Stream Cipher Applications Research Articles

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 applications, 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.

Recovering the MSS-sequence via CA

A cryptographic sequence generator, the modified self-shrinking generator (MSSG), was recently designed as a novel version of the self-shrinking generator. Taking advantage of the cryptographic properties of the irregularly decimated generator class, the MSSG was mainly created to be used in stream cipher applications and hardware implementations. Nevertheless, in this work it is shown that the MSSG output sequence, the so-called modified self-shrunken sequence, is generated as one of the output sequences of a linear model based on Cellular Automata that use rule 60 for their computations. Thus, the linearity of these structures can be advantageous exploited to recover the complete modified self-shrunken sequence from a number of intercepted bits.

Generalization of the Self-Shrinking Generator in the Galois Field

The proposed by Meier and Staffelbach Self-Shrinking Generator (SSG) which has efficient hardware implementation only with a single Linear Feedback Shift Register is suitable for low-cost and fast stream cipher applications. In this paper we generalize the idea of the SSG for arbitrary Galois Field . The proposed variant of the SSG is called the -ary Generalized Self-Shrinking Generator (pGSSG). We suggest a method for transformation of a non-binary self-shrunken pGSSG sequence into balanced binary sequence. We prove that the keystreams of the pGSSG have large period and good statistical properties. The analysis of the experimental results shows that the pGSSG sequences have good randomness properties. We examine the complexity of exhaustive search and entropy attacks of the pGSSG. We show that the pGSSG is more secure than SSG and Modified SSG against these attacks. We prove that the complexity of the used pGSSG attacks increases with increasing the prime . Previously mentioned properties give the reason to say that the pGSSG satisfy the basic security requirements for a stream chipper and can be useful as a part of modern stream ciphers.

Cryptosystems based on continued fractions

AbstractIn this paper, we propose three secret‐key cryptosystems based on the theory of continued fractions for possible use in cryptographic applications. We present and analyze a sequence of rational numbers, whose randomness properties are demonstrated using well‐know statistical packages. Accordingly, we propose a cryptosystem that acts on a group of characters at a time. Then, a binary keystream generator, generating keystreams with good randomness properties, is suggested for possible use in stream cipher applications. Finally, we propose a cryptosystem related to the well‐known Baptista's cryptosystem that is based on a chaotic logistic map. However, our cryptosystem is based on the theory of continued fractions, and is shown to exhibit better properties and decrypts information much faster than Baptista's cryptosystem. Copyright © 2010 John Wiley & Sons, Ltd.

An Efficient PRBG Based on Chaotic Map and Engel Continued Fractions

In recent years, a variety of chaos-based cryptosystems have been proposed. Some of these systems are used in designing a pseudo random bit generator (PRBG) for stream cipher applications. Most of the chaotic systems used in cryptography have good chaotic properties like ergodicity, sensitivity to initial values and sensitivity to control parameters. However, some of them are not very suitable for use in cryptography because of their non-uniform density function, and their relatively small key space. To be used in cryptography, a PRBG may need to meet stronger requirements than for other applications. In particular, various statistical tests can be applied to the outputs of such generators to conclude whether the generator produces a truly random sequence or not. In this paper, we propose a PRBG based on the use of the standard chaotic map with large key space and the Engle Continued Fractions (ECF) map. The outputs of the standard map are used as the inputs of ECF-map. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. The numerical simulation analysis indicates that our PRBG produces bit sequences possessing excellent statistical and cryptographic properties.

Encryption System with Variable Number of Registers

Encryption in wireless communication systems is an extremely important factor to protect information and prevent fraud. In this paper, we propose a new encryption system for use in stream cipher applications. The design proposed is intended for hardware implementation and based on ( n + 1 ) feedback shift registers interconnected in such a way that one register controls the clocking of the other n registers. The aim of this construction is to allow the production of a large family of distinct keystreams when the initial states and feedback functions of the feedback shift registers are unchanged. The produced keystreams are shown to possess the basic security requirements for cryptographic sequences such as long period, high linear complexity and good statistical properties, provided that suitable parameters are chosen. Furthermore, the design is shown to resist various types of cryptanalytic attacks. These characteristics and properties enhance its use as a suitable encryption system for stream cipher applications.

