On the Role of the Inner State Size in Stream Ciphers

Many modern stream ciphers consist of a keystream generator and a key schedule algorithm. In fielded systems, security of the keystream generator is often based on a large inner state rather than an inherently secure design. Note, however, that little theory on the initialisation of large inner states exists, and many practical designs are based on an ad-hoc approach. As a consequence, an increasing number of attacks on stream ciphers exploit the (re-)initialisation of large inner states by a weak key schedule algorithm. In this paper, we propose a strict separation of keystream generator and key schedule algorithm in stream cipher design. A formal definition of inner state size is given, and lower bounds on the necessary inner state size are proposed. After giving a construction for a secure stream cipher from an insecure keystream generator, the limitations of such an approach are discussed. We introduce the notion of inner state size efficiency and compare it for a number of fielded stream ciphers, indicating that a secure cipher can be based on reasonable inner state sizes. Concluding, we ask a number of open questions that may give rise to a new field of research that is concerned with the security of key schedule algorithms

Some Results on Distinguishing Attacks on Stream Ciphers

Stream ciphers are cryptographic primitives that are used to ensure the privacy of a message that is sent over a digital communication channel. In this thesis we will present new cryptanalytic results for several stream ciphers. The thesis provides a general introduction to cryptology, explains the basic concepts, gives an overview of various cryptographic primitives and discusses a number of different attack models. The first new attack given is a linear correlation attack in the form of a distinguishing attack. In this attack a specific class of weak feedback polynomials for LFSRs is identified. If the feedback polynomial is of a particular form the attack will be efficient. Two new distinguishing attacks are given on classical stream cipher constructions, namely the filter generator and the irregularly clocked filter generator. It is also demonstrated how these attacks can be applied to modern constructions. A key recovery attack is described for LILI-128 and a distinguishing attack for LILI-II is given. The European network of excellence, called eSTREAM, is an effort to find new efficient and secure stream ciphers. We analyze a number of the eSTREAM candidates. Firstly, distinguishing attacks are described for the candidate Dragon and a family of candidates called Pomaranch. Secondly, we describe resynchronization attacks on eSTREAM candidates. A general square root resynchronization attack which can be used to recover parts of a message is given. The attack is demonstrated on the candidates LEX and Pomaranch. A chosen IV distinguishing attack is then presented which can be used to evaluate the initialization procedure of stream ciphers. The technique is demonstrated on four candidates: Grain, Trivium, Decim and LEX

ECSC-128: New Stream Cipher Based On Elliptic Curve Discrete Logarithm Problem.

Ecsc-128 is a new stream cipher based on the intractability of the Elliptic curve discrete logarithm problem. The design of ECSC-l2g is divided into three important stages: Initialization Stage, Keystream Generation stage, and the Encryption Stage. The design goal of ECSC-128 is to come up with a secure stream cipher for data encryption. Ecsc-l2g was designed based on some hard mathematical problems instead of using simple logical operations. In terms of performance and security, Ecsc-l2g was slower, but it provided high level of security against all possible cryptanalysis attacks

State convergence and keyspace reduction of the Mixer stream cipher

This paper presents an analysis of the stream cipher Mixer, a bit-based cipher with structural components similar to the well-known Grain cipher and the LILI family of keystream generators. Mixer uses a 128-bit key and 64-bit IV to initialise a 217-bit internal state. The analysis is focused on the initialisation function of Mixer and shows that there exist multiple key-IV pairs which, after initialisation, produce the same initial state, and consequently will generate the same keystream. Furthermore, if the number of iterations of the state update function performed during initialisation is increased, then the number of distinct initial states that can be obtained decreases. It is also shown that there exist some distinct initial states which produce the same keystream, resulting in a further reduction of the effective key space

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

Remotely Keyed CryptoGraphics - Secure Remote Display Access Using (Mostly) Untrusted Hardware - Extended Version

Software that covertly monitors user actions, also known as spyware, has become a first-level security threat due to its ubiquity and the difficulty of detecting and removing it. Such software may be inadvertently installed by a user that is casually browsing the web, or may be purposely installed by an attacker or even the owner of a system. This is particularly problematic in the case of utility computing, early manifestations of which are Internet cafes and thin-client computing. Traditional trusted computing approaches offer a partial solution to this by significantly increasing the size of the trusted computing base (TCB) to include the operating system and other software. We examine the problem of protecting a user accessing specific services in such an environment. We focus on secure video broadcasts and remote desktop access when using any convenient, and often untrusted, terminal as two example applications. We posit that, at least for such applications, the TCB can be confined to a suitably modified graphics processing unit (GPU). Specifically, to prevent spyware on untrusted clients from accessing the user's data, we restrict the boundary of trust to the client's GPU by moving image decryption into GPUs. We use the GPU in order to leverage existing capabilities as opposed to designing a new component from scratch. We discuss the applicability of GPU-based decryption in these two sample scenarios and identify the limitations of the current generation of GPUs. We propose straightforward modifications to future GPUs that will allow the realization of the full approach