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

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

How Far Can We Go Beyond Linear Cryptanalysis?

Several generalizations of linear cryptanalysis have been proposed in the past, as well as very similar attacks in a statistical point of view. In this paper, we define a rigorous general statistical framework which allows to interpret most of these attacks in a simple and unified way. Then, we explicitely construct optimal distinguishers, we evaluate their performance, and we prove that a block cipher immune to classical linear cryptanalysis possesses some resistance to a wide class of generalized versions, but not all. Finally, we derive tools which are necessary to set up more elaborate extensions of linear cryptanalysis, and to generalize the notions of bias, characteristic, and piling-up lemma

The conditional correlation attack: a practical attack on Bluetooth encryption

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 EO, 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 223.8 frames and with 238 computations. This is clearly the fastest and only practical known-plaintext attack on Bluetooth encryption compared with all existing attacks. Current experiments confirm our analysi

Design Space Exploration of Galois and Fibonacci Configuration based on Espresso Stream Cipher

Galois and Fibonacci are two different configurations of stream ciphers. Because the Fibonacci configuration is more convenient for cryptanalysis, most ciphers are designed as Fibonacci-configured. So far, although many transformations between Fibonacci and Galois configurations have been proposed, there is no sufficient analysis of their respective hardware performance. The 128-bit secret key stream cipher Espresso, its Fibonacciconfigured variant and linear Fibonacci variant have a similar security level. We take them as examples to design the optimization strategies in terms of both area and throughput, investigate which configuration is more efficient in a certain aspect. The Fibonacci-configured Espresso occupies 52 slices on Spartan-3 and 22 slices on Virtex-7, which are the minimum solutions among those three Espresso schemes or even smaller than 80-bit secret key ciphers. Based on our throughput improvement strategy, parallel Espresso design can perform 4.1 Gbps on Virtex-7 FPGA and 1.9 Gbps on Spartan-3 FPGA at most. In brief, the Fibonacci cipher is more suitable for extremely resource-constrained or extremely high-throughput applications, while the Galois cipher seems like a compromise between area and speed. Besides, the transformation from nonlinear feedback to linear feedback is not recommended for any hardware implementations

Cryptanalysis of Bluetooth keystream generator two-level E0

Abstract. In this paper, we carefully study both distinguishing and keyrecovery attacks against Bluetooth two-level E0 given many short frames. Based on a flaw in the resynchronization of Bluetooth E0, we are able to fully exploit the largest bias of the finite state machine inside E0 for our attacks. Our key-recovery attack works with 2 40 simple operations given the first 24 bits of 2 35 frames. Compared with all existing attacks against two-level E0, this is the best one so far.

Ongoing Research Areas in Symmetric Cryptography

This report is a deliverable for the ECRYPT European network of excellence in cryptology. It gives a brief summary of some of the research trends in symmetric cryptography at the time of writing. The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the recently proposed algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

D.STVL.9 - Ongoing Research Areas in Symmetric Cryptography

This report gives a brief summary of some of the research trends in symmetric cryptography at the time of writing (2008). The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

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