07021 Abstracts Collection -- Symmetric Cryptography

From .. to .., the Dagstuhl Seminar 07021 ``Symmetric Cryptography\u27\u27 automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

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

Attacks based on Conditional Correlations against the Nonlinear Filter Generator

In this paper we extend the conditional correlation attack ([LCPP96]) against the nonlinear filter generator (NLFG) by introducing new conditions and generalisations and present two known-plaintext attacks, called hybrid correlation attack and concentration attack. The NLFG is a well known LFSR-based keystream generator which could be used as a basic building block in a synchronous stream cipher system. Both new attacks use methods from the conditional correlation attack and additional from fast correlation attacks to derive the unknown initial state of the LFSR of the NLFG. The basic principle of iteratively cumulating and updating conditional correlations for the NLFG was proposed in [Loh01] and for general combiners with memory in [GBM02]. With the hybrid correlation attack it is possible to successfully attack the NLFG by applying a fast correlation attack, even if the filter function $f$ of the NLFG is highly nonlinear, e.g. the normalised nonlinearity $p_{e,f}$ is $\ge 0.45$. The concentration attack maps all computed conditional correlations to $D-B$ unknown LFSR bits, where $D \ge k$ and $1 \le B \le k$ are parameters which can be chosen by the attacker, and $k$ is the length of the LFSR of the NLFG. Even with low values of conditional correlations, it is possible to mount the hybrid correlation attack and the concentration attack successfully. This is not the case for the originally version of the conditional correlation attack ([LCPP96]) in a time lower than a full search over all possible initial states

Selected Cryptographic Methods for Securing Low-End Devices

We consider in this thesis the security goals confidentiality of messages and authenticity of entities in electronic communication with special focus on applications in environments with restricted computational power, e.g., RFID-tags or mobile phones. We introduce the concept of stream ciphers, describe and analyze their most important building blocks, analyze their security features, and indicate ways to improve their resistance against certain types of attacks. In the context of entity authentication, we describe special protocols based on randomly choosing elements from a secret set of linear vector spaces and relate the security of these protocols to the hardness of a certain learning problem

LIZARD – A Lightweight Stream Cipher for Power-constrained Devices

Time-memory-data (TMD) tradeoff attacks limit the security level of many classical stream ciphers (like E0, A5/1, Trivium, Grain) to 1/2n, where n denotes the inner state length of the underlying keystream generator. In this paper, we present Lizard, a lightweight stream cipher for power-constrained devices like passive RFID tags. Its hardware efficiency results from combining a Grain-like design with the FP(1)-mode, a recently suggested construction principle for the state initialization of stream ciphers, which offers provable 2/3n-security against TMD tradeoff attacks aiming at key recovery. Lizard uses 120-bit keys, 64-bit IVs and has an inner state length of 121 bit. It is supposed to provide 80-bit security against key recovery attacks. Lizard allows to generate up to 218 keystream bits per key/IV pair, which would be sufficient for many existing communication scenarios like Bluetooth, WLAN or HTTPS

Selected Topics in Cryptanalysis of Symmetric Ciphers

It is well established that a symmetric cipher may be described as a system of Boolean polynomials, and that the security of the cipher cannot be better than the difficulty of solving said system. Compressed Right-Hand Side (CRHS) Equations is but one way of describing a symmetric cipher in terms of Boolean polynomials. The first paper of this thesis provides a comprehensive treatment firstly of the relationship between Boolean functions in algebraic normal form, Binary Decision Diagrams and CRHS equations. Secondly, of how CRHS equations may be used to describe certain kinds of symmetric ciphers and how this model may be used to attempt a key-recovery attack. This technique is not left as a theoretical exercise, as the process have been implemented as an open-source project named CryptaPath. To ensure accessibility for researchers unfamiliar with algebraic cryptanalysis, CryptaPath can convert a reference implementation of the target cipher, as specified by a Rust trait, into the CRHS equations model automatically. CRHS equations are not limited to key-recovery attacks, and Paper II explores one such avenue of CRHS equations flexibility. Linear and differential cryptanalysis have long since established their position as two of the most important cryptanalytical attacks, and every new design since must show resistance to both. For some ciphers, like the AES, this resistance can be mathematically proven, but many others are left to heuristic arguments and computer aided proofs. This work is tedious, and most of the tools require good background knowledge of a tool/technique to transform a design to the right input format, with a notable exception in CryptaGraph. CryptaGraph is written in Rust and transforms a reference implementation into CryptaGraphs underlying data structure automatically. Paper II introduces a new way to use CRHS equations to model a symmetric cipher, this time in such a way that linear and differential trail searches are possible. In addition, a new set of operations allowing us to count the number of active S-boxes in a path is presented. Due to CRHS equations effective initial data compression, all possible trails are captured in the initial system description. As is the case with CRHS equations, the crux is the memory consumption. However, this approach also enables the graph of a CRHS equation to be pruned, allowing the memory consumption to be kept at manageable levels. Unfortunately, pruning nodes also means that we will lose valid, incomplete paths, meaning that the hulls found are probably incomplete. On the flip side, all paths, and their corresponding probabilities, found by the tool are guaranteed to be valid trails for the cipher. This theory is also implemented in an extension of CryptaPath, and the name is PathFinder. PathFinder is also able to automatically turn a reference implementation of a cipher into its CRHS equations-based model. As an additional bonus, PathFinder supports the reference implementation specifications specified by CryptaGraph, meaning that the same reference implementation can be used for both CryptaGraph and PathFinder. Paper III shifts focus onto symmetric ciphers designed to be used in conjunction with FHE schemes. Symmetric ciphers designed for this purpose are relatively new and have naturally had a strong focus on reducing the number of multiplications performed. A multiplication is considered expensive on the noise budget of the FHE scheme, while linear operations are viewed as cheap. These ciphers are all assuming that it is possible to find parameters in the various FHE schemes which allow these ciphers to work well in symbiosis with the FHE scheme. Unfortunately, this is not always possible, with the consequence that the decryption process becomes more costly than necessary. Paper III therefore proposes Fasta, a stream cipher which has its parameters and linear layer especially chosen to allow efficient implementation over the BGV scheme, particularly as implemented in the HElib library. The linear layers are drawn from a family of rotation-based linear transformations, as cyclic rotations are cheap to do in FHE schemes that allow packing of multiple plaintext elements in one FHE ciphertext. Fasta follows the same design philosophy as Rasta, and will never use the same linear layer twice under the same key. The result is a stream cipher tailor-made for fast evaluation in HElib. Fasta shows an improvement in throughput of a factor more than 7 when compared to the most efficient implementation of Rasta.Doktorgradsavhandlin

