Permutation Layer Research Articles

LPHD: A low power and high diffusion lightweight block cipher

AbstractSmart door locks pose a large number of threats such as network attacks. Its storage area and power of cipher are severely limited because the wireless nodes of smart door locks are mostly battery‐powered. Therefore, effective security solutions are urgently needed. In this paper, a new lightweight block cipher with low power named LPHD is proposed to ensure the security of the master control chip of the smart door lock terminal. We design a scheme of low power S‐box and construct the two‐stage permutation layer (TP structure) suitable for LPHD by filtering the sets of 8‐bit permutations. LPHD proposes a variant of the 8‐branch generalized Feistel structure (GFS) to realize that the bits of all branches are affected in one encryption round. The problem of slow diffusion in the standard Feistel structure is solved. The key schedule adopts the nonlinear design and reuses the encryption process of LPHD. It improves the security of the cipher and reduces hardware overhead. Moreover, we evaluate the hardware implementation and security of LPHD. The results show that LPHD for the unified encryption and decryption circuits requires only 1276 Gate Equivalents (GEs) and 1.914 W on UMC 0.18 m, which is better than other lightweight block ciphers such as SKINNY, PRESENT, and IVLBC. In summary, LPHD provides sufficient security for the master control chip of the smart door lock terminal.

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.

Low area and high throughput hardware implementations for the LILLIPUT cipher

SummaryThe widespread use of Internet of Things devices has increased the demand for lower cost and more efficient lightweight ciphers. However, there is a difficult trade‐off between cost and efficiency for lightweight block ciphers. The optimizations of area and throughput are important for some constrained environments. This paper proposes two novel hardware architectures for the LILLIPUT cipher. In the novel low area structure, a new permutation layer is provided for LILLIPUT. The relationship between encryption algorithm and key scheduling algorithm is utilized to achieve optimal sharing among components, which significantly reduces hardware area. The experimental results show that the number of XOR gates and S‐boxes required for low area optimization is reduced by 52 and 8, respectively. The total area is reduced by about 18%. For high throughput structure, this paper provides 2‐round, 5‐round, and 15‐round loop unrolling designs for LILLIPUT to improve throughput. The experimental results show that the throughput of the 5‐round loop unrolling structure reaches a good level, which is relatively the most cost‐effective. In practical application, ciphers can be unrolled implementations according to the needs of devices to improve the execution speed, which can greatly reduce the execution time and complexity of the algorithm.

A LIGHTWEIGHT ENCRYPTION ALGORITHM TO SECURE IOT DEVICES

Lightweight cryptography is an effective solution for ensuring confidentiality and privacy in resource-constrained environments, particularly in Internet of Things (IoT) systems. These systems consist of a large number of IoT devices, such as sensor nodes and embedded devices that handle sensitive data and are connected via the Internet, making them susceptible to various types of attacks. Considering the constrained processing capability, memory size, and energy of these devices, this article proposes a lightweight block cipher that aims to provide security for IoT devices, with a focus on achieving efficient software implementation, particularly in devices with 32-bit processors. The structural design of the suggested algorithm is based on Type-2 Generalized Feistel Networks (GFN), which are based on four branches of 32-bit and simple key scheduling. To enhance the diffusion and strength of the GFN structure, a partial permutation layer has been added to the cipher. Moreover, to reduce the implementation cost, a simple round function has been designed using low-cost operations like Addition, XOR, and Rotation. Security of the suggested algorithm has been validated through security analysis, and the results show meeting the criteria for avalanche effect with 50.97% Key Sensitivity and 50.58% Plaintext Sensitivity, and the correlation coefficienttest results indicate a weak correlation between the plaintext and ciphertext, this makes it difficult to retrieve the plaintext from the ciphertext. When designing lightweight algorithms, one of the primary objectives is to enhance performance. To evaluate the algorithm's performance, we tested its execution time, code size, memory consumption, and throughput on real IoT devices, such as ESP8266 and ESP32, as an embedded cryptographic module. Based on the experimental results and security analysis, the suggested algorithm showed a good grade of security and higher performance in encryption and decryption operations than other lightweight algorithms, which makes it capable of providing a framework for securing data in the restricted IoT environment.

