Some Words on Cryptanalysis of Stream Ciphers

In the world of cryptography, stream ciphers are known as primitives used to ensure privacy over a communication channel. One common way to build a stream cipher is to use a keystream generator to produce a pseudo-random sequence of symbols. In such algorithms, the ciphertext is the sum of the keystream and the plaintext, resembling the one-time pad principal. Although the idea behind stream ciphers is simple, serious investigation of these primitives has started only in the late 20th century. Therefore, cryptanalysis and design of stream ciphers are important. In recent years, many designs of stream ciphers have been proposed in an effort to find a proper candidate to be chosen as a world standard for data encryption. That potential candidate should be proven good by time and by the results of cryptanalysis. Different methods of analysis, in fact, explain how a stream cipher should be constructed. Thus, techniques for cryptanalysis are also important. This thesis starts with an overview of cryptography in general, and introduces the reader to modern cryptography. Later, we focus on basic principles of design and analysis of stream ciphers. Since statistical methods are the most important cryptanalysis techniques, they will be described in detail. The practice of statistical methods reveals several bottlenecks when implementing various analysis algorithms. For example, a common property of a cipher to produce n-bit words instead of just bits makes it more natural to perform a multidimensional analysis of such a design. However, in practice, one often has to truncate the words simply because the tools needed for analysis are missing. We propose a set of algorithms and data structures for multidimensional cryptanalysis when distributions over a large probability space have to be constructed. This thesis also includes results of cryptanalysis for various cryptographic primitives, such as A5/1, Grain, SNOW 2.0, Scream, Dragon, VMPC, RC4, and RC4A. Most of these results were achieved with the help of intensive use of the proposed tools for cryptanalysis

A practical attack on the fixed RC4 in the wep mode

Abstract. In this paper we revisit a known but ignored weakness of the RC4 keystream generator, where secret state info leaks to the generated keystream, and show that this leakage, also known as Jenkins’ correlation or the RC4 glimpse, can be used to attack RC4 in several modes. Our main result is a practical key recovery attack on RC4 when an IV modifier is concatenated to the beginning of a secret root key to generate a session key. As opposed to the WEP attack from [FMS01] the new attack is applicable even in the case where the first 256 bytes of the keystream are thrown and its complexity grows only linearly with the length of the key. In an exemplifying parameter setting the attack recoversa16-bytekeyin2 48 steps using 2 17 short keystreams generated from different chosen IVs. A second attacked mode is when the IV succeeds the secret root key. We mount a key recovery attack that recovers the secret root key by analyzing a single word from 2 22 keystreams generated from different IVs, improving the attack from [FMS01] on this mode. A third result is an attack on RC4 that is applicable when the attacker can inject faults to the execution of RC4. The attacker derives the internal state and the secret key by analyzing 2 14 faulted keystreams generated from this key

Tabu search against permutation based stream ciphers

Encryption is one of the most effective methods of securing data confidentiality, whether stored on hard drives or transferred (e.g. by e-mail or phone call). In this paper a new state recovery attack with tabu search is introduced. Based on research and theoretical approximation it is shown that the internal state can be recovered after checking 2^52 internal states for RC4 and 2^180 for VMPC

Tabu search against permutation based stream ciphers

Encryption is one of the most effective methods of securing data confidentiality, whether stored on hard drives or transferred (e.g. by e-mail or phone call). In this paper a new state recovery attack with tabu search is introduced. Based on research and theoretical approximation it is shown that the internal state can be recovered after checking 252 internal states for RC4 and 2180 for VMPC

Tabu Cryptanalysis of VMPC Stream Cipher

In the era of global informatization, transmitting and storing information in digital form it is very important to ensure an adequate level of security of ciphers used. Cryptanalysis deals with studying the level of security, thus exposing the weakness of theoretical and implemented cryptographic solutions. In this paper cryptanalysis of stream cipher VMPC using Tabu Search is shown. From estimates made on a full version of VMPC cipher we concluded that about 2157 possibilities needs to be checked in order to find the proper one, which would be the best attack known so far

VMPC-R Cryptographically Secure Pseudo-Random Number Generator Alternative to RC4

We present a new Cryptographically Secure Pseudo-Random Number Generator. It uses permutations as its internal state, similarly to the RC4 stream cipher. We describe a statistical test which revealed non-random patterns in a sample of $2^{16.6}$ outputs of a 3-bit RC4. Our new algorithm produced $2^{46.8}$ undistinguishable from random 3-bit outputs in the same test. We probed $2^{51}$ outputs of the algorithm in different statistical tests with different word sizes and found no way of distinguishing the keystream from a random source. The size of the algorithm\u27s internal state is $2^{3424}$ (for an 8-bit implementation). The algorithm is cryptographically secure to the extent we were able to analyse it. Its design is simple and easy to implement. We present the generator along with a key scheduling algorithm processing both keys and initialization vectors

Statistical weakness in Spritz against VMPC-R: in search for the RC4 replacement

We found a statistical weakness in the Spritz algorithm designed by Ronald L. Rivest and Jacob C. N. Schuldt. For N=8: Prob(output(x)=output(x+2)) = 1/N + 0.000498. The bias becomes statistically significant (for N=8) after observing about 2^21.9 outputs. Analogous bias occurs for N=16. We propose an algorithm (VMPC-R) which for N=8 produced 2^46.8 (31 million times more) outputs which remained undistinguishable from random in the same battery of tests. Supported by a series of additional statistical tests and security analyses we present VMPC-R as an algorithm we hope can be considered a worthwhile replacement for RC4

Design and Analysis of RC4-like Stream Ciphers

RC4 is one of the most widely used ciphers in practical software applications. In this thesis we examine security and design aspects of RC4. First we describe the functioning of RC4 and present previously published analyses. We then present a new cipher, Chameleon which uses a similar internal organization to RC4 but uses different methods. The remainder of the thesis uses ideas from both Chameleon and RC4 to develop design strategies for new ciphers. In particular, we develop a new cipher, RC4B, with the goal of greater security with an algorithm comparable in simplicity to RC4. We also present design strategies for ciphers and two new ciphers for 32-bit processors. Finally we present versions of Chameleon and RC4B that are implemented using playing-cards

Image Encryption using Gingerbreadman Map And RC4A Stream Cipher

Day to day increasing flow of sensitive or confidential information, such as images, audio, video, etc., over unsecured medium (like Internet) has motivated more concentration for concrete crypto algorithms. In this paper, an image encryption algorithm based on a permutation and substitution cipher has been proposed. In permutation stage, image pixels are shuffled using gingerbreadman map while in substitution stage, pixels are bit-wise XOR-ed with the keystream generated using RC4A (Rivest Cipher 4A) stream cipher algorithm. For the proposed scheme, statistical analyses, like histogram, adjacent pixels correlation coefficient, and information entropy are given. Security analyses, like key sensitivity, occlusion analysis are also given in this paper. The occlusion analysis shows that the proposed method is resistant to the occlusion attack. These statistical and security analyses support the concreteness of the proposed method

Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions