computing attacks.