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.

Symmetrical Cryptosystems based on Cellular Automata

This paper deals with the development of two symmetric encryption algorithms on the basis of cellular automata: a block cipher, that is based on AES and uses three-dimensional cellular automata; a stream cipher, that exploits a hardware-software entropy generation (tracking of keystrokes and mouse pointer movement), as well as the developed hash function, based on “cryptographic sponge” architecture of SHA-3, modified by cellular automata transformations. The block cipher is designed in architecture of SP-network and uses the AES substitution block. Permutation layer and key generation is designed on the basis of cellular automata rules (rules “22”, “105” and “150”). The optimal number of rounds to achieve maximum crypto resistance is determined. The stream cipher is designed on the basis of hardware-software entropy generation and uses the cryptographic hash-function in the SHA-3 architecture. Permutation function is developed on the basis of cellular automata rules (rules “30” and “146”). The procedures of shift and permutation of rows and columns is used for better permutation. A final permutation of state elements is used to improve the avalanche effect. The received results are analyzed and summarized; the conclusions and justifications about cipher parameters (like number of rounds, where needed) are made.

Light-Weight Present Block Cipher Model for IoT Security on FPGA

The Internet of Things (IoT) plays an essential role in connecting a small number of billion devices with people for diverse applications. The security and privacy with authentication are challenging work for IoT devices. A light-weight block cipher is designed and modeled with IoT security for real-time scenarios to overcome the above challenges. The light-weight PRESENT module with the integration of encryption (E)-decryption (D) is modeled and implemented on FPGA. The PRESENT module has 64-bit data input with 80/128/256-bit symmetric keys for IoT security. The PRESENT module performs16/32/64 round operations for state register and key updation. The design mainly uses Substitution-permutation (SP) network for state updation. The permutation layer is used to create more diffusion and confusion in the state for unauthorized access. The results and analysis of the PRESENT-80/128/256 are designed using Verilog-HDL with Xilinx Environment and implemented on Artix-7 FPGA. The PRESENT-80/128/256 module is compared with similar recent works with performance improvements. Similarly, the proposed work is compared with different light-weight algorithms with improvements for better security in IoT devices. The proposed PRESENT-256 module with 64-rounds on Artix-7 FPGA utilizes less than 2% Chip area (Slices and LUTs), works at 412.4 MHz frequency, and consumes 192 mW total power and 0.58 Mbps/slice of hardware efficiency.

CTET+: A Beyond-Birthday-Bound Secure Tweakable Enciphering Scheme Using a Single Pseudorandom Permutation

In this work, we propose a construction of 2-round tweakable substitutionpermutation networks using a single secret S-box. This construction is based on non-linear permutation layers using independent round keys, and achieves security beyond the birthday bound in the random permutation model. When instantiated with an n-bit block cipher with ωn-bit keys, the resulting tweakable block cipher, dubbed CTET+, can be viewed as a tweakable enciphering scheme that encrypts ωκ-bit messages for any integer ω ≥ 2 using 5n + κ-bit keys and n-bit tweaks, providing 2n/3-bit security.Compared to the 2-round non-linear SPN analyzed in [CDK+18], we both minimize it by requiring a single permutation, and weaken the requirements on the middle linear layer, allowing better performance. As a result, CTET+ becomes the first tweakable enciphering scheme that provides beyond-birthday-bound security using a single permutation, while its efficiency is still comparable to existing schemes including AES-XTS, EME, XCB and TET. Furthermore, we propose a new tweakable enciphering scheme, dubbed AES6-CTET+, which is an actual instantiation of CTET+ using a reduced round AES block cipher as the underlying secret S-box. Extensivecryptanalysis of this algorithm allows us to claim 127 bits of security.Such tweakable enciphering schemes with huge block sizes become desirable in the context of disk encryption, since processing a whole sector as a single block significantly worsens the granularity for attackers when compared to, for example, AES-XTS, which treats every 16-byte block on the disk independently. Besides, as a huge amount of data is being stored and encrypted at rest under many different keys in clouds, beyond-birthday-bound security will most likely become necessary in the short term.

