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

On the Security of Stream Cipher CryptMT v3

CryptMT v3 is a stream cipher submitted to eStream project, and has entered the third evaluation phase. Any attack has not been found until now. In this paper, we mainly discuss the security of the state initialization process of CryptMT v3. For the key and IV setup function $f_K$, we can construct a probabilistic testing algorithm $A^{f_K}$ with a distinguishing probability 1, which indicates that for each key $K$, $f_K$ is a non-PRF. However, we have not found any non-randomness about the keystream output

Bitstream Modification of Trivium

In this paper we present a bitstream modification attack on the Trivium cipher, an international standard under ISO/IEC 29192-3. By changing the content of three LUTs in the bitstream, we reduce the non-linear state updating function of Trivium to a linear one. This makes it possible to recover the key from 288 keystream bits using at most $2^{19.41}$ operations. We also propose a countermeasure against bitstream modification attacks which obfuscates the bitstream using dummy and camouflaged LUTs which look legitimate to the attacker. We present an algorithm for injecting dummy LUTs directly into the bitstream without causing any performance or power penalty

On the sliding property of SNOW 3G and SNOW 2.0

SNOW 3G is a stream cipher chosen by the 3rd Generation Partnership Project (3GPP) as a crypto-primitive to substitute KASUMI in case its security is compromised. SNOW 2.0 is one of the stream ciphers chosen for the ISO/IEC standard IS 18033-4. In this study, the authors show that the initialisation procedure of the two ciphers admits a sliding property, resulting in several sets of related-key pairs. In case of SNOW 3G, a set of 232 related-key pairs is presented, whereas in the case of SNOW 2.0, several such sets are found, out of which the largest are of size 264 and 2192 for the 128-bit and 256-bit variant of the cipher, respectively. In addition to allowing related-key recovery attacks against SNOW 2.0 with 256-bit keys, the presented properties reveal non-random behaviour that yields related-key distinguishers and also questions the validity of the security proofs of protocols that are based on the assumption that SNOW 3G and SNOW 2.0 behave like perfect random functions of the key-IV

Leaked-State-Forgery Attack Against The Authenticated Encryption Algorithm ALE

ALE is a new authenticated encryption algorithm published at FSE 2013. The authentication component of ALE is based on the strong Pelican MAC, and the authentication security of ALE is claimed to be 128-bit. In this paper, we propose the leaked-state-forgery attack (LSFA) against ALE by exploiting the state information leaked from the encryption of ALE. The LSFA is a new type of differential cryptanalysis in which part of the state information is known and exploited to improve the differential probability. Our attack shows that the authentication security of ALE is only 97-bit. And the results may be further improved to around 93-bit if the whitening key layer is removed. We implemented our attacks against a small version of ALE (using 64-bit block size instead of 128-bit block size). The experimental results match well with the theoretical results

Design and Analysis of Security Schemes for Low-cost RFID Systems

With the remarkable progress in microelectronics and low-power semiconductor technologies, Radio Frequency IDentification technology (RFID) has moved from obscurity into mainstream applications, which essentially provides an indispensable foundation to realize ubiquitous computing and machine perception. However, the catching and exclusive characteristics of RFID systems introduce growing security and privacy concerns. To address these issues are particularly challenging for low-cost RFID systems, where tags are extremely constrained in resources, power and cost. The primary reasons are: (1) the security requirements of low-cost RFID systems are even more rigorous due to large operation range and mass deployment; and (2) the passive tags' modest capabilities and the necessity to keep their prices low present a novel problem that goes beyond the well-studied problems of traditional cryptography. This thesis presents our research results on the design and the analysis of security schemes for low-cost RFID systems. Motivated by the recent attention on exploiting physical layer resources in the design of security schemes, we investigate how to solve the eavesdropping, modification and one particular type of relay attacks toward the tag-to-reader communication in passive RFID systems without requiring lightweight ciphers. To this end, we propose a novel physical layer scheme, called Backscatter modulation- and Uncoordinated frequency hopping-assisted Physical Layer Enhancement (BUPLE). The idea behind it is to use the amplitude of the carrier to transmit messages as normal, while to utilize its periodically varied frequency to hide the transmission from the eavesdropper/relayer and to exploit a random sequence modulated to the carrier's phase to defeat malicious modifications. We further improve its eavesdropping resistance through the coding in the physical layer, since BUPLE ensures that the tag-to-eavesdropper channel is strictly noisier than the tag-to-reader channel. Three practical Wiretap Channel Codes (WCCs) for passive tags are then proposed: two of them are constructed from linear error correcting codes, and the other one is constructed from a resilient vector Boolean function. The security and usability of BUPLE in conjunction with WCCs are further confirmed by our proof-of-concept implementation and testing. Eavesdropping the communication between a legitimate reader and a victim tag to obtain raw data is a basic tool for the adversary. However, given the fundamentality of eavesdropping attacks, there are limited prior work investigating its intension and extension for passive RFID systems. To this end, we firstly identified a brand-new attack, working at physical layer, against backscattered RFID communications, called unidirectional active eavesdropping, which defeats the customary impression that eavesdropping is a ``passive" attack. To launch this attack, the adversary transmits an un-modulated carrier (called blank carrier) at a certain frequency while a valid reader and a tag interacts at another frequency channel. Once the tag modulates the amplitude of reader's signal, it causes fluctuations on the blank carrier as well. By carefully examining the amplitude of the backscattered versions of the blank carrier and the reader's carrier, the adversary could intercept the ongoing reader-tag communication with either significantly lower bit error rate or from a significantly greater distance away. Our concept is demonstrated and empirically analyzed towards a popular low-cost RFID system, i.e., EPC Gen2. Although active eavesdropping in general is not trivial to be prohibited, for a particular type of active eavesdropper, namely a greedy proactive eavesdropper, we propose a simple countermeasure without introducing extra cost to current RFID systems. The needs of cryptographic primitives on constraint devices keep increasing with the growing pervasiveness of these devices. One recent design of the lightweight block cipher is Hummingbird-2. We study its cryptographic strength under a novel technique we developed, called Differential Sequence Attack (DSA), and present the first cryptanalytic result on this cipher. In particular, our full attack can be divided into two phases: preparation phase and key recovery phase. During the key recovery phase, we exploit the fact that the differential sequence for the last round of Hummingbird-2 can be retrieved by querying the full cipher, due to which, the search space of the secret key can be significantly reduced. Thus, by attacking the encryption (decryption resp.) of Hummingbird-2, our algorithm recovers 36-bit (another 28-bit resp.) out of 128-bit key with $2^{68}$ ($2^{60}$ resp.) time complexity if particular differential conditions of the internal states and of the keys at one round can be imposed. Additionally, the rest 64-bit of the key can be exhaustively searched and the overall time complexity is dominated by $2^{68}$. During the preparation phase, by investing $2^{81}$ effort in time, the adversary is able to create the differential conditions required in the key recovery phase with at least 0.5 probability. As an additional effort, we examine the cryptanalytic strength of another lightweight candidate known as A2U2, which is the most lightweight cryptographic primitive proposed so far for low-cost tags. Our chosen-plaintext-attack fully breaks this cipher by recovering its secret key with only querying the encryption twice on the victim tag and solving 32 sparse systems of linear equations (where each system has 56 unknowns and around 28 unknowns can be directly obtained without computation) in the worst case, which takes around 0.16 second on a Thinkpad T410 laptop