An efficient cryptosystem Delta for stream cipher applications

The need for wireless communication systems has increased rapidly in the past few years and wireless communication has become more convenient in business and society. However, the air interface is vulnerable to eavesdropping, hence encryption in wireless communication systems is a necessity to keep sensitive information confidential and to prevent fraud. Furthermore, wireless devices such as Bluetooth devices and mobile phones require an encryption algorithm that is secure, fast and simple to implement. There are several cryptosystems for stream cipher applications such as A5/x used in GSM mobile communications. However, A5/x are vulnerable to cryptanalytic attacks. In this paper, a new clock-controlled cryptosystem intended for hardware implementation is proposed. The design has attractive properties such as simplicity and scalability. The cryptographical properties including period, balancedness, linear complexity and probability distribution are analyzed. The design provides the basic security requirements, and is resistant to known cryptanalytic attacks. It is shown that the irregular clocking introduced provides a certain level of strengthened security against several cryptanalytic attacks. These properties enhance its use as a suitable cryptosystem for stream cipher applications.

Logistic chaotic maps for binary numbers generations

Two pseudorandom binary sequence generators, based on logistic chaotic maps intended for stream cipher applications, are proposed. The first is based on a single one-dimensional logistic map which exhibits random, noise-like properties at given certain parameter values, and the second is based on a combination of two logistic maps. The encryption step proposed in both algorithms consists of a simple bitwise XOR operation of the plaintext binary sequence with the keystream binary sequence to produce the ciphertext binary sequence. A threshold function is applied to convert the floating-point iterates into binary form. Experimental results show that the produced sequences possess high linear complexity and very good statistical properties. The systems are put forward for security evaluation by the cryptographic committees.

Embedding Probabilities for the Alternating Step Generator

The edit distance correlation attack on the well- known alternating step generator for stream cipher applications was proposed by Golic and Menicocci. The attack can be successful only if the probability of the zero edit distance, the so-called embedding probability, conditioned on a given segment of the output sequence, decreases with the segment length, and if the decrease is exponential, then the required segment length is linear in the total length of the two linear feedback shift registers involved. The exponential decrease for the maximal value of the embedding probability, regarded as a function of the output segment, was estimated experimentally by Golic and Menicocci. In this paper, by using the connection with the interleaving and decimation operations, the embedding probability is analyzed theoretically. Exponentially small upper bounds on the maximal embedding probability are thus derived. An exact expression for the minimal embedding probability is also determined

Cryptographically significant Boolean functions with five valued Walsh spectra

We describe methods to construct balanced (resp. 1-resilient) functions of odd number of variables n achieving the bent concatenation nonlinearity and having algebraic degree n−1 (resp. n−2). The technique is to algebraically modify the concatenation of two properly chosen (n−1)-variable Maiorana–McFarland bent functions. The constructed functions can be used with certain recursive operators to provide higher order resilient functions with maximum possible degree and high nonlinearity. Such functions are well suited for stream cipher applications. Interestingly, all the constructed functions have a five valued Walsh spectra.

On distribution properties of sequences with perfect linear complexity profile

The linear complexity and the linear complexity profile of sequences are used as unpredictability criteria in stream cipher applications. In this context, sequences with perfect linear complexity profile (PLCP) are of special interest. Further unpredictability requirements are given by the distribution properties of the sequence elements that should be similar to the distribution properties of a real random sequence. In this paper, the distribution of binary symbols for the class of PLCP-sequences is given by means of statistical moments. These moments are compared with the corresponding moments of real random sequences.

Generalized inversion attack on nonlinear filter generators

A nonlinear filter generator is a basic keystream generator for stream cipher applications consisting of a single linear feedback shift register whose output is filtered by a nonlinear combining function. A binary nonlinear filter generator is viewed as a finite input memory automaton with one binary input and one binary output. The generalized inversion attack on a binary nonlinear filter generator is developed and analyzed by the theory of critical branching processes. Its objective is to recover the unknown input sequence from a given segment of the output sequence, provided that the filter function is known. Unlike the inversion attack, which requires that the filter function be linear in the first or the last input variable, this attack can be applied for any filter function. Both theory and systematic experiments show that its time complexity remains dose to 2/sup M/, which is the time complexity of the inversion attack, where M denotes the input memory size in bits.

Intrinsic weakness of variable-memory keystream generators

A cryptographic weakness in a pseudorandom binary sequence generator proposed in the literature as a keystream generator for stream cipher applications is pointed out. Some results obtained by computer simulation are presented.