High-Speed Implementation of PRESENT on AVR Microcontroller

We propose the compact PRESENT on embedded processors. To obtain high-performance, PRESENT operations, including an add-round-key, a substitute layer and permutation layer operations are efficiently implemented on target embedded processors. Novel PRESENT implementations support the Electronic Code Book (ECB) and Counter (CTR). The implementation of CTR is improved by using the pre-computation for one substitute layer, two diffusion layer, and two add-round-key operations. Finally, compact PRESENT on target microcontrollers achieved 504.2, 488.2, 488.7, and 491.6 clock cycles per byte for PRESENT-ECB, 16-bit PRESENT-CTR (RAM-based implementation), 16-bit PRESENT-CTR (ROM-based implementation), and 32-bit PRESENT-CTR (ROM-based implementation) modes of operation, respectively. Compared with former implementation, the execution timing is improved by 62.6%, 63.8%, 63.7%, and 63.5% for PRESENT-ECB, 16-bit PRESENT-CTR (RAM based implementation), 16-bit PRESENT-CTR (ROM-based implementation), and 32-bit PRESENT-CTR (ROM-based implementation) modes of operation, respectively.

Fast Frequency Sweep Analysis of Passive Miniature RF Circuits Based on Analytic Extension of Eigenvalues

The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with $4$-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by 0.15dB--0.3dB when we use CRC-aided SCL decoder with list size $32$ for both codes. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar

Swap and Rotate: Lightweight Linear Layers for SPN-based Blockciphers

In CHES 2017, Jean et al. presented a paper on “Bit-Sliding” in which the authors proposed lightweight constructions for SPN based block ciphers like AES, PRESENT and SKINNY. The main idea behind these constructions was to reduce the length of the datapath to 1 bit and to reformulate the linear layer for these ciphers so that they require fewer scan flip-flops (which have built-in multiplexer functionality and so larger in area as compared to a simple flip-flop). In this paper, we develop their idea even further in few separate directions.First, we prove that given an arbitrary linear transformation, it is always possible to construct the linear layer using merely 2 scan flip-flops. This points to an optimistic venue to follow to gain further GE reductions, yet the straightforward application of the techniques in our proof to PRESENT and GIFT leads to inefficient implementations of the linear layer, as reducing ourselves to 2 scan flip-flops setting requires thousands of clock cycles and leads to very high latency.Equipped with the well-established formalism on permutation groups, we explore whether we can reduce the number of clock cycles to a practical level, i.e. few hundreds, by adding few more pairs of scan flip flops. For PRESENT, we show that 4 (resp. 8, 12) scan flip-flops are sufficient to complete the permutation layer in 384 (resp. 256, 128) clock cycles. For GIFT, we show that 4 (resp. 8, 10) scan flip flops correspond to 320 (resp. 192, 128) clock cycles. Finally, in order to provide the best of the two worlds (i.e. circuit area and latency), we push our scan flip-flop choices even further to completely eliminate the latency incurred by the permutation layer, without compromising our stringent GE budget. We show that not only 12 scan flip flops are sufficient to execute PRESENT permutation in 64 clock cycles, but also the same scan flip flops can be used readily in a combined encryption decryption circuit. Our final design of PRESENT and GIFT beat the record of Jean et al. and Banik et al. in both latency and in circuit-size metric. We believe that the techniques presented in our work can also be used at choosing bit-sliding-friendly linear layer permutations for the future SPN-based designs.

Key-Dependent Permutation Layer Based on Two Dimensional Discretized Chaotic Maps for Lightweight Block Ciphers

This paper proposes a design of a key-dependent permutation layer. Based on the comparison of the properties for different two-dimensional discretised chaotic maps, the Standard map is chosen with good diffusion properties to construct a chaos-based permutation layer in block ciphers. The proposed construction has both high security strength and hardware efficiency. The result of the hardware implementation shows that it is suitable for lightweight block ciphers due to its low resource utilisation.

