Statistical and Algebraic Cryptanalysis of Lightweight and Ultra-Lightweight Symmetric Primitives

Symmetric cryptographic primitives such as block and stream ciphers are the building blocks in many cryptographic protocols. Having such blocks which provide provable security against various types of attacks is often hard. On the other hand, if possible, such designs are often too costly to be implemented and are usually ignored by practitioners. Moreover, in RFID protocols or sensor networks, we need lightweight and ultra-lightweight algorithms. Hence, cryptographers often search for a fair trade-off between security and usability depending on the application. Contrary to public key primitives, which are often based on some hard problems, security in symmetric key is often based on some heuristic assumptions. Often, the researchers in this area argue that the security is based on the confidence level the community has in their design. Consequently, everyday symmetric protocols appear in the literature and stay secure until someone breaks them. In this thesis, we evaluate the security of multiple symmetric primitives against statistical and algebraic attacks. This thesis is composed of two distinct parts: In the first part, we investigate the security of RC4 stream cipher against statistical attacks. We focus on its applications in WEP and WPA protocols. We revisit the previous attacks on RC4 and optimize them. In fact, we propose a framework on how to deal with a pool of biases for RC4 in an optimized manner. During this work, we found multiple new weaknesses in the corresponding applications. We show that the current best attack on WEP can still be improved. We compare our results with the state of the art implementation of the WEP attack on Aircrack-ng program and improve its success rate. Next, we propose a theoretical key recovery and distinguishing attacks on WPA, which cryptographically break the protocol. We perform an extreme amount of experiments to make sure that the proposed theory matches the experiments. Finally, we propose a concrete theoretical and empirical proof of all our claims. These are currently the best known attacks on WEP and WPA. In the second part, we shed some lights on the theory behind ElimLin, which is an algorithm for solving multivariate polynomial systems of equations. We attack PRESENT and LBlock block ciphers with ElimLin algorithm and compare their security using this algebraic technique. Then, we investigate the security of KATAN family of block ciphers and multi-purpose cryptographic primitive ARMADILLO against algebraic attacks. We break reduced-round versions of several members of KATAN family by proposing a novel pre-processing technique on the original algebraic representation of the cipher before feeding it to a SAT solver. Finally, we propose a devastating practical key recovery attack against the ARMADILLO1 protocol, which breaks it in polynomial time using a few challenge-response pairs

The Eye of The Mirage: On the Elusive Nature of Consciousness

Is there a distilled, core, phenomenal feel that sits at the heart of conscious experience? In a usual debate about consciousness, there are often two sides involved: the physicalist, who reminds us that many mysteries of the past have now been shown to have been entirely misguided notions as our scientific understanding of the world has advanced, and the anti-physicalist, who emphasizes that consciousness stands apart since our very understanding of science is filtered through the senses, making consciousness the very existence one cannot possibly doubt. Clearly, regarding the topic of consciousness, even the explanandum is heavily debated, and perhaps finding a neutral explanandum is practically impossible, even if one believes in a perfect separation of facts and theory. By pointing out the limitations of both physicalist and non-physicalist ontologies, this paper explores the possibility of a neutral explanandum and argues even if one exists, it has an elusive nature

Predicting Outcomes of ElimLin Attack on Lightweight Block Cipher Simon

There are two major families in cryptanalytic attacks on symmetric ciphers: statistical attacks and algebraic attacks. In this position paper we argue that algebraic cryptanalysis has not yet been developed properly due to the weakness of the theory which has substantial difficulty to prove most basic results on the number of linearly independent equations in algebraic attacks. Consequently most authors present a restricted range of attacks which are shown experimentally to work with their computer but refrain from claiming results which would work on a larger computer but have not yet been tested. For example in recent 2015 work of Raddum we discover that (experimentally) ElimLin attack breaks up to 16 rounds of Simon block cipher however it is hard to know what happens for 17 rounds. In this paper we argue that one CAN predict and model the behavior of such attacks and evaluate complexity of the attacks which we cannot yet execute. To the best of our knowledge this has never been done before

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

The best way of selecting samples in algebraic attacks against block ciphers is not well explored and understood. We introduce a simple strategy for selecting the plaintexts and demonstrate its strength by breaking reduced-round KATAN32 and LBlock. In both cases, we present a practical attack which outperforms previous attempts of algebraic cryptanalysis whose complexities were close to exhaustive search. The attack is based on the selection of samples using cube attack and ElimLin which was presented at FSE’12, and a new technique called Universal Proning. In the case of LBlock, we break 10 out of 32 rounds. In KATAN32, we break 78 out of 254 rounds. Unlike previous attempts which break smaller number of rounds, we do not guess any bit of the key and we only use structural properties of the cipher to be able to break a higher number of rounds with much lower complexity. We show that cube attacks owe their success to the same properties and therefore, can be used as a heuristic for selecting the samples in an algebraic attack. The performance of ElimLin is further enhanced by the new Universal Proning technique, which allows to discover linear equations that are not found by ElimLin

Discovery and Exploitation of New Biases in RC4

In this paper, we present several weaknesses in the stream cipher RC4. First, we present a technique to automatically reveal linear correlations in the PRGA of RC4. With this method, 48 new exploitable correlations have been discovered. Then we bind these new biases in the PRGA with known KSA weaknesses to provide practical key recovery attacks. Henceforth, we apply a similar technique on RC4 as a black box, i.e. the secret key words as input and the keystream words as output. Our objective is to exhaustively find linear correlations between these elements. Thanks to this technique, 9 new exploitable correlations have been revealed. Finally, we exploit these weaknesses on RC4 to some practical examples, such as the WEP protocol. We show that these correlations lead to a key recovery attack on WEP with only 9800 encrypted packets (less than 20 seconds), instead of 24200 for the best previous attack

On Selection of Samples in Algebraic Attacks and a New Technique to Find Hidden Low Degree Equations

The best way of selecting samples in algebraic attacks against block ciphers is not well explored and understood. We introduce a simple strategy for selecting the plaintexts and demonstrate its strength by breaking reduced-round KATAN, LBLOCK and SIMON. For each case, we present a practical attack on reduced round version which outperforms previous attempts of algebraic cryptanalysis whose complexities were close to exhaustive search. The attack is based on the selection of samples using cube attack and ELIMLIN which was presented at FSE'12, and a new technique called proning. In the case of LBLOCK, we break 10 out of 32 rounds. In KATAN, we break 78 out of 254 rounds. Unlike previous attempts which break smaller number of rounds, we do not guess any bit of the key and we only use structural properties of the cipher to be able to break a higher number of rounds with much lower complexity. We show that cube attacks owe their success to the same properties and therefore, can be used as a heuristic for selecting the samples in an algebraic attack. The performance of ELIMLIN is further enhanced by the new proning technique, which allows to discover linear equations that are not found by ELIMLIN

Tornado Attack on RC4 with Applications to WEP & WPA

In this paper, we construct several tools for building and manipulating pools of biases in the analysis of RC4. We report extremely fast and optimized active and passive attacks against IEEE 802.11 wireless communication protocol WEP and a key recovery and a distinguishing attack against WPA. This was achieved through a huge amount of theoretical and experimental analysis (capturing WiFi packets), refinement and optimization of all the former known attacks and methodologies against RC4 stream cipher in WEP and WPA modes. We support all our claims on WEP by providing an implementation of this attack as a publicly available patch on Aircrack-ng. Our new attack improves its success probability drastically. Our active attack, based on ARP injection, requires 22500 packets to gain success probability of 50\% against a 104-bit WEP key, using Aircrack-ng in non-interactive mode. It runs in less than 5 seconds on an off-the-shelf PC. Using the same number of packets, Aicrack-ng yields around 3\% success rate. Furthermore, we describe very fast passive only attacks by just eavesdropping TCP/IPv4 packets in a WiFi communication. Our passive attack requires 27500 packets. This is much less than the number of packets Aircrack-ng requires in active mode (around 37500), which is a huge improvement. Deploying a similar theory, we also describe several attacks on WPA. Firstly, we describe a distinguisher for WPA with complexity 2^{42} and advantage 0.5 which uses 2^{42} packets. Then, based on several partial temporary key recovery attacks, we recover the full 128-bit temporary key of WPA by using 2^{42} packets. It works with complexity 2^{96}. So far, this is the best key recovery attack against WPA. We believe that our analysis brings on further insight to the security of RC4

ElimLin Algorithm Revisited

ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generated by the system. We report a number of key theorems on ElimLin. Our main result is to characterize ElimLin in terms of a sequence of intersections of vector spaces. It implies that the linear space generated by ElimLin is invariant with respect to any variable ordering during elimination and substitution. This can be seen as surprising given the fact that it eliminates variables. On the contrary, monomial ordering is a crucial factor in Grobner basis algorithms such as F4. Moreover, we prove that the result of ElimLin is invariant with respect to any affine bijective variable change. Analyzing an overdefined dense system of equations, we argue that to obtain more linear equations in the succeeding iteration in ElimLin some restrictions should be satisfied. Finally, we compare the security of LBlock and MIBS block ciphers with respect to algebraic attacks and propose several attacks on Courtois Toy Cipher version 2 (CTC2) with distinct parameters using ElimLin

Algebraic, AIDA/Cube and Side Channel Analysis of KATAN Family of Block Ciphers

This paper presents the first results on AIDA/cube, algebraic and side-channel attacks on variable number of rounds of all members of the KATAN family of block ciphers. Our cube attacks reach 60, 40 and 30 rounds of KATAN32, KATAN48 and KATAN64, respectively. In our algebraic attacks, we use SAT solvers as a tool to solve the quadratic equations representation of all KATAN ciphers. We introduced a novel pre-processing stage on the equations system before feeding it to the SAT solver. This way, we could break 79, 64 and 60 rounds of KATAN32, KATAN48, KATAN64, respectively. We show how to perform side channel attacks on the full 254-round KATAN32 with one-bit information leak- age from the internal state by cube attacks. Finally, we show how to reduce the attack complexity by combining the cube attack with the algebraic attack to re- cover the full 80-bit key. Further contributions include new phenomena observed in cube, algebraic and side-channel attacks on the KATAN ciphers. For the cube attacks, we observed that the same maxterms suggested more than one cube equation, thus reducing the overall data and time complexities. For the algebraic at- tacks, a novel pre-processing step led to a speed up of the SAT solver program. For the side-channel attacks, 29 linearly independent cube equations were recovered after 40-round KATAN32. Finally, the combined algebraic and cube attack, a leakage of key bits after 71 rounds led to a speed up of the algebraic attack