Hardware Implementations for Symmetric Key Cryptosystems

The utilization of global communications network for supporting new electronic applications is growing. Many applications provided over the global communications network involve exchange of security-sensitive information between different entities. Often, communicating entities are located at different locations around the globe. This demands deployment of certain mechanisms for providing secure communications channels between these entities. For this purpose, cryptographic algorithms are used by many of today\u27s electronic applications to maintain security. Cryptographic algorithms provide set of primitives for achieving different security goals such as: confidentiality, data integrity, authenticity, and non-repudiation. In general, two main categories of cryptographic algorithms can be used to accomplish any of these security goals, namely, asymmetric key algorithms and symmetric key algorithms. The security of asymmetric key algorithms is based on the hardness of the underlying computational problems, which usually require large overhead of space and time complexities. On the other hand, the security of symmetric key algorithms is based on non-linear transformations and permutations, which provide efficient implementations compared to the asymmetric key ones. Therefore, it is common to use asymmetric key algorithms for key exchange, while symmetric key counterparts are deployed in securing the communications sessions. This thesis focuses on finding efficient hardware implementations for symmetric key cryptosystems targeting mobile communications and resource constrained applications. First, efficient lightweight hardware implementations of two members of the Welch-Gong (WG) family of stream ciphers, the WG$\left(29,11\right)$ and WG-$16$, are considered for the mobile communications domain. Optimizations in the WG$\left(29,11\right)$ stream cipher are considered when the $GF\left(2^{29}\right)$ elements are represented in either the Optimal normal basis type-II (ONB-II) or the Polynomial basis (PB). For WG-$16$, optimizations are considered only for PB representations of the $GF\left(2^{16}\right)$ elements. In this regard, optimizations for both ciphers are accomplished mainly at the arithmetic level through reducing the number of field multipliers, based on novel trace properties. In addition, other optimization techniques such as serialization and pipelining, are also considered. After this, the thesis explores efficient hardware implementations for digit-level multiplication over binary extension fields $GF\left(2^{m}\right)$. Efficient digit-level $GF\left(2^{m}\right)$ multiplications are advantageous for ultra-lightweight implementations, not only in symmetric key algorithms, but also in asymmetric key algorithms. The thesis introduces new architectures for digit-level $GF\left(2^{m}\right)$ multipliers considering the Gaussian normal basis (GNB) and PB representations of the field elements. The new digit-level $GF\left(2^{m}\right)$ single multipliers do not require loading of the two input field elements in advance to computations. This feature results in high throughput fast multiplication in resource constrained applications with limited capacity of input data-paths. The new digit-level $GF\left(2^{m}\right)$ single multipliers are considered for both the GNB and PB. In addition, for the GNB representation, new architectures for digit-level $GF\left(2^{m}\right)$ hybrid-double and hybrid-triple multipliers are introduced. The new digit-level $GF\left(2^{m}\right)$ hybrid-double and hybrid-triple GNB multipliers, respectively, accomplish the multiplication of three and four field elements using the latency required for multiplying two field elements. Furthermore, a new hardware architecture for the eight-ary exponentiation scheme is proposed by utilizing the new digit-level $GF\left(2^{m}\right)$ hybrid-triple GNB multipliers

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