Quantum Time/Memory/Data Tradeoff Attacks

One of the most celebrated and useful cryptanalytic algorithms is Hellman\u27s time/memory tradeoff (and its Rainbow Table variant), which can be used to invert random-looking functions on $N$ possible values with time and space complexities satisfying $TM^2=N^2$. As a search problem, one can always transform it into the quantum setting by using Grover\u27s algorithm, but this algorithm does not benefit from the possible availability of auxiliary advice obtained during a free preprocessing stage. However, at FOCS\u2720 it was rigorously shown that a small amount of quantum auxiliary advice (which can be stored in a quantum memory of size $M \leq O(\sqrt{N})$) cannot possibly yield an attack which is better than Grover\u27s algorithm. In this paper we develop new quantum versions of Hellman\u27s cryptanalytic attack which use large memories in the standard QACM (Quantum Accessible Classical Memory) model of computation. In particular, we improve Hellman\u27s tradeoff curve to $T^{4/3}M^2=N^2$. When we generalize the cryptanalytic problem to a time/memory/data tradeoff attack (in which one has to invert $f$ for at least one of $D$ given values), we get the generalized curve $T^{4/3}M^2D^2=N^2$. A typical point on this curve is $D=N^{0.2}$, $M=N^{0.6}$, and $T=N^{0.3}$, whose time is strictly lower than both Grover\u27s algorithm and the classical Hellman algorithm (both of which require $T=N^{0.4}$ for these $D$ and $M$ parameters)

Tight Bounds on Online Checkpointing Algorithms

The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints as evenly spread out as possible at all times. At ICALP\u2713 Bringmann et al. studied this problem as a special case of an online/offline optimization problem in which the deviation from uniformity is measured by the natural discrepancy metric of the worst case ratio between real and ideal segment lengths. They showed this discrepancy is smaller than 1.59-o(1) for all k, and smaller than ln4-o(1)~~1.39 for the sparse subset of k\u27s which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k. In this paper we solve the main problems left open in the ICALP\u2713 paper by proving that ln4 is a tight upper and lower bound on the asymptotic discrepancy for all large k, and by providing tight upper and lower bounds (in the form of provably optimal checkpointing algorithms, some of which are in fact better than those of Bringmann et al.) for all the small values of k <= 10

IoT Goes Nuclear: Creating a ZigBee Chain Reaction

Within the next few years, billions of IoT devices will densely populate our cities. In this paper we describe a new type of threat in which adjacent IoT devices will infect each other with a worm that will spread explosively over large areas in a kind of nuclear chain reaction, provided that the density of compatible IoT devices exceeds a certain critical mass. In particular, we developed and verified such an infection using the popular Philips Hue smart lamps as a platform. The worm spreads by jumping directly from one lamp to its neighbors, using only their built-in ZigBee wireless connectivity and their physical proximity. The attack can start by plugging in a single infected bulb anywhere in the city, and then catastrophically spread everywhere within minutes, enabling the attacker to turn all the city lights on or off, permanently brick them, or exploit them in a massive DDOS attack. To demonstrate the risks involved, we use results from percolation theory to estimate the critical mass of installed devices for a typical city such as Paris whose area is about 105 square kilometers: The chain reaction will fizzle if there are fewer than about 15,000 randomly located smart lights in the whole city, but will spread everywhere when the number exceeds this critical mass (which had almost certainly been surpassed already). To make such an attack possible, we had to find a way to remotely yank already installed lamps from their current networks, and to perform over-the-air firmware updates. We overcame the first problem by discovering and exploiting a major bug in the implementation of the Touchlink part of the ZigBee Light Link protocol, which is supposed to stop such attempts with a proximity test. To solve the second problem, we developed a new version of a side channel attack to extract the global AES-CCM key (for each device type) that Philips uses to encrypt and authenticate new firmware. We used only readily available equipment costing a few hundred dollars, and managed to find this key without seeing any actual updates. This demonstrates once again how difficult it is to get security right even for a large company that uses standard cryptographic techniques to protect a major product