Key-dependent permutation layer based on two dimensional discretised chaotic maps for lightweight block ciphers

Key-dependent permutation layer based on two dimensional discretised chaotic maps for lightweight block ciphers

Compact Lightweight Cryptographic Algorithmfor Optimizationof Resources

The study of Lightweight cryptography has been one of the intresting topics in symmetric cryptography in the recent years. Lightweight symmetric ciphers has gained interest due to the increasing demand for security services in constrained computing environments, such as in the Internet of Things(IoT). Though the protocols of light weight in are providingingmore security in variousapplications,resource utility is more in key generation, key scheduling, permutation layer and substitution box layer operations. More resource usage make possibletohave highutilization of power andoverhead of area. In this paper, a novel method is proposed to decrease theutility of resoures, which followsregister reutilization scheme. The resource reutilization is coordinating with the delay inSubstitutionPermutation Network (SPN).Our design is compared, using area, throughput, power, and latency as metrics.

A New Method for Finding Impossible Differentials of Generalized Feistel Structures

Impossible differential cryptanalysis is one of the most powerful attacks against modern block ciphers. In most cases, the resistance of a block cipher against impossible differential cryptanalysis can be measured by the length of the longest impossible differentials. By taking a closer look into the round function, we present a new method to find longer impossible differentials of wordoriented generalized Feistel structures. We conclude the existence of impossible differentials by the nonzero points of the XOR-ed masked differences in the middle round. This method uses differential style and its nonzero point to find the impossible differential, which is much easier than the classical impossible differential searching method. By applying our method, we can find several longest impossible differentials of some famous block cipher structures with SP (Substitution-permutation) round functions. If some extra conditions of the round function are taken into consideration (e.g. the permutation layer is designed as binary matrix or some sparse matrix), longer impossible differentials could be achieved by our method.

Fault Attacks Made Easy: Differential Fault Analysis Automation on Assembly Code

Over the past decades, fault injection attacks have been extensively studied due to their capability to efficiently break cryptographic implementations. Fault injection attack models are normally determined by analyzing the cipher structure and finding exploitable spots in non-linear and permutation layers. However, this level of abstraction is often too high to distinguish vulnerable parts of software implementations, due to specific operations and optimizations. On the other hand, manually analyzing the assembly code requires non-negligible amount of time and expertise. In this paper, we propose an automated approach for analyzing cipher implementations in assembly. We represent the whole assembly program as a data flow graph so that the vulnerable spots can be found efficiently. Fault propagation is analyzed in a subgraph constructed from each vulnerable spot, allowing equations for Differential Fault Analysis (DFA) to be automatically generated. We have created a tool that implements our approach: DATAC – DFA Automation Tool for Assembly Code. We have successfully used this tool for attacking PRESENT- 80, being able to find implementation-specific vulnerabilities that can be exploited in order to recover the last round key with 16 faults. Our results show that DATAC is useful in finding attack spots that are not visible from the cipher structure, but can be easily exploited when dealing with real-world implementations.

Tight Bounds of Differentially and Linearly Active S-Boxes and Division Property of Lilliput

This paper provides security analysis of a lightweight block cipher called Lilliput , which was proposed in IEEE Transactions on Computers in 2015. Lilliput adopts an extended generalized Feistel network (EGFN). EGFN consists of non-linear, linear, and permutation layers, and the linear layer updates a part of the state only linearly, which causes several security concerns. Our first discovery is that the lower bounds of the number of differentially active S-boxes provided by the designers are incorrect. Thus the new bounds are derived by using mixed integer linear programming (MILP). We apply a two-stage search procedure introduced by Sun et al. that leads to tight bounds even for a large number of rounds. The search tool is then converted for linear cryptanalysis. With those updates, the challenging problem of evaluating Lilliput 's security against differential and linear cryptanalysis is closed. Another contribution is the best third-party cryptanalysis. The designers expected EGFN to efficiently enhance security against integral cryptanalysis. However, security is not as enhanced as the designers expected. In fact, division property finds a 13-round distinguisher that improves on the previous distinguisher by 4 rounds. The distinguisher is further extended to a 17-round key recovery that improves on the previous best attack by 3 rounds.

