A Novel Framework to Construct S-Box Quantum Circuits Using System Modeling: Application to 4-Bit S-Boxes

Quantum computers accelerate many algorithms based on the superposition principle of quantum mechanics.The Grover algorithm provides significant performance to malicious users attacking symmetric key systems.Since the performance of attacks using quantum computers depends on the efficiency of the quantum circuit of the encryption algorithms,research research on the implementation of quantum circuits is essential.This paper presents a new framework to construct quantum circuits of substitution boxes(S-boxes)using system modeling.We model the quantum circuits of S-boxes using two layers:Toffoli and linear layers.We generate vector spaces based on the values of qubits used in the linear layers and apply them to find quantum circuits.The framework finds the circuit bymatching elements of vector spaces generated fromthe input and output of a given S-box,using the forward search or themeet-in-the-middle strategy.We developed a tool to apply this framework to 4-bit S-boxes.While the 4-bit S-box quantum circuit construction tool LIGHTER-R only finds circuits that can be implemented with four qubits,the proposed tool achieves the circuits with five qubits.The proposed tool can find quantum circuits of 4-bit odd permutations based on the controlled NOT,NOT,and Toffoli gates,whereas LIGHTER-R is unable to perform this task in the same environment.We expect this technique to become a critical step toward optimizing S-box quantum circuits.

A High Efficiency Hardware Implementation of S-Boxes Based on Composite Field for Advanced Encryption Standard

The SubBytes (S-box) transformation is the most crucial operation in the AES algorithm, significantly impacting the implementation performance of AES chips. To design a high-performance S-box, a segmented optimization implementation of the S-box is proposed based on the composite field inverse operation in this paper. This proposed S-box implementation is modeled using Verilog language and synthesized using Design Complier software under the premise of ensuring the correctness of the simulation result. The synthesis results show that, compared to several current S-box implementation schemes, the proposed implementation of the S-box significantly reduces the area overhead and critical path delay, then gets higher hardware efficiency. This provides strong support for realizing efficient and compact S-box ASIC designs.

Efficient image encryption scheme with synchronous substitution and diffusion based on double S-boxes

Single or multiple S-boxes are widely used in image encryption schemes, and in many image encryption schemes the asynchronous encryption structure is utilized, which separates the processes of substitution and diffusion. In this paper, we analyze the defects of this structure based on the example of an article and crack it using a simpler method. To address the defects of the asynchronous encryption structure, a novel encryption scheme is proposed, in which the structure of synchronous substitution and diffusion based on double S-boxes is utilized, so the processes of substitution and diffusion are combined together and the attackers cannot crack the cryptosystem by any of the processes. The simulation results and security analysis show that the proposed encryption scheme is safer and more efficient to expediently use in the real-time system.

Genetic Algorithm-Based Approaches for Optimizing S-Boxes

Multi-objective genetic algorithm is much suitable for solving multi-objective optimization problems. By use of Genetic algorithm, the optimization of S-boxes is explored in this paper. Results of the experiments show that, with heuristic mutation strategy, the algorithm has high searching efficiency and fast convergence speed. Meanwhile, we also have take the avalanche probability of S-boxes into account, besides nonlinearity and difference uniformity. Under this method, an effective genetic algorithm for 6×6 S-boxes is provided and a number of S-boxes with good cryptographic capability can be obtained.

Effective method for the design of S-Boxes satisfying the strict avalanche criterion(SAC)

The strict avalanche criterion(SAC)is one of the most important cryptographic criteria for substitution boxes(S-boxes)used in many symmetric encryption systems.However,there are few constructive methods for S-boxes fulfilling the SAC until now.In this paper,to construct S-boxes satisfying the SAC directly,we generalize the concatenation techniques of Boolean functions to S-boxes.Using the idea of concatenating small variable S-boxes,we present a simple yet effective construction method of S-boxes satisfying the SAC.Finally,a simple example on how to construct SAC S-boxes with large input variables by small variables SAC S-boxes is given.

Design of strong S-boxes based on spatiotemporal chaotic system

A substitution box (S-box) plays an important role in cryptographic algorithms.The design of S-box using chaotic systems has attracted a great deal of attention in recent years.A new method for obtaining cryptographically strong S-boxes based on spatiotemporal chaotic system is proposed in this paper.The discretized Baker map and affine transformation are used orderly by an algorithm to shuffle the table generated by the spatiotemporal chaotic system.The cryptographical properties of these S-boxes such as bijection,nonlinearity,strict avalanche,output bits independence and equiprobable input /output XOR distribution are analyzed.The results of numerical analysis show that the S-box designed by this method can against several attacks and all the criteria for designing good S-box can be satisfied approximately.More strong S-boxes can be obtained by this method with the change of the original conditions or control parameters of the spatiotemporal chaos system.Furthermore,our approach is suitable for practical application in designing cryptosystem.

A Review of Existing 4-Bit Crypto S-Box Cryptanalysis Techniques and Two New Techniques with 4-Bit Boolean Functions for Cryptanalysis of 4-Bit Crypto S-Boxes

4-bit linear relations play an important role in cryptanalysis of 4-bit crypto S-boxes. 4-bit finite differences have also been a major part of cryptanalysis of 4-bit S-boxes. Existence of all 4-bit linear relations have been counted for all of 16 input and 16 output 4-bit bit patterns of 4-bit Crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these two cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new analysis techniques, one to search for the existing linear approximations among the input vectors (IPVs) and output Boolean functions (BFs) of a particular S-box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number of existent linear relations among all 16, 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security.

Dynamic inhomogeneous S-Boxes in AES: a novel countermeasure against power analysis attacks

Substitution boxes (S-Boxes) in advanced encryption standard (AES) are vulnerable to attacks bypower analysis.The general S-Boxes masking schemes in circuit level need to adjust the design flow andlibrary databases.The masking strategies in algorithm level view each S-Box as an independent moduleand mask them respectively,which are costly in size and power for non-linear characteristic of S-Boxes.The new method uses dynamic inhomogeneous S-Boxes instead of traditional homogeneous S-Boxes,andarranges the S-Boxes randomly.So the power and data path delay of substitution unit become unpre-dictable.The experimental results demonstrate that this scheme takes advantages of the circuit character-istics of various S-Box implementations to eliminate the correlation between crypto operation and power.Itneeds less extra circuits and suits resource constrained applications.

A New S-Box Design System for Data Encryption Using Artificial Bee Colony Algorithm

Securing digital image data is a key concern in today’s information-driven society.Effective encryption techniques are required to protect sensitive image data,with the Substitution-box(S-box)often playing a pivotal role in many symmetric encryption systems.This study introduces an innovative approach to creating S-boxes for encryption algorithms.The proposed S-boxes are tested for validity and non-linearity by incorporating them into an image encryption scheme.The nonlinearity measure of the proposed S-boxes is 112.These qualities significantly enhance its resistance to common cryptographic attacks,ensuring high image data security.Furthermore,to assess the robustness of the S-boxes,an encryption system has also been proposed and the proposed S-boxes have been integrated into the designed encryption system.To validate the effectiveness of the proposed encryption system,a comprehensive security analysis including brute force attack and histogram analysis has been performed.In addition,to determine the level of security during the transmission and storage of digital content,the encryption system’s Number of Pixel Change Rate(NPCR),and Unified Averaged Changed Intensity(UACI)are calculated.The results indicate a 99.71%NPCR and 33.51%UACI.These results demonstrate that the proposed S-boxes offer a significant level of security for digital content throughout its transmission and storage.

A Novel S-Box GenerationMethodology Based on the Optimized GANModel

S-boxes can be the core component of block ciphers,and how to efficiently generate S-boxes with strong cryptographic properties appears to be an important task in the design of block ciphers.In this work,an optimized model based on the generative adversarial network(GAN)is proposed to generate 8-bit S-boxes.The central idea of this optimized model is to use loss function constraints for GAN.More specially,the Advanced Encryption Standard(AES)S-box is used to construct the sample dataset via the affine equivalence property.Then,three models are respectively built and cross-trained to generate 8-bit S-boxes based on three extended frameworks of GAN,i.e.,Deep Convolution Generative Adversarial Networks(DCGAN),Wasserstein Generative Adversarial Networks(WGAN),and WassersteinGenerativeAdversarial NetworkwithGradient Penalty(WGANGP).Besides,an optimized model based onWGAN-GP referred to asWGPIM is also proposed,which adds the loss function constraints to the generator network of the WGAN-GP model,including bijection loss,differential uniformity loss,and nonlinearity loss.In this case,8-bit S-boxes can be generated with cross-training.Experimental results illustrate that the WGP-IM model can generate S-boxes with excellent cryptographic properties.In particular,the optimal differential uniformity of the generated S-boxes can be reduced to 8,and the nonlinearity can be up to 104.Compared with previous S-box generation methods,this new method is simpler and it can generate S-boxes with excellent cryptographic properties.

一种基于Hierarchy LUT的可重构S-box实现方法

基于查找表方法构建的Substitution box (S-box)在可重构分组密码实现中广泛使用,然而因消耗的资源过大,其面积利用效率低。为提高可重构S-box面积利用效率,提出一种基于4R/1W存储结构的分层查找表(Hierarchy LUT),构建可重构S-box。所提出的4R/1W存储结构能减少存储单元的例化数量,提高存储密度。在40nmCMOS工艺下,实现基于HierarchyLUT的可重构S-box,其面积利用效率得到改善,对比TableLookupUnit (TLU)和Memory Sharing的可重构S-box方案,效率分别提高了51.76%和6.88%。

Rijndael S-box仿射运算研究

证明了有限域上q 多项式、n阶矩阵和线性函数间的等价关系;然后通过证明有限域上同一线性函数在严格不同基下对应不同矩阵,扩展出一种通用的方法快速确定有限域上线性函数和n阶矩阵间的线性关系;提出了有限域上q 多项式和n阶矩阵相互确定的一种新方案,从本质上解释了RijndaelS box代数表达式的简洁性.

