A Survey of ARX-based Symmetric-key Primitives

Addition Rotation XOR is suitable for fast implementation symmetric –key primitives, such as stream and block ciphers. This paper presents a review of several block and stream ciphers based on ARX construction followed by the discussion on the security analysis of symmetric key primitives where the best attack for every cipher was carried out. We benchmark the implementation on software and hardware according to the evaluation metrics. Therefore, this paper aims at providing a reference for a better selection of ARX design strategy

User-controlled cyber-security using automated key generation

Traditionally, several different methods are fully capable of providing an adequate degree of security to the threats and attacks that exists for revealing different keys. Though almost all the traditional methods give a good level of immunity to any possible breach in security keys, the biggest issue that exist with these methods is the dependency over third-party applications. Therefore, use of third-party applications is not an acceptable method to be used by high-security applications. For high-security applications, it is more secure that the key generation process is in the hands of the end users rather than a third-party. Giving access to third parties for high-security applications can also make the applications more venerable to data theft, security breach or even a loss in their integrity. In this research, the evolutionary computing tool Eureqa is used for the generation of encryption keys obtained by modelling pseudo-random input data. Previous approaches using this tool have required a calculation time too long for practical use and addressing this drawback is the main focus of the research. The work proposes a number of new approaches to the generation of secret keys for the encryption and decryption of data files and they are compared in their ability to operate in a secure manner using a range of statistical tests and in their ability to reduce calculation time using realistic practical assessments. A number of common tests of performance are the throughput, chi-square, histogram, time for encryption and decryption, key sensitivity and entropy analysis. From the results of the statistical tests, it can be concluded that the proposed data encryption and decryption algorithms are both reliable and secure. Being both reliable and secure eliminates the need for the dependency over third-party applications for the security keys. It also takes less time for the users to generate highly secure keys compared to the previously known techniques.The keys generated via Eureqa also have great potential to be adapted to data communication applications which require high security

On the Design of Cryptographic Primitives

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed

Software and hardware implementation of the RSA public key cipher

Cryptographic systems and their use in communications are presented. The advantages obtained by the use of a public key cipher and the importance of this in a commercial environment are stressed. Two two main public key ciphers are considered. The RSA public key cipher is introduced and various methods for implementing this cipher on a standard, nondedicated, 8 bit microprocessor are investigated. The performance of the different algorithms are evaluated and compared. Various ways of increasing the performance are considered. The limitations imposed by the performance on the practical use of the cipher are discussed. The importance of the key to the security of the cipher is assessed. Different forms of attack are mentioned and a procedure for generating keys, which minimise the probability of a sucessful attack is presented. This procedure is implemented on a minicomputer. Use of the method on personal computers or microprocessors is examined. Methods for performing multiplication in hardware, with particular emphasis on the use of these methods in modular multiplication, are detailed. An algorithm for performing part of the encryption function in hardware and the hardware necessary for it is described. Different methods for implementing the hardware are discussed and one is choosen. A description of the hardware unit is given. The design and development of an application specific integrated circuit (ASIC) to perform key elements of the encryption function is described. The various stages of the design process are detailed. The results expected from this device and its integration into the overall encryption scheme are presented

