Abstract A major research area in discrete geometry is to consider the best way to partition the d -dimensional Euclidean space $$\mathbb {R}^d$$ R d under various quality criteria. In this paper we introduce a new type of space partitioning that is motivated by the problem of rounding noisy measurements from the continuous space $$\mathbb {R}^d$$ R d to a discrete subset of representative values. Specifically, we study partitions of $$\mathbb {R}^d$$ R d into bounded-size tiles colored by one of k colors, such that tiles of the same color have a distance of at least t from each other. Such tilings allow for error-resilient rounding, as two points of the same color and distance less than t from each other are guaranteed to belong to the same tile, and thus, to be rounded to the same point. The main problem we study in this paper is characterizing the achievable tradeoffs between the number of colors k and the distance t , for various dimensions d . On the qualitative side, we show that in $$\mathbb {R}^d$$ R d , using $$k=d+1$$ k = d + 1 colors is both sufficient and necessary to achieve $$t>0$$ t > 0 . On the quantitative side, we achieve numerous upper and lower bounds on t as a function of k . In particular, for $$d=3,4,8,24$$ d = 3 , 4 , 8 , 24 , we obtain sharp asymptotic bounds on t , as $$k \rightarrow \infty $$ k → ∞ . We obtain our results with a variety of techniques including isoperimetric inequalities, the Brunn-Minkowski theorem, sphere packing bounds, Bapat’s connector-free lemma, and Čech cohomology.

Modern attestation based on Trusted Execution Environments (TEEs) can significantly reduce the risk of secret compromise, allowing users to securely perform sensitive computations such as running cryptographic protocols for authentication across security critical services. However, this has made TEEs a high-value target, driving an arms race between novel compromise attacks and continuous TEEs updates. Ideally, we want to achieve Post-Compromise Security (PCS): even after a TEE compromise, we can update it back into a secure state. However, at the same time, we would like to guarantee the privacy of users, in particular preventing providers (such as Intel, Google, or Samsung) or services from tracking users across services. This requires unlinkability, which seems incompatible with standard PCS healing mechanisms. In this work, we develop TokenWeaver, the first privacy-preserving post-compromise secure attestation method with automated formal proofs for its core properties. Our construction weaves together two types of token chains, one of which is linkable and the other is unlinkable. We provide the formal models based on the Tamarin and DeepSec provers, including protocol, security properties, and proofs for reproducibility, as well as a proof-of-concept implementation in python that shows the simplicity and applicability of our solution.

An essential step for mounting cache attacks is finding eviction sets, collections of memory locations that contend on cache space. On Intel processors, one of the main challenges for identifying contending addresses is the sliced cache design, where the processor hashes the physical address to determine where in the cache a memory location is stored. While past works have demonstrated that the hash function can be reversed, they also showed that it depends on physical address bits that the adversary does not know. In this work, we make three main contributions to the art of finding eviction sets. We first exploit microarchitectural races to compare memory access times and identify the cache slice to which an address maps. We then use the known hash function to both reduce the error rate in our slice identification method and to reduce the work by extrapolating slice mappings to untested memory addresses. Finally, we show how to propagate information on eviction sets across different page offsets for the hitherto unexplored case of non-linear hash functions. Our contributions allow for entire LLC eviction set generation in 0.7 seconds on the Intel i7-9850H and 1.6 seconds on the i9-10900K, both using non-linear functions. This represents a significant improvement compared to state-of-the-art techniques taking 9× and 10× longer, respectively.

Over the last two decades, microarchitectural side channels have been the focus of a large body of research on the development of new attack techniques, exploiting them to attack various classes of targets and designing mitigations. One line of work focuses on increasing the speed of the attacks, achieving higher levels of temporal resolution that can allow attackers to learn finer-grained information. The most recent addition to this line of work is Prime+Scope [CCS '21], which only requires a single access to the L1 cache to confirm the absence of victim activity in a cache set. While significantly faster than prior attacks, Prime+Scope is still an order of magnitude slower than cache access. In this work, we set out to close this gap.

Video conferencing apps like Zoom have hundreds of millions of daily users, making them a high-value target for surveillance and subversion. While such apps claim to achieve some forms of end-to-end encryption, they usually assume an incorruptible server that is able to identify and authenticate all the parties in a meeting. Concretely this means that, e.g., even when using the "end-to-end encrypted" setting, malicious Zoom servers could eavesdrop or impersonate in arbitrary groups.In this work, we show how security against malicious servers can be improved by changing the way in which such protocols use passwords (known as passcodes in Zoom) and integrating a password-authenticated key exchange (PAKE) protocol.To formally prove that our approach achieves its goals, we formalize a class of cryptographic protocols suitable for this setting, and define a basic security notion for them, in which group security can be achieved assuming the server is trusted to correctly authorize the group members. We prove that Zoom indeed meets this notion. We then propose a stronger security notion that can provide security against malicious servers, and propose a transformation that can achieve this notion. We show how we can apply our transformation to Zoom to provably achieve stronger security against malicious servers, notably without introducing new security elements.

Intel’s Software Guard Extensions (SGX) promises an isolated execution environment, protected from all software running on the machine. As such, numerous works have sought to leverage SGX to provide confidentiality and integrity guarantees for code running in adversarial environments. In the past few years however, SGX has come under heavy fire, threatened by numerous hardware attacks. With Intel repeatedly patching SGX to regain security while consistently launching new (micro)architectures, it is increasingly difficult to track the applicability of various attack techniques across the SGX design landscape.Thus, in this paper we set out to survey and categorize various SGX attacks, their applicability to different SGX architectures, as well as the information leaked by them. We then set out to explore the effectiveness of SGX’s update mechanisms in preventing attacks on real-world deployments. Here, we study two commercial SGX applications. First, we investigate the SECRET network, an SGX-backed blockchain aiming to provide privacy-preserving smart contracts. Next, we also consider PowerDVD, a UHD Blu-Ray Digital Rights Management (DRM) software licensed to play discs on PCs. We show that in both cases vendors are unable to meet security goals originally envisioned for their products, presumably due to SGX’s long update timelines and the complexities of a manual update process. This in turn forces vendors to make difficult security/usability trade offs, resulting in security compromises.

Abstract Boomerang attacks are extensions of differential attacks that make it possible to combine two unrelated differential properties of the first and second part of a cryptosystem with probabilities p and q into a new differential-like property of the whole cryptosystem with probability $$p^2q^2$$ p 2 q 2 (since each one of the properties has to be satisfied twice). In this paper, we describe a new version of boomerang attacks which uses the counterintuitive idea of throwing out most of the data in order to force equalities between certain values on the ciphertext side. In certain cases, this creates a correlation between the four probabilistic events, which increases the probability of the combined property to $$p^2q$$ p 2 q and increases the signal-to-noise ratio of the resultant distinguisher. We call this variant a retracing boomerang attack since we make sure that the boomerang we throw follows the same path on its forward and backward directions. To demonstrate the power of the new technique, we apply it to the case of 5-round AES. This version of AES was repeatedly attacked by a large variety of techniques, but for twenty years its complexity had remained stuck at $$2^{32}$$ 2 32 . At Crypto’18, it was finally reduced to $$2^{24}$$ 2 24 (for full key recovery), and with our new technique, we can further reduce the complexity of full key recovery to the surprisingly low value of $$2^{16.5}$$ 2 16.5 (i.e., only 90, 000 encryption/decryption operations are required for a full key recovery). In addition to improving previous attacks, our new technique unveils a hidden relationship between boomerang attacks and two other cryptanalytic techniques, the yoyo game and the recently introduced mixture differentials.

SPHINCS+ [CCS ’19] is one of the selected post-quantum digital signature schemes of NIST’s post-quantum standardization process. The scheme is a hash-based signature and is considered one of the most secure and robust proposals. The proposal includes a fast (but larger) variant and a small (but slower) variant for each security level. The main problem that might hinder its adoption is its large signature size. Although SPHINCS+ supports a trade-off between signature size and the computational cost of signing, further reducing the signature size (below the small variants) results in a prohibitively high computational cost for the signer.This paper presents several novel methods for further compressing the signature size while requiring negligible added computational costs for the signer and further reducing verification time. Moreover, our approach enables a much more efficient trade-off curve between signature size and the computational costs of the signer. In many parameter settings, we achieve small signatures and faster running times simultaneously. For example, for 128-bit (classical) security, the small signature variant of SPHINCS+ is 7856 bytes long, while our variant is only 6304 bytes long: a compression of approximately 20% while still reducing the signer’s running time. However, other trade-offs that focus, e.g., on verification speed, are possible.The main insight behind our scheme is that there are predefined specific subsets of messages for which the WOTS+ and FORS signatures (that SPHINCS+ uses) can be compressed, and generation can be made faster while maintaining the same security guarantees. Although most messages will not come from these subsets, we can search for suitable hashed values to sign. We sign a hash of the message concatenated with a counter that was chosen such that the hashed value is in the subset. The resulting signature is both smaller and faster to sign and verify.Our schemes are simple to describe and implement. We provide an implementation, a theoretical analysis of speed and security, as well as benchmark results.

