Fast algebraic immunity of Boolean functions and LCD codes

Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems

Performance Analysis Of Secured Synchronous Stream Ciphers

The new information and communication technologies require adequate security. In the past decades ,we have witnessed an explosive growth of the digital storage and communication of data ,triggered by some important breakthroughs such as the Internet and the expansive growth of wireless communications. In the world of cryptography ,stream ciphers are known as primitives used to ensure privacy over communication channel and these are widely used for fast encryption of sensitive data. Lots of old stream ciphers that have been formerly used no longer be considered secure ,because of their vulnerability to newly developed cryptanalysis techniques. Many designs stream ciphers have been proposed in an effort to find a proper candidate to be chosen as world standard for data encryption. From these designs, the stream ciphers which are Trivium,Edon80 and Mickey are implemented in ‘c’ language with out affecting their security .Actually these algorithms are particularly suited for hardware oriented environments which provides considerable security and efficiency aspects. We will be targeting hardware applications, and good measure for efficiency of a stream cipher in this environment is the number of key stream bits generated per cycle per gate. For good efficiency we are approaching two ways .One approach is minimizing the number of gates.The other approach is to dramatically increase the number of bits for cycle. This allows reducing the clock frequency at the cost of an increased gate count. Apart from the implementation the analysis which includes the security of these algorithms against some attacks related to stream ciphers such as guess and deterministic attacks, correlation attacks, divide and conquer attacks and algebraic attacks are presented

On the Design and Analysis of Stream Ciphers

This thesis presents new cryptanalysis results for several different stream cipher constructions. In addition, it also presents two new stream ciphers, both based on the same design principle. The first attack is a general attack targeting a nonlinear combiner. A new class of weak feedback polynomials for linear feedback shift registers is identified. By taking samples corresponding to the linear recurrence relation, it is shown that if the feedback polynomial has taps close together an adversary to take advantage of this by considering the samples in a vector form. Next, the self-shrinking generator and the bit-search generator are analyzed. Both designs are based on irregular decimation. For the self-shrinking generator, it is shown how to recover the internal state knowing only a few keystream bits. The complexity of the attack is similar to the previously best known but uses a negligible amount of memory. An attack requiring a large keystream segment is also presented. It is shown to be asymptotically better than all previously known attacks. For the bit-search generator, an algorithm that recovers the internal state is given as well as a distinguishing attack that can be very efficient if the feedback polynomial is not carefully chosen. Following this, two recently proposed stream cipher designs, Pomaranch and Achterbahn, are analyzed. Both stream ciphers are designed with small hardware complexity in mind. For Pomaranch Version 2, based on an improvement of previous analysis of the design idea, a key recovery attack is given. Also, for all three versions of Pomaranch, a distinguishing attack is given. For Achterbahn, it is shown how to recover the key of the latest version, known as Achterbahn-128/80. The last part of the thesis introduces two new stream cipher designs, namely Grain and Grain-128. The ciphers are designed to be very small in hardware. They also have the distinguishing feature of allowing users to increase the speed of the ciphers by adding extra hardware

The Conditional Correlation Attack: A Practical Attack on Bluetooth Encryption

Abstract. Motivated by the security of the nonlinear filter generator, the concept of correlation was previously extended to the conditional correlation, that studied the linear correlation of the inputs conditioned on a given (short) output pattern of some specific nonlinear function. Based on the conditional correlations, conditional correlation attacks were shown to be successful and efficient against the nonlinear filter generator. In this paper, we further generalize the concept of conditional correlations by assigning it with a different meaning, i.e. the correlation of the output of an arbitrary function conditioned on the unknown (partial) input which is uniformly distributed. Based on this generalized conditional correlation, a general statistical model is studied for dedicated key-recovery distinguishers. It is shown that the generalized conditional correlation is no smaller than the unconditional correlation. Consequently, our distinguisher improves on the traditional one (in the worst case it degrades into the traditional one). In particular, the distinguisher may be successful even if no ordinary correlation exists. As an application, a conditional correlation attack is developed and optimized against Bluetooth two-level E0. The attack is based on a recently detected flaw in the resynchronization of E0, as well as the investigation of conditional correlations in the Finite State Machine (FSM) governing the keystream output of E0. Our best attack finds the original encryption key for two-level E0 using the first 24 bits of 2 23.8 frames and with 2 38 computations. This is clearly the fastest and only practical known-plaintext attack on Bluetooth encryption compared with all existing attacks. Current experiments confirm our analysis

Algebraic attacks on certain stream ciphers

To encrypt data streams of arbitrary lengths, keystream generators are used in modern cryptography which transform a secret initial value, called the key, into a long sequence of seemingly random bits. Many designs are based on linear feedback shift registers (LFSRs), which can be constructed in such a way that the output stream has optimal statistical and periodical properties and which can be efficiently implemented in hardware. Particularly prominent is a certain class of LFSR-based keystream generators, called (ι,m)-combiners or simply combiners. The maybe most famous example is the E0 keystream generator deployed in the Bluetooth standard for encryption. To evaluate the combiner’s security, cryptographers adopted an adversary model where the design and some parts of the input and output are known. An attack is a method to derive the key using the given knowledge. In the last decades, several kinds of attacks against LFSR-based keystream generators have been developed. In 2002 a new kind of attacks came up, named ”algebraic attacks”. The basic idea is to model the knowledge by a system of equation whose solution is the secret key. For several existing combiners, algebraic attacks represent the fastest theoretical attacks publicly known so far. This thesis discusses algebraic attacks against combiners. After providing the required mathematical fundament and a background on combiners, we describe algebraic attacks and explore the two main steps (generating the system of equations and computing the solution) in detail. The efficiency of algebraic attacks is closely connected to the degree of the equations. Thus, we examine the existence of low-degree equations in several situations and discuss multiple design principles to thwart their existence. Furthermore, we investigate ”fast algebraic attacks”, an extension of algebraic attacks.To encrypt data streams of arbitrary lengths, keystream generators are used in modern cryptography which transform a secret initial value, called the key, into a long sequence of seemingly random bits. Many designs are based on linear feedback shift registers (LFSRs), which can be constructed in such a way that the output stream has optimal statistical and periodical properties and which can be efficiently implemented in hardware. Particularly prominent is a certain class of LFSR-based keystream generators, called (ι,m)-combiners or simply combiners. The maybe most famous example is the E0 keystream generator deployed in the Bluetooth standard for encryption. To evaluate the combiner’s security, cryptographers adopted an adversary model where the design and some parts of the input and output are known. An attack is a method to derive the key using the given knowledge. In the last decades, several kinds of attacks against LFSR-based keystream generators have been developed. In 2002 a new kind of attacks came up, named ”algebraic attacks”. The basic idea is to model the knowledge by a system of equation whose solution is the secret key. For several existing combiners, algebraic attacks represent the fastest theoretical attacks publicly known so far. This thesis discusses algebraic attacks against combiners. After providing the required mathematical fundament and a background on combiners, we describe algebraic attacks and explore the two main steps (generating the system of equations and computing the solution) in detail. The efficiency of algebraic attacks is closely connected to the degree of the equations. Thus, we examine the existence of low-degree equations in several situations and discuss multiple design principles to thwart their existence. Furthermore, we investigate ”fast algebraic attacks”, an extension of algebraic attacks