实现AES算法中S-BOX和INV-S-BOX的高效方法

介绍了AES中的S-BOX和INV-S-BOX的算法原理,分析目前广泛使用的实现S-BOX和INV-S-BOX的三种方法:直接查表法,扩展欧几里德算法和基于复合域GF((22)2)2)的算法。对直接查表法和基于复合域GF((22)2)2)的算法进行改进,提出了两种改进电路结构。通过综合仿真,给出了按照上述方法实现的硬件电路的面积和关键路径上的时间延迟。结果表明,提出的两种新实现方法与传统实现方法相比,电路面积分别有28%和22%的优化。

基于FPGA的国密算法SM4和ZUC可重构设计

提出了一种SM4和ZUC-256密码的硬件实现方案.首先对两个密码算法进行硬件语言描述,然后构建了两个可重构单元--可重构寄存器和可重构S-box单元,从而在实现两个密码算法的基础上,有效降低了资源消耗,提高了资源利用率.在现场可编程逻辑门阵列(field programmable gate array, FPGA)上进行硬件验证.结果表明,本密码可重构方案中的硬件开销有明显的降低.

一种基于有限域求逆的S-Box实现算法

S-Box是AES密码算法硬件实现的关键,目前主要有两种实现方法:一种是基于查找表,一种是基于有限域求逆。文章首先经过数学变换将有限域GF(28)上的元素映射到有限域GF(24)2上,并把GF(24)2上的一个元素变换为GF(24)上的两个元素的线性运算。在此基础上,把GF(28)上的求逆问题转化为GF(24)上的求逆,从而提出了一种基于有限域求逆的低硬件开销的S-Box实现算法。该算法和查找表实现相比,面积减少了57%,适用于诸如智能卡、移动设备等对面积要求比较严格的场合。

基于FPGA的AES和ECC算法图像加密

随着数字图像的使用次数日益增多,保护机密图像数据免受未经授权的访问较为重要。针对数字图像在通信、存储和传输等领域存在的安全问题,文中基于对称算法模型和非对称算法模型的优点提出一种具有高安全性和高速度性的数字信封技术密码方案。该方案以AES(Advanced Encryption Standard)和ECC(Elliptic Curve Cryptography)为基础,经优化后用于对称密钥共享的ECC硬件架构来提高密钥的安全性。通过加入伪随机数、使用列移位替代列混淆运算以及三维S-box等方式对传统AES进行优化,在保持香农扩散和混淆原理的同时降低了时间复杂性。基于FPGA(Field Programmable Gate Array)实现AES算法的数字图像加密仿真以及性能测试。测试结果表明,所提密码方案具有快速性、高安全性和有效性等优点,能够有效地实现图像加密。

AES的结构及其S-box分析

分析了 AES的加解密原理和密钥生成器的结构 ,S- box的分布特性。指出了 AES与其密钥生成器之间存在一种结构上的同步性 ,这种同步性可能成为 AES的弱点 ;AES的 S- box具有短周期 ,不具有良好的分布特性。这给 AES的密码分析提供了可能 ,也许会成为 AES的致命弱点。

一种基于离散混沌系统的S-Box候选算法设计

S-Box是现行分组密码中唯一的非线性部件,主要提供了分组密码算法中必需的混淆作用,其密码强度决定了整个分组密码的安全强度。为进一步提高S-Box的强度,结合离散混沌系统的内在随机性、有界性、非周期性及对初始条件和参数极度敏感等特点,提出一种采用多混沌映射和交叉映射生成S-Box的生成算法。实验分析表明,该算法生成的样本密钥敏感性强,随机性好,既能较好地满足S-Box设计所要求的各项准则和特性,安全性高,同时又能降低计算复杂度,提高计算速度,且易于生成和扩展,因而是一种性能良好的S-Box候选算法。

AES加密算法中S-BOX的算法与VLSI实现

基于GF(24)域映射的方法,采用定制方式完成了AES加密算法中关键部件S-Box的设计与实现。设计上基于中芯国际(SMIC)的0.18滋m1P6M设计工艺,经过电路设计与验证、电路仿真、版图设计与验证、版图后仿真得到最终物理版图实现。经过与基于自动综合和布局布线得到的设计的时延和面积的比较,证明该设计是有效的。

Constructions of correlation immnue S-boxes with high nonlinearity

S-boxes play a central role in the design of symmetric cipher schemes.For stream cipher appli-cations,an s-box should satisfy several criteria such as high nonlinearity,balanceness,correlation immunity,and so on.In this paper,by using disjoint linear codes,a class of s-boxes possessing high nonlinearity and 1st-order correlation immunity is given.It is shown that the constructed correlation immune S-boxes can possess currently best known nonlinearity,which is confirmed by the example 1st-order correlation immune(12,3)s-box with nonlinearity 2000.In addition,two other frameworks concerning the criteria of balanced and resiliency are obtained respectively.