Substitution-permutation Network Research Articles

SPN based RGB image encryption over Gaussian integers

This research paper proposes a novel approach for constructing substitution boxes (S-boxes) over Gaussian integers, which are complex numbers with integer coefficients. The proposed method is based on the properties of the Gaussian integers and their arithmetic operations and ensures the S-boxes exhibit strong cryptographic properties. Furthermore, the paper demonstrates how these S-boxes can be utilized for image encryption through a substitution-permutation network (SPN) over Gaussian integers. The SPN involves iteratively applying the S-box and a permutation layer to the input image, which effectively scrambles the image data. Experimental results show that the proposed method achieves high security and robustness against various attacks while providing efficient encryption and decryption performance. This research thus provides a promising avenue for developing secure image encryption schemes based on Gaussian integers.

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

In the realm of smart communication systems, where the ubiquity of 5G/6G networks and IoT applications demands robust data confidentiality, the cryptographic integrity of block and stream cipher mechanisms plays a pivotal role. This paper focuses on the enhancement of cryptographic strength in these systems through an innovative approach to generating substitution boxes (S-boxes), which are integral in achieving confusion and diffusion properties in substitution–permutation networks. These properties are critical in thwarting statistical, differential, linear, and other forms of cryptanalysis, and are equally vital in pseudorandom number generation and cryptographic hashing algorithms. The paper addresses the challenge of rapidly producing random S-boxes with desired cryptographic attributes, a task notably arduous given the complexity of existing generation algorithms. We delve into the hill climbing algorithm, exploring various cost functions and their impact on computational complexity for generating S-boxes with a target nonlinearity of 104. Our contribution lies in proposing a new cost function that markedly reduces the generation complexity, bringing down the iteration count to under 50,000 for achieving the desired S-box. This advancement is particularly significant in the context of smart communication environments, where the balance between security and performance is paramount.

RAZOR A Lightweight Block Cipher for Security in IoT

Rapid technological developments prompted a need to do everything from anywhere and that is growing due to modern lifestyle. The Internet of Things (IoT) technology is helping to provide the solutions by inter-connecting the smart devices. Lightweight block ciphers are deployed to enable the security in such devices. In this paper, a new lightweight block cipher RAZOR is proposed that is based on a hybrid design technique. The round function of RAZOR is designed by mixing the Feistel and substitution permutation network techniques. The rotation and XOR based diffusion function is applied on 32-bit input with 8 branches and branch number 7 to optimize the security. The strength of RAZOR is proved against differential, linear, and impossible differential attacks. The number of active S-boxes in any 5-round differential characteristic of RAZOR is 21 in comparison to the 10, 6, 4, 7, and 6 for PRESENT, Rectangle, LBlock, GIFT, and SCENERY respectively. RAZOR provides better security than the existing lightweight designs. The average throughput of 1.47 mega bytes per second to encrypt the large files makes it a better choice for software oriented IoT applications.

Secure and Efficient NVM Usage for Embedded Systems Using AES-128 and Huffman Compression

Embedded systems are customized systems designed to meet functionality and specific usage purposes. These systems often grapple with challenges such as power interruptions, limited memory space, and the expectation of a long operational lifespan. It is in this context that Non-Volatile Memory (NVM) plays a vital role. NVM is a type of memory that ensures data persistence even in situations of temporary power loss or signal interruptions. Efficiently utilizing NVM is a critical necessity for the effectiveness and reliability of these systems. Efficient utilization of NVM necessitates the effective management of write and read cycles. Previous studies have demonstrated the efficient utilization of NVM sectors by ensuring that no garbage bytes remain unallocated. Previous studies have demonstrated the efficient utilization of NVM by compressing the data to be written into NVM using the Huffman compression algorithm, and filling sectors without any residual garbage bytes. This paper aspires to advance beyond prior research by integrating the Advanced Encryption Standard (AES-128) block encryption algorithm, aiming to optimize the utilization of NVM to a greater extent. The AES-128 algorithm provides data security with encryption and decryption operations. By applying AES-128 encryption to the data before writing it to the NVM, this work adds a data security layer to the developed software module. Data is divided into blocks using this algorithm. Each block is encrypted independently and then reassembled. The encryption process includes key management, substitution-permutation network layers, and multiple rounds, all of which make substantial contributions to high-level data security. The resulting encrypted data is compressed using the Huffman compression algorithm. This process enhances both the security and efficiency of data storage. The data is written to NVM with maximum efficiency, ensuring that no residual garbage bytes remain, upon the completion of the encryption and compression processes. This study surpasses previous research by enhancing storage security and efficiency through these processes. Moreover, the developed secure and efficient NVM usage, as it fills the NVM with data without leaving any garbage bytes, results in slower processing speed compared to standard NVM usage. Therefore, in future research, interventions with code optimization techniques can be applied to the developed algorithms to enhance write and read speeds.

