Decryption errors play a crucial role in the security of KEMs based on Fujisaki-Okamoto because the concrete security guarantees provided by this transformation directly depend on the probability of such an event being bounded by a small real number. In this paper we present an approach to formally verify the claims of statistical probabilistic bounds for incorrect decryption in lattice-based KEM constructions. Our main motivating example is the PKE encryption scheme underlying ML-KEM. We formalize the statistical event that is used in the literature to heuristically approximate ML-KEM decryption errors and confirm that the upper bounds given in the literature for this event are correct. We consider FrodoKEM as an additional example, to demonstrate the wider applicability of the approach and the verification of a correctness bound without heuristic approximations. We also discuss other (non-approximate) approaches to bounding the probability of ML-KEM decryption.

Spectre attacks void the guarantees of constant-time cryptographic code by leaking secrets during speculative execution. Recent research shows that such code can be protected from Spectre-v1 attacks with minimal overhead, but leaves open the question of protecting against other Spectre variants. In this work, we design, validate, implement, and verify a new approach to protect cryptographic code against all known classes of Spectre attacks, in particular Spectre-RSB. Our approach combines a new value-dependent information-flow type system that ensures that no secrets leak even under speculative execution and a compiler transformation that enables it on the generated low-level code. We first prove the soundness of the type system and the correctness of the compiler transformation using the Coq proof assistant. We then implement our approach in the Jasmin framework for high-assurance cryptography and demonstrate that the overhead incurred by all Spectre protections is below 2% for most cryptographic primitives and reaches only about 5-7% for the more complex post-quantum key-encapsulation mechanism Kyber.

It is a widely accepted standard practice to implement cryptographic software so that secret inputs do not influence the cycle count. Software following this paradigm is often referred to