Three Third Generation Attacks on the Format Preserving Encryption Scheme FF3

Format-Preserving Encryption (FPE) schemes accept plaintexts from any finite set of values (such as social security numbers or birth dates) and produce ciphertexts that belong to the same set. They are extremely useful in practice since they make it possible to encrypt existing databases or communication packets without changing their format. Due to industry demand, NIST had standardized in 2016 two such encryption schemes called FF1 and FF3. They immediately attracted considerable cryptanalytic attention with decreasing attack complexities. The best currently known attack on the Feistel construction FF3 has data and memory complexity of ${O}(N^{11/6})$ and time complexity of ${O}(N^{17/6})$, where the input belongs to a domain of size $N \times N$. In this paper, we present and experimentally verify three improved attacks on FF3. Our best attack achieves the tradeoff curve $D=M=\tilde{O}(N^{2-t})$, $T=\tilde{O}(N^{2+t})$ for all $t \leq 0.5$. In particular, we can reduce the data and memory complexities to the more practical $\tilde{O}(N^{1.5})$, and at the same time, reduce the time complexity to $\tilde{O}(N^{2.5})$. We also identify another attack vector against FPE schemes, the related-domain attack. We show how one can mount powerful attacks when the adversary is given access to the encryption under the same key in different domains, and show how to apply it to efficiently distinguish FF3 and FF3-1 instances

Efficient Detection of High Probability Statistical Properties of Cryptosystems via Surrogate Differentiation

A central problem in cryptanalysis is to find all the significant deviations from randomness in a given $n$-bit cryptographic primitive. When $n$ is small (e.g., an $8$-bit S-box), this is easy to do, but for large $n$, the only practical way to find such statistical properties was to exploit the internal structure of the primitive and to speed up the search with a variety of heuristic rules of thumb. However, such bottom-up techniques can miss many properties, especially in cryptosystems which are designed to have hidden trapdoors. In this paper we consider the top-down version of the problem in which the cryptographic primitive is given as a structureless black box, and reduce the complexity of the best known techniques for finding all its significant differential and linear properties by a large factor of $2^{n/2}$. Our main new tool is the idea of using {\it surrogate differentiation}. In the context of finding differential properties, it enables us to simultaneously find information about all the differentials of the form $f(x) \oplus f(x \oplus \alpha)$ in all possible directions $\alpha$ by differentiating $f$ in a single arbitrarily chosen direction $\gamma$ (which is unrelated to the $\alpha$\u27s). In the context of finding linear properties, surrogate differentiation can be combined in a highly effective way with the Fast Fourier Transform. For $64$-bit cryptographic primitives, this technique makes it possible to automatically find in about $2^{64}$ time all their differentials with probability $p \geq 2^{-32}$ and all their linear approximations with bias $|p| \geq 2^{-16}$; previous algorithms for these problems required at least $2^{96}$ time. Similar techniques can be used to significantly improve the best known time complexities of finding related key differentials, second-order differentials, and boomerangs. In addition, we show how to run variants of these algorithms which require no memory, and how to detect such statistical properties even in trapdoored cryptosystems whose designers specifically try to evade our techniques

The 9 Lives of Bleichenbacher\u27s CAT: New Cache ATtacks on TLS Implementations

At CRYPTO’98, Bleichenbacher published his seminal paper which described a padding oracle attack against RSA implementations that follow the PKCS #1 v1.5 standard. Over the last twenty years researchers and implementors had spent a huge amount of effort in developing and deploying numerous mitigation techniques which were supposed to plug all the possible sources of Bleichenbacher-like leakages. However, as we show in this paper most implementations are still vulnerable to several novel types of attack based on leakage from various microarchitectural side channels: Out of nine popular implementations of TLS that we tested, we were able to break the security of seven implementations with practical proof-of-concept attacks. We demonstrate the feasibility of using those Cache-like ATacks (CATs) to perform a downgrade attack against any TLS connection to a vulnerable server, using a BEAST-like Man in the Browser attack. The main difficulty we face is how to perform the thousands of oracle queries required before the browser’s imposed timeout (which is 30 seconds for almost all browsers, with the exception of Firefox which can be tricked into extending this period). The attack seems to be inherently sequential (due to its use of adaptive chosen ciphertext queries), but we describe a new way to parallelize Bleichenbacher-like padding attacks by exploiting any available number of TLS servers that share the same public key certificate. With this improvement, we could demonstrate the feasibility of a downgrade attack which could recover all the 2048 bits of the RSA plaintext (including the premaster secret value, which suffices to establish a secure connection) from five available TLS servers in under 30 seconds. This sequential-to-parallel transformation of such attacks can be of independent interest, speeding up and facilitating other side channel attacks on RSA implementations