Abstract The Pilsung cipher is part of the North Korean Red Star operating system, which was leaked to the West in 2014. Initial analysis by Kryptos Logic reported a possibility of a class of weak keys due to the use of pseudo-random diffusion. Following this lead, we analyzed the cipher and identified a small class of such weak keys. We developed techniques for searching for a key that belongs to the class. After spending thousands of CPU hours, we found a supposedly weak key for a slightly weaker version of Pilsung, but the key did not behave as we expected. On further investigation we found out a crucial misunderstanding in a critical part of the cipher and that no such class of weak keys exists in Pilsung. Thus, this paper makes two main contributions to the art of cryptanalysis. First, it identifies and shows how to investigate a potential weakness in randomizing diffusion, which although does not exist in Pilsung, may affect future designs. Second, it highlights the need for early verification of results in order to identify errors before expending significant resources.

The discovery of the Spectre attack in 2018 has sent shockwaves through the computer industry, affecting processor vendors, OS providers, programming language developers, and more. Because web browsers execute untrusted code while potentially accessing sensitive information, they were considered prime targets for attacks and underwent significant changes to protect users from speculative execution attacks. In particular, the Google Chrome browser adopted the strict site isolation policy that prevents leakage by ensuring that content from different domains is not shared in the same address space. The perceived level of risk that Spectre poses to web browsers stands in stark contrast with the paucity of published demonstrations of the attack. Before mid-March 2021, there was no public proof-of-concept demonstrating leakage of information that is otherwise inaccessible to an attacker. Moreover, Google’s leaky.page, the only current proof-of-concept that can read such information, is severely restricted to only a subset of the address space and does not perform cross-website accesses. In this paper, we demonstrate that the absence of published attacks does not indicate that the risk is mitigated. We present Spook.js, a JavaScript-based Spectre attack that can read from the entire address space of the attacking webpage. We further investigate the implementation of strict site isolation in Chrome, and demonstrate limitations that allow Spook.js to read sensitive information from other webpages. We further show that Spectre adversely affects the security model of extensions in Chrome, demonstrating leaks of usernames and passwords from the LastPass password manager. Finally, we show that the problem also affects other Chromium-based browsers, such as Microsoft Edge and Brave.

A major research area in discrete geometry is to consider the best way to partition the $d$-dimensional Euclidean space $\mathbb{R}^d$ under various quality criteria. In this paper we introduce a new type of space partitioning that is motivated by the problem of rounding noisy measurements from the continuous space $\mathbb{R}^d$ to a discrete subset of representative values. Specifically, we study partitions of $\mathbb{R}^d$ into bounded-size tiles colored by one of $k$ colors, such that tiles of the same color have a distance of at least $t$ from each other. Such tilings allow for \emph{error-resilient} rounding, as two points of the same color and distance less than $t$ from each other are guaranteed to belong to the same tile, and thus, to be rounded to the same point. The main problem we study in this paper is characterizing the achievable tradeoffs between the number of colors $k$ and the distance $t$, for various dimensions $d$. On the qualitative side, we show that in $\mathbb{R}^d$, using $k=d+1$ colors is both sufficient and necessary to achieve $t>0$. On the quantitative side, we achieve numerous upper and lower bounds on $t$ as a function of $k$. In particular, for $d=3,4,8,24$, we obtain sharp asymptotic bounds on $t$, as $k \to \infty$. We obtain our results with a variety of techniques including isoperimetric inequalities, the Brunn-Minkowski theorem, sphere packing bounds, Bapat's connector-free lemma, and Čech cohomology.

Modern cryptography requires the ability to securely generate pseudorandom numbers. However, despite decades of work on side-channel attacks, there is little discussion of their application to pseudorandom number generators (PRGs). In this work we set out to address this gap, empirically evaluating the side-channel resistance of common PRG implementations.We find that hard-learned lessons about side-channel leakage from encryption primitives have not been applied to PRGs, at all abstraction levels. At the design level, the NIST-recommended CTR_DRBG does not have forward security if an attacker is able to compromise the state (e.g., via a side-channel). At the primitive level, popular implementations of CTR_DRBG such as OpenSSL's FIPS module and NetBSD's kernel use leaky T-table AES as their underlying cipher, enabling cache side-channel attacks. Finally, we find that many implementations make parameter choices that enable an attacker to fully exploit side-channels and recover secret keys from TLS connections.We empirically demonstrate our attack in two scenarios. First, we carry out a cache attack that recovers the private state from vulnerable CTR_DRBG implementations when the TLS client connects to an attacker-controlled server. We then subsequently use the recovered state to compute the client's long-term authentication keys, thereby allowing the attacker to impersonate the client. In the second scenario, we show that an attacker can exploit the high temporal resolution provided by Intel SGX to carry out a blind attack to recover CTR_DRBG's state within three AES encryptions, without viewing output, and thus decrypt passively collected TLS connections from the victim.