Deterministic Chaos in Digital Cryptography

This thesis studies the application of deterministic chaos to digital cryptography. Cryptographic systems such as pseudo-random generators (PRNG), block ciphers and hash functions are regarded as a dynamic system (X, j), where X is a state space (Le. message space) and f : X -+ X is an iterated function. In both chaos theory and cryptography, the object of study is a dynamic system that performs an iterative nonlinear transformation of information in an apparently unpredictable but deterministic manner. In terms of chaos theory, the sensitivity to the initial conditions together with the mixing property ensures cryptographic confusion (statistical independence) and diffusion (uniform propagation of plaintext and key randomness into cihertext). This synergetic relationship between the properties of chaotic and cryptographic systems is considered at both the theoretical and practical levels: The theoretical background upon which this relationship is based, includes discussions on chaos, ergodicity, complexity, randomness, unpredictability and entropy. Two approaches to the finite-state implementation of chaotic systems (Le. pseudo-chaos) are considered: (i) floating-point approximation of continuous-state chaos; (ii) binary pseudo-chaos. An overview is given of chaotic systems underpinning cryptographic algorithms along with their strengths and weaknesses. Though all conventional cryposystems are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are sufficient to guarantee cryptographic strength and security. A dynamic system is said to have an analytical solution Xn = (xo) if any trajectory point Xn can be computed directly from the initial conditions Xo, without performing n iterations. A chaotic system with an analytical solution may have a unpredictable multi-valued map Xn+l = f(xn). Their floating-point approximation is studied in the context of pseudo-random generators. A cryptographic software system E-Larm ™ implementing a multistream pseudo-chaotic generator is described. Several pseudo-chaotic systems including the logistic map, sine map, tangent- and logarithm feedback maps, sawteeth and tent maps are evaluated by means of floating point computations. Two types of partitioning are used to extract pseudo-random from the floating-point state variable: (i) combining the last significant bits of the floating-point number (for nonlinear maps); and (ii) threshold partitioning (for piecewise linear maps). Multi-round iterations are produced to decrease the bit dependence and increase non-linearity. Relationships between pseudo-chaotic systems are introduced to avoid short cycles (each system influences periodically the states of other systems used in the encryption session). An evaluation of cryptographic properties of E-Larm is given using graphical plots such as state distributions, phase-space portraits, spectral density Fourier transform, approximated entropy (APEN), cycle length histogram, as well as a variety of statistical tests from the National Institute of Standards and Technology (NIST) suite. Though E-Larm passes all tests recommended by NIST, an approach based on the floating-point approximation of chaos is inefficient in terms of the quality/performance ratio (compared with existing PRNG algorithms). Also no solution is known to control short cycles. In conclusion, the role of chaos theory in cryptography is identified; disadvantages of floating-point pseudo-chaos are emphasized although binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite

SAFE-NET: Secure and Fast Encryption using Network of Pseudo-Random Number Generators

We propose a general framework to design a general class of random number generators suit- able for both computer simulation and computer security applications. It can include newly pro- posed generators SAFE (Secure And Fast Encryption) and ChaCha, a variant of Salsa, one of the four finalists of the eSTREAM ciphers. Two requirements for ciphers to be considered se- cure is that they must be unpredictable with a nice distributional property. Proposed SAFE-NET is a network of n nodes with external pseudo-random number generators as inputs nodes, several inner layers of nodes with a sequence of random variates through ARX (Addition, Rotation, XOR) transformations to diffuse the components of the initial state vector. After several rounds of transformations (with complex inner connections) are done, the output layer with n nodes are outputted via additional transformations. By utilizing random number generators with desirable empirical properties, SAFE-NET injects randomness into the keystream generation process and constantly updates the cipher’s state with external pseudo-random numbers during each iteration. Through the integration of shuffle tables and advanced output functions, extra layers of security are provided, making it harder for attackers to exploit weaknesses in the cipher. Empirical results demonstrate that SAFE-NET requires fewer operations than ChaCha while still producing a sequence of uniformly distributed random numbers

ANALYSIS OF SECURITY MEASURES FOR SEQUENCES

Stream ciphers are private key cryptosystems used for security in communication and data transmission systems. Because they are used to encrypt streams of data, it is necessary for stream ciphers to use primitives that are easy to implement and fast to operate. LFSRs and the recently invented FCSRs are two such primitives, which give rise to certain security measures for the cryptographic strength of sequences, which we refer to as complexity measures henceforth following the convention. The linear (resp. N-adic) complexity of a sequence is the length of the shortest LFSR (resp. FCSR) that can generate the sequence. Due to the availability of shift register synthesis algorithms, sequences used for cryptographic purposes should have high values for these complexity measures. It is also essential that the complexity of these sequences does not decrease when a few symbols are changed. The k-error complexity of a sequence is the smallest value of the complexity of a sequence obtained by altering k or fewer symbols in the given sequence. For a sequence to be considered cryptographically ‘strong’ it should have both high complexity and high error complexity values. An important problem regarding sequence complexity measures is to determine good bounds on a specific complexity measure for a given sequence. In this thesis we derive new nontrivial lower bounds on the k-operation complexity of periodic sequences in both the linear and N-adic cases. Here the operations considered are combinations of insertions, deletions, and substitutions. We show that our bounds are tight and also derive several auxiliary results based on them. A second problem on sequence complexity measures useful in the design and analysis of stream ciphers is to determine the number of sequences with a given fixed (error) complexity value. In this thesis we address this problem for the k-error linear complexity of 2n-periodic binary sequences. More specifically: 1. We characterize 2n-periodic binary sequences with fixed 2- or 3-error linear complexity and obtain the counting function for the number of such sequences with fixed k-error linear complexity for k = 2 or 3. 2. We obtain partial results on the number of 2n-periodic binary sequences with fixed k-error linear complexity when k is the minimum number of changes required to lower the linear complexity