An innovative approach for dynamic key dependent S-Box to enhance security of IoT systems

The Internet of Things (IoT) foresees pervasive and connected smart nodes that interact independently while offering varied services. Today, IoT nodes are a treasure house of data and hence security has become a major concern in IoT networks. Conventional cryptography faces many challenges during implementation in IoT devices. These challenges can be tackled by lightweight cryptography which is highly secure with less resource requirements. The vital characteristic of security is fulfilled by one out of 6 inner structures such as Substitution-Permutation Network, Feistel Network, General Feistel Network, Add-Rotate-XOR, Non Linear-Feedback Shift Register and Hybrid. PRESENT, which is a NIST approved lightweight cryptographic algorithm with SPN structure uses fixed or static S-Box. This permits attackers to explore S-Box and identify weaknesses of the algorithm. Key dependent approaches are better because it impedes an attacker from any offline analyses of attacks on the S-Box. Additionally, this is susceptible to linear and differential attacks. The static S Box does not possess superior diffusion and does not have a good rate of avalanche effect. So, the solution is to create a robust dynamic key dependent algorithm with nonlinear S-Boxes to secure the communication between IoT devices and platform. Security analysis is done on Non-linearity, Differential and Linear Cryptanalysis and Avalanche characteristics, besides, encryption of IoT data to demonstrate its aptness for cold chain security applications.© 2017 Elsevier Inc. All rights reserved.

Pincering SKINNY by Exploiting Slow Diffusion

Lightweight cryptography is an emerging field where designers are testing the limits of symmetric cryptography. We investigate the resistance against sidechannel attacks of a new class of lighter blockciphers, which use a classic substitution–permutation network with slow diffusion and many rounds.Among these ciphers, we focus on SKINNY, a primitive used up to the final round ofNIST’s recent lightweight standardisation effort. We show that the lack of diffusion in the key scheduler allows an attacker to combine leakage from the first and the last rounds, effectively pincering its target. Furthermore, the slow diffusion used by its partial key-absorption and linear layers enable, on both sides, to target S-Boxes from several rounds deep.As some of these S-boxes leak on the same part of the key, full key recovery exploiting all leakage requires a clever combining strategy. We introduce the use of cluster graph inference (an established tool from probabilistic graphical model theory) to enhance both unprofiled or profiled differential power analysis, enabling us to handlethe increase of S-Boxes with their intertwined leakage.We evaluate the strength of our attack both in the Hamming weight model and against two implementations running on an STM32F303 ARM Cortex-M4 hosted on a ChipWhisperer target board, showing that our attack reduces the number of traces required to attack SKINNY by a factor of around 2.75.

Algebraic Attacks against Grendel: An Arithmetization-Oriented Primitive with the Legendre Symbol

The rise of modern cryptographic protocols such as Zero-Knowledge proofs and secure Multi-party Computation has led to an increased demand for a new class of symmetric primitives. Unlike traditional platforms such as servers, microcontrollers, and desktop computers, these primitives are designed to be implemented in arithmetical circuits. In terms of security evaluation, arithmetization-oriented primitives are more complex compared to traditional symmetric cryptographic primitives. The arithmetization-oriented permutation Grendel employs the Legendre Symbol to increase the growth of algebraic degrees in its nonlinear layer. To analyze the security of Grendel thoroughly, it is crucial to investigate its resilience against algebraic attacks. This paper presents a preimage attack on the sponge hash function instantiated with the complete rounds of the Grendel permutation, employing algebraic methods. A technique is introduced that enables the elimination of two complete rounds of substitution permutation networks (SPN) in the sponge hash function without significant additional cost. This method can be combined with univariate root-finding techniques and Gröbner basis attacks to break the number of rounds claimed by the designers. By employing this strategy, our attack achieves a gain of two additional rounds compared to the previous state-of-the-art attack. With no compromise to its security margin, this approach deepens our understanding of the design and analysis of such cryptographic primitives.