The WPA3 certification aims to secure home networks, while EAP-pwd is used by certain enterprise Wi-Fi networks to authenticate users. Both use the Dragonfly handshake to provide forward secrecy and resistance to dictionary attacks. In this paper, we systematically evaluate Dragonfly's security. First, we audit implementations, and present timing leaks and authentication bypasses in EAP-pwd and WPA3 daemons. We then study Dragonfly's design and discuss downgrade and denial-of-service attacks. Our next and main results are side-channel attacks against Dragonfly's password encoding method (e.g. hash-to-curve). We believe that these side-channel leaks are inherent to Dragonfly. For example, after our initial disclosure, patched software was still affected by a novel side-channel leak. We also analyze the complexity of using the leaked information to brute-force the password. For instance, brute-forcing a dictionary of size 1010requires less than $1 in Amazon EC2 instances. These results are also of general interest due to ongoing standardization efforts on Dragonfly as a TLS handshake, Password-Authenticated Key Exchanges (PAKEs), and hash-to-curve. Finally, we discuss backwards-compatible defenses, and propose protocol fixes that prevent attacks. Our work resulted in a new draft of the protocols incorporating our proposed design changes.

The problem of online checkpointing is a classical problem with numerous applications that has 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. Bringmann, Doerr, Neumann, and Sliacan 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 ln 4-o(1)≈ 1.39 for the sparse subset of k ’s, which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k . In this article, we solve the main problems left open in the above-mentioned paper by proving that ln 4 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. In the last part of the article, we describe some new applications of this online checkpointing problem.

Bad choices of passwords were and are a pervasive problem. Users choosing weak passwords do not only compromise themselves, but the whole ecosystem. E.g, common and default passwords in IoT devices were exploited by hackers to create botnets and mount severe attacks on large Internet services, such as the Mirai botnet DDoS attack. We present a method to help protect the Internet from such large scale attacks. Our method enables a server to identify popular passwords (heavy hitters), and publish a list of over-popular passwords that must be avoided. This filter ensures that no single password can be used to compromise a large percentage of the users. The list is dynamic and can be changed as new users are added or when current users change their passwords. We apply maliciously secure two-party computation and differential privacy to protect the users' password privacy. Our solution does not require extra hardware or cost, and is transparent to the user. Our private heavy hitters construction is secure even against a malicious coalition of devices which tries to manipulate the protocol to hide the popularity of some password that the attacker is exploiting. It also ensures differential privacy under continual observation of the blacklist as it changes over time. As a reality check we conducted three tests: computed the guarantees that the system provides wrt a few publicly available databases, ran full simulations on those databases, and implemented and analyzed a proof-of-concept on an IoT device. Our construction can also be used in other settings to privately learn heavy hitters in the presence of an active malicious adversary. E.g., learning the most popular sites accessed by the Tor network.

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). Due to its use of adaptive chosen ciphertext queries, the attack seems to be inherently sequential, 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 can 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.

Today, about 10% of TLS connections are still using CBC-mode cipher suites, despite a long history of attacks and the availability of better options (e.g. AES-GCM). In this work, we present three new types of attack against four popular fully patched implementations of TLS (Amazon's s2n, GnuTLS, mbed TLS and wolfSSL) which elected to use "pseudo constant time" countermeasures against the Lucky 13 attack on CBC-mode. Our attacks combine several variants of the PRIME+PROBE cache timing technique with a new extension of the original Lucky 13 attack. They apply in a cross-VM attack setting and are capable of recovering most of the plaintext whilst requiring only a moderate number of TLS connections. Along the way, we uncovered additional serious (but easy to patch) bugs in all four of the TLS implementations that we studied; in three cases, these bugs lead to Lucky 13 style attacks that can be mounted remotely with no access to a shared cache. Our work shows that adopting pseudo constant time countermeasures is not sufficient to attain real security in TLS implementations in CBC mode.

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'13 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's 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'13 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.

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 rapidly spread over large areas, 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. It enables the attacker to turn all the city lights on or off, to permanently brick them, or to 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 lamps 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.

In this paper we consider the security aspects of Internet of Things (IoT) devices, which bridge the physical and virtual worlds. We propose a new taxonomy of attacks, which classifies them into four broad categories. The most interesting category (which we call functionality extension attacks) uses the designed functionality of the IoT device to achieve a totally different effect. To demonstrate this type of attack, we consider the case of smart lights (whose original functionality is just to control the color and intensity of the lights in a particular room) and show how to use them to achieve unrelated effects. In the first attack, we use smart lights as a covert LIFI communication system to exfiltrate data from a highly secure (or even fully airgapped) office building. We implemented the attack and were able to read the leaked data from a distance of over 100 meters using only cheap and readily available equipment. In another attack, we showed that an attacker can strobe the lights at a frequency which may trigger seizures in people suffering from photosensitive epilepsy (in the same way that rapidly flashing video games can cause such seizures). In our experiments, we have tested both high-end and lower-end smart light systems, ranging from an expensive Philips HUE system to a cheap system manufactured by LimitlessLED. In addition, we consider other weaknesses of the systems we tested, and propose feasible remedies for the problems we found.