BORON: an ultra-lightweight and low power encryption design for pervasive computing

We propose an ultra-lightweight, compact, and low power block cipher BORON. BORON is a substitution and permutation based network, which operates on a 64-bit plain text and supports a key length of 128/80 bits. BORON has a compact structure which requires 1939 gate equivalents (GEs) for a 128-bit key and 1626 GEs for an 80-bit key. The BORON cipher includes shift operators, round permutation layers, and XOR operations. Its unique design helps generate a large number of active S-boxes in fewer rounds, which thwarts the linear and differential attacks on the cipher. BORON shows good performance on both hardware and software platforms. BORON consumes less power as compared to the lightweight cipher LED and it has a higher throughput as compared to other existing SP network ciphers. We also present the security analysis of BORON and its performance as an ultra-lightweight compact cipher. BORON is a well-suited cipher design for applications where both a small footprint area and low power dissipation play a crucial role.

A Random PRESENT Encryption Algorithm Based on Dynamic S-box

S-box mainly plays the role of confusion in the encryption process as an important component. For the new encryption algorithm PRESENT proposed in 2007, S-box impacts on the security of the encryption algorithm directly. This paper briefly describes the process of PRESENT algorithm and proposes an improved S-box to solve the problem that the original PRESENT S-box has anti-fixed point. Then a random PRESENT encryption algorithm based on dynamic S-box is proposed. The dynamic multiple S-boxes technology is used to implement random PRESENT algorithm, to enhance the security of the cryptographic algorithm. Finally, the security analysis is done, and it suggests that dynamic S-box has a superior ability to resist differential attack and linear attack. By comparison to the diffusion rate of original PRESENT S-box, our dynamic S-box has better avalanche effect. With the rapid development of the Internet of Things, the radio frequency identification (RFID), wireless sensor network (WSN), and other new technologies go deep into all aspects of people's work and life. However, RFID and WSN are based on wireless network to transfer information. The transmission of information is not difficult to be obtained, interfered, and even destroyed by the attackers. So information security technology is widely used in protecting networks to enhance the safety of secret information. And the traditional symmetric encryption algorithm is often restricted by hardware, which cannot achieve good effects under the condition of limited hardware and power consumption. Therefore, lightweight cipher algorithm such as PRESENT(1) and LED(2) has gradually become the realistic choice to ensure the information security of Internet of Things. The lightweight block encryption algorithm PRESENT (1), put forward by Bogdanov in 2007, is carefully designed with area and power constraints uppermost in limited conditions. So the PRESENT algorithm still has high security in the application of limited space and power consumption, such as sensor network node. However, the permutation transformation of PRESENT algorithm is different with the column confusion of AES. It uses bit as the permutation function input unit while AES uses byte for permutation. The permutation layer of PRESENT encryption algorithm is a perfectly symmetrical structure and easy implemented. Because the structure of this kind of design has poor diffusibility, the PRESENT algorithm diffusively quality mainly depends on the diffusion properties of S-box. So S-box, as a nonlinear component in lightweight block encryption algorithm, affects the strength of the whole structure of the cipher. To strengthen DES by using existing hardware, an improved method of DES which uses the S-box related to a key is put forward in paper (4), and the researcher has demonstrated the safety of the improved method. Meanwhile, a new key related

MANTRA: An Ultra lightweight cipher design for ubiquitous computing

In this paper, we are proposing an ultra lightweight cipher MANTRA. MANTRA is a Feistel-based network which operates on 64-bit plain text and supports 128/80-bit key length. It needs very less footprint area and consumes only 1662 gate equivalents for the 128-bit key length and 1374 for 80-bit key length. The novel design of MANTRA uses a Feistel within a Feistel structure. Its memory size is less as compared to existing lightweight ciphers. In this paper, we have presented the security analysis of MANTRA and its performance as an ultra lightweight cipher. A strong permutation layer in MANTRA prevents clustering of linear and differential trails when the cipher is attacked. MANTRA shows good resistance against Biclique and zero correlation attacks. MANTRA is a cipher design well suited for the applications where small footprint area and low power dissipation play crucial role.