IVLBC: An Involutive Lightweight Block Cipher for Internet of Things

Nowadays, the use of the Internet of Things has reached a commanding height in a new round of economic and technological upsurge. Its data transmission security has attracted much attention. It is well known that substitution permutation networks (SPNs) ciphers with high diffusion are not advantageous in unified encryption and decryption circuits with extremely resources constrained. Although some research has been carried out to address this issue, there are still insufficiencies. In this article, we propose a new 64-bit lightweight block cipher based on SPN named IVLBC, whose key allows 80 and 128 bits. The components of IVLBC are involutions. In particular, we propose a Feistel with tree structure to obtain a compact and involutive S-box. Also, the nibble-based involutive permutation is proposed to obtain the involutive permutation. Decryption can reuse encrypted code and circuitry in both software and hardware implementations. We prove that the costs of IVLBC are less than PRESENT, PRINCE, Midori, I-PRESENTTM, CRAFT, etc., in unified encryption and decryption circuits. In addition, we conduct other performance tests on IVLBC such as the differential attack, linear attack, integral attack, algebraic attack, invariant attacks, etc.

Basic Cryptographic Concepts and Open Problems in Hash Function Security

JOHNNA SMITH, Dept of Mathematics, Shepherd University, Shepherdstown, WV, 25443, and DONALD MILLS, Dept of Computer Sciences, Mathematics, and Engineering, Shepherd University, Shepherdstown, WV, 25443. Analysis of basic cryptographic concepts and recent open problems in hash function security. 
 
 The objectives of this study are to show an understanding of cryptographic concepts as well as highlight recent open problems involving hash function security. The method of study used included reading the first five chapters of Cryptography: Theory and Practice by Stinson and Paterson as well as a recent paper that outlined open problems in hash function security. Then, written reports were delivered on the information learned which included selected proofs and solved examples. The essentials of the opening report introduce the basic elements of cryptography: cryptosystems, cryptographic tools, message integrity, protocols, and security approaches. Chapter 2 of “Cryptography” describes various types of ciphers including Shift, Substitution, Affine, Vigenère, Hill, Permutation, and Stream Ciphers, as well as how to cryptanalyze them. The third report focuses on the One-time Pad, entropy, perfect security, and cryptographic security, specifically unconditional security, as introduced by Claude Shannon in his work on information theory. Throughout the fourth report, block and stream ciphers, including substitution-permutation networks, attacks such as linear and differential cryptanalysis, and modes of operation are discussed. In the fifth report, basic concepts of cryptography, hash function and message authentication are discussed, including iterated hash function, sponge construction, and unconditionally secure MACS. Using the information learned from the previous reports, current problems in hash functions were then researched. In conclusion, open problems in hash function security include collision resistance, preimage resistance, and resistant to length extension attacks. The project was sponsored by the NSF S-STEM Grant (DUE-2130267).

Modified Generalized Feistel Network Block Cipher for the Internet of Things

With the advent of the Internet-of-Things (IoT) technologies, millions of low-resource devices are constantly used at the network’s edge. As a result, the large amount of private and sensitive data generated by these devices must be securely transported, stored, and processed, posing a challenge because these resource-constrained IoT devices cannot meet the criteria of conventional encryption ciphers. Due to this limitation on IoT-enabled devices, lightweight cryptography has emerged as a new area of study. Lightweight block ciphers, a subfield of lightweight cryptography, include the substitution–permutation network (SPN) and Feistel-based networks. Feistel networks are further divided into two types: classical Feistel networks and generalized Feistel networks (GFN). While classical Feistel ciphers divide a message into two sub-blocks, GFN divides a message into k sub-blocks for some k > 2 called the partition number. One popular form of GFN is the so-called Type-II. Unfortunately, this type of Feistel structure needs a large number of rounds to obtain a full diffusion property. A full diffusion means all output sub-blocks are affected by all input sub-blocks. Therefore, this paper proposed a new lightweight block cipher by modifying the GFN structure, focusing on providing optimal security to the cipher with a small number of rounds. The algorithm was subjected to a series of statistical and cryptographic randomization analyses in order to investigate the avalanche effect on the ciphertext and the algorithm’s random properties, such as confusion, diffusion, and independence. The avalanche criterion and output randomness results show that this algorithm meets the fundamental security requirement for a lightweight block cipher.

