Investigations of cellular automata-based stream ciphers

In this thesis paper, we survey the literature arising from Stephan Wolfram\u27s original paper, “Cryptography with Cellular Automata” [WOL86] that first suggested stream ciphers could be constructed with cellular automata. All published research directly and indirectly quoting this paper are summarized up until the present. We also present a novel stream cipher design called Sum4 that is shown to have good randomness properties and resistance to approximation using linear finite shift registers. Sum4 is further studied to determine its effective strength with respect to key size given that an attack with a SAT solver is more efficient than a bruteforce attack. Lastly, we give ideas for further research into improving the Sum4 cipher

Cryptographic requirements for chaotic secure communications

In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.Comment: 13 pages, 3 figure

Graphic cryptography with pseudorandom bit generators and cellular automata

In this paper we propose a new graphic symmetrical cryptosystem in order to encrypt a colored image defined by pixels and by any number of colors. This cryptosystem is based on a reversible bidimensional cellular automaton and uses a pseudorandom bit generator. As the key of the cryptosystem is the seed of the pseudorandom bit generator, the latter has to be cryptographically secure. Moreover, the recovered image from the ciphered image has not loss of resolution and the ratio between the ciphered image and the original one, i.e., the factor expansion of the cryptosystem, is $1$.Peer reviewe

Cellular automata for dynamic S-boxes in cryptography.

In today\u27s world of private information and mass communication, there is an ever increasing need for new methods of maintaining and protecting privacy and integrity of information. This thesis attempts to combine the chaotic world of cellular automata and the paranoid world of cryptography to enhance the S-box of many Substitution Permutation Network (SPN) ciphers, specifically Rijndael/AES. The success of this enhancement is measured in terms of security and performance. The results show that it is possible to use Cellular Automata (CA) to enhance the security of an 8-bit S-box by further randomizing the structure. This secure use of CA to scramble the S-box, removes the 9-term algebraic expression [20] [21] that typical Galois generated S-boxes share. This cryptosystem securely uses a Margolis class, partitioned block, uniform gas, cellular automata to create unique S-boxes for each block of data to be processed. The system improves the base Rijndael algorithm in the following ways. First, it utilizes a new S-box for each block of data. This effectively limits the amount of data that can be gathered for statistical analysis to the blocksize being used. Secondly, the S-boxes are not stored in the compiled binary, which protects against an S-box Blanking [22] attack. Thirdly, the algebraic expression hidden within each galois generated S-box is destroyed after one CA generation, which also modifies key expansion results. Finally, the thesis succeeds in combining Cellular Automata and Cryptography securely, though it is not the most efficient solution to dynamic S-boxes

Joint block and stream cipher based on a modified skew tent map

Image encryption is very different from that of texts due to the bulk data capacity and the high redundancy of images. Thus, traditional methods are difficult to use for image encryption as their pseudo-random sequences have small space. Chaotic cryptography use chaos theory in specific systems working such as computing algorithms to accomplish dissimilar cryptographic tasks in a cryptosystem with a fast throughput. For higher security, encryption is the approach to guard information and prevent its leakage. In this paper, a hybrid encryption scheme that combines both stream and block ciphering algorithms is proposed in order to achieve the required level of security with the minimum encryption time. This scheme is based on an improved mathematical model to cover the defects in the previous discredited model proposed by Masuda. The proposed chaos-based cryptosystem uses the improved Skew Tent Map (STM) RQ-FSTM as a substitution layer. This map is based on a lookup table to overcome various problems, such as the fixed point, the key space restrictions, and the limitation of mapping between plain text and cipher text. It uses the same map as a generator to change the byte position to achieve the required confusion and diffusion effects. This modification improves the security level of the original STM. The robustness of the proposed cryptosystem is proven by the performance and the security analysis, as well as the high encryption speed. Depending on the results of the security analysis the proposed system has a better dynamic key space than previous ones using STM, a double encryption quality and a better security analysis than others in the literature with speed convenience to real-time applications

Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in \F_{p^m}[x] of degree $d$ over the finite field \F_{p^m}, one can view it as a map from \F_{p^m} to \F_{p^m}, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}

Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Key-Recovery Attack on the ASASA Cryptosystem with Expanding S-boxes

We present a cryptanalysis of the ASASA public key cipher introduced at Asiacrypt 2014. This scheme alternates three layers of affine transformations A with two layers of quadratic substitutions S. We show that the partial derivatives of the public key polynomials contain information about the intermediate layer. This enables us to present a very simple distinguisher between an ASASA public key and random polynomials. We then expand upon the ideas of the distinguisher to achieve a full secret key recovery. This method uses only linear algebra and has a complexity dominated by the cost of computing the kernels of $2^{26}$ small matrices with entries in $\mathbb F_{16}$

New Classes of Binary Random Sequences for Cryptography

In the vision for the 5G wireless communications advancement that yield new security prerequisites and challenges we propose a catalog of three new classes of pseudorandom random sequence generators. This dissertation starts with a review on the requirements of 5G wireless networking systems and the most recent development of the wireless security services applied to 5G, such as private-keys generation, key protection, and flexible authentication. This dissertation proposes new complexity theory-based, number-theoretic approaches to generate lightweight pseudorandom sequences, which protect the private information using spread spectrum techniques. For the class of new pseudorandom sequences, we obtain the generalization. Authentication issues of communicating parties in the basic model of Piggy Bank cryptography is considered and a flexible authentication using a certified authority is proposed