Cryptanalysis of Bluetooth Keystream Generator Two-level E0

In this paper, we carefully study both distinguishing and key-recovery attacks against Bluetooth two-level EO given many short frames. Based on a flaw in the resynchronization of Bluetooth EO, we are able to fully exploit the largest bias of the finite state machine inside EO for our attacks. Our key-recovery attack works with 240 simple operations given the first 24 bits of 235 frames. Compared with all existing attacks against two-level EO, this is the best one so fa

On Cryptographic Properties of LFSR-based Pseudorandom Generators

Pseudorandom Generators (PRGs) werden in der modernen Kryptographie verwendet, um einen kleinen Startwert in eine lange Folge scheinbar zufälliger Bits umzuwandeln. Viele Designs für PRGs basieren auf linear feedback shift registers (LFSRs), die so gewählt sind, dass sie optimale statistische und periodische Eigenschaften besitzen. Diese Arbeit diskutiert Konstruktionsprinzipien und kryptanalytische Angriffe gegen LFSR-basierte PRGs. Nachdem wir einen vollständigen Überblick über existierende kryptanalytische Ergebnisse gegeben haben, führen wir den dynamic linear consistency test (DLCT) ein und analysieren ihn. Der DLCT ist eine suchbaum-basierte Methode, die den inneren Zustand eines PRGs rekonstruiert. Wir beschließen die Arbeit mit der Diskussion der erforderlichen Zustandsgröße für PRGs, geben untere Schranken an und Beispiele aus der Praxis, die veranschaulichen, welche Größe sichere PRGs haben müssen

Lightweight cryptography on ultra-constrained RFID devices

Devices of extremely small computational power like RFID tags are used in practice to a rapidly growing extent, a trend commonly referred to as ubiquitous computing. Despite their severely constrained resources, the security burden which these devices have to carry is often enormous, as their fields of application range from everyday access control to human-implantable chips providing sensitive medical information about a person. Unfortunately, established cryptographic primitives such as AES are way to 'heavy' (e.g., in terms of circuit size or power consumption) to be used in corresponding RFID systems, calling for new solutions and thus initiating the research area of lightweight cryptography. In this thesis, we focus on the currently most restricted form of such devices and will refer to them as ultra-constrained RFIDs. To fill this notion with life and in order to create a profound basis for our subsequent cryptographic development, we start this work by providing a comprehensive summary of conditions that should be met by lightweight cryptographic schemes targeting ultra-constrained RFID devices. Building on these insights, we then turn towards the two main topics of this thesis: lightweight authentication and lightweight stream ciphers. To this end, we first provide a general introduction to the broad field of authentication and study existing (allegedly) lightweight approaches. Drawing on this, with the (n,k,L)^-protocol, we suggest our own lightweight authentication scheme and, on the basis of corresponding hardware implementations for FPGAs and ASICs, demonstrate its suitability for ultra-constrained RFIDs. Subsequently, we leave the path of searching for dedicated authentication protocols and turn towards stream cipher design, where we first revisit some prominent classical examples and, in particular, analyze their state initialization algorithms. Following this, we investigate the rather young area of small-state stream ciphers, which try to overcome the limit imposed by time-memory-data tradeoff (TMD-TO) attacks on the security of classical stream ciphers. Here, we present some new attacks, but also corresponding design ideas how to counter these. Paving the way for our own small-state stream cipher, we then propose and analyze the LIZARD-construction, which combines the explicit use of packet mode with a new type of state initialization algorithm. For corresponding keystream generator-based designs of inner state length n, we prove a tight (2n/3)-bound on the security against TMD-TO key recovery attacks. Building on these theoretical results, we finally present LIZARD, our new lightweight stream cipher for ultra-constrained RFIDs. Its hardware efficiency and security result from combining a Grain-like design with the LIZARD-construction. Most notably, besides lower area requirements, the estimated power consumption of LIZARD is also about 16 percent below that of Grain v1, making it particularly suitable for passive RFID tags, which obtain their energy exclusively through an electromagnetic field radiated by the reading device. The thesis is concluded by an extensive 'Future Research Directions' chapter, introducing various new ideas and thus showing that the search for lightweight cryptographic solutions is far from being completed