SPISE: A tiny, cost effective, speedy block cipher for low resourced devices

The Internet of Things has come up as a blessing in this fast paced technologically advanced world where it finds huge role in everyday life of people in the form of various sensors embedded in various systems which are connected with the Internet. Transmission and reception of data in digitized form is done by the IoT devices after collection of varied forms of data from various sources. In present times of IoT technology data safety is a blooming concern that hampers the confidentiality of valuable data greatly. A novel lightweight encryption strategy is devised by keeping the concern of data security by the name of SPISE which is aimed for general computing and IoT devices. SPISE enjoys both the architectural benefits of substitution permutation network and that of General Feistel structure to ensure better security. The new crafted method has achieved very low count of equivalent gates as low as 728 GE and is exceedingly swift with very low computational time of 1.364 ns with ultra-low power consumption of 32.16 µW when tested in Cadence Genus using 65 nm process technology and when synthesized on XC7VX330T Virtex 7 FPGA board in Xilinx ISE 14.7.

Design of a Lightweight Cryptographic Scheme for Resource-Constrained Internet of Things Devices

We propose an ultra-lightweight cryptographic scheme called “Small Lightweight Cryptographic Algorithm (SLA)”. The SLA relies on substitution–permutation network (SPN). It utilizes 64-bit plaintext and supports a key length of 80/128-bits. The SLA cipher includes nonlinear layers, XOR operations, and round permutation layers. The S-box serves to introduce nonlinearity in the entire scheme design. It plays a vital role in increasing the complexity and robustness of the design. The S-box can thwart attacks such as linear and differential attacks. The scheme makes it possible to breed many active S-boxes in a short number of rounds, hindering analytical attacks on the cipher. When compared to other currently used ciphers, SLA has a higher throughput. Additionally, we demonstrate the SLA’s performance as an ultra-lightweight compact cipher, and its security analysis. The SLA cipher’s design is well suited for applications where small-scale embedded system dissipation is critical. The SLA algorithm is implemented using Python.

A novel design of audio signals encryption with substitution permutation network based on the Genesio-Tesi chaotic system

A novel design of audio signals encryption with substitution permutation network based on the Genesio-Tesi chaotic system

A novel encryption algorithm using multiple semifield S-boxes based on permutation of symmetric group

There is a need of secure and robust encryption algorithm that can be implemented on each and diverse software and hardware platforms. In this paper, we investigate semifield substitution boxes using permutation of symmetric group on a set of size 8 S_8 and establish an effective procedure for generating S_8 semifield substitution boxes having same algebraic properties. Further, the strength analysis of the generated substitution boxes is carried out using the well-known standards, namely bijectivity, non-linearity, strict avalanche criterion, bit independence criterion, XOR table and differential invariant. As application, an encryption algorithm is proposed that can be employed to strengthen any kind of secure communication. The presented algorithm is mainly based on the Shannon idea of substitution–permutation network where the process of substitution is performed by the proposed S_8 semifield substitution boxes and permutation operation is performed by the binary cyclic shift of substitution box transformed data. In addition, the proposed encryption algorithm utilizes two different chaotic maps. To ensure the appropriate utilization of these chaotic maps, we carry out in-depth analyses of their behavior in the context of secure communication and apply the pseudo-random sequences of chaotic maps in the proposed image encryption algorithm accordingly.

Design of highly nonlinear confusion component based on entangled points of quantum spin states

Cryptosystems are commonly deployed to secure data transmission over an insecure line of communication. To provide confusion in the data over insecure networks, substitution boxes are the solitary components for delivering a nonlinear mapping between inputs and outputs. A confusion component of a block cipher with high nonlinearity and low differential and linear approximation probabilities is considered secure against cryptanalysis. This study aims to design a highly nonlinear substitution-permutation network using the blotch symmetry of quantum spin states on the Galois field GF (28). To observe the efficiency of the proposed methodology, some common and advanced measures were evaluated for performance, randomness, and cryptanalytics. The outcomes of these analyses validate that the generated nonlinear confusion components are effective for block ciphers and attain better cryptographic strength with a high signal-to-noise ratio in comparison to state-of-the-art techniques.

A New Construction Method for Keystream Generators

We introduce a new construction method of diffusion layers for Substitution Permutation Network (SPN) structures along with its security proofs. The new method can be used in block ciphers, stream ciphers, hash functions, and sponge constructions. Moreover, we define a new stream cipher mode of operation through a fixed pseudorandom permutation and provide its security proofs in the indistinguishability model. We refer to a stream cipher as a Small Internal State Stream (SISS) cipher if its internal state size is less than twice its key size. There are not many studies about how to design and analyze SISS ciphers due to the criterion on the internal state sizes, resulting from the classical tradeoff attacks. We utilize our new mode and diffusion layer construction to design an SISS cipher having two versions, which we call DIZY. We further provide security analyses and hardware implementations of DIZY. In terms of area cost, power, and energy consumption, the hardware performance is among the best when compared to some prominent stream ciphers, especially for frame-based encryptions that need frequent initialization. Unlike recent SISS ciphers such as Sprout, Plantlet, LILLE, and Fruit; DIZY does not have a keyed update function, enabling efficient key changing.

Improved Linear Cryptanalysis of Block Cipher BORON

Abstract BORON is a lightweight substitution–permutation network cipher proposed in 2017. We reduce the number of guessed key bits by key-bridging technology and first utilize Fast Walsh Transform on BORON to minimize the time complexity. Finally, this paper gives the better key-recovery attack against block cipher BORON than previously proposed by 2 rounds: we realize a 11-round key-recovery attack on BORON-80 and 13-round key-recovery attack on BORON-128. The attacks proposed in this paper are the best attacks against BORON-80/128 to date.

Decomposing Linear Layers

There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not been paid that much attention so far. To fill this gap, in this work, we develop a systematic approach to decomposing structure in the linear layer of a substitutionpermutation network (SPN), covering the case in which the specification of the linear layer is obfuscated by applying secret linear transformations to the S-boxes. We first present algorithms to decide whether an ms x ms matrix with entries in a prime field Fp can be represented as an m x m matrix over the extension field Fps . We then study the case of recovering structure in MDS matrices by investigating whether a given MDS matrix follows a Cauchy construction. As an application, for the first time, we show that the 8 x 8 MDS matrix over F28 used in the hash function Streebog is a Cauchy matrix.

Reevaluating Graph-Neural-Network-Based Runtime Prediction of SAT-Based Circuit Deobfuscation

Logic locking is a technique that can help hinder reverse-engineering-based attacks in the IC supply chain from untrusted foundries or end-users. In 2015, the Boolean Satisfiability (SAT) attack was introduced. Although the SAT attack is effective in deobfuscating a wide range of logic locking schemes, its execution time varies widely from a few seconds to months. Previous research has shown that Graph Convolutional Networks (GCN) may be used to estimate this deobfuscation time for locked circuits with varied key sizes. In this paper, we explore whether GCN models truly understand/capture the structural/functional sources of deobfuscation hardness. In order to tackle this, we generate different curated training datasets: traditional ISCAS benchmark circuits locked with varying key sizes, as well as an important novel class of synthetic benchmarks: Substitution-Permutation Networks (SPN), which are circuit structures used to produce the most secure and efficient keyed-functions used today: block-ciphers. We then test whether a GCN trained on a traditional benchmark can predict the simple fact that a deeper SPN is superior to a wide SPN of the same size. We find that surprisingly the GCN model fails at this. We propose to overcome this limitation by proposing a set of circuit features motivated by block-cipher design principles. These features can be used as stand-alone or combined with GCN models to provide deeper topological cues than what GCNs can access.

Proposed new modification of AES algorithm for data security

In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as cipher text. Ideally, only authorized parties can decipher a cipher text back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. AES is based on a design principle known as a substitution–permutation network, and is efficient in both software and hardware. Unlike its predecessor DES, AES does not use a Feistel network. AES is a variant of Rijndael, with a fixed block size of 128 bits, and a key size of 128, 192, or 256 bits. By contrast, Rijndael per se is specified with block and key sizes that may be any multiple of 32 bits, with a minimum of 128 and a maximum of 256 bits. In this research, a method has been suggested using the encryption algorithm multiple and serially since it was used4) - AES (implemented serially. The proposed algorithm is faster because it encrypts 64 bytes together. It encrypts all kinds of data and the number of files that are encrypted (2048) file and in one as it is possible to encrypt several files or one file at the same time. The performance of this technique has been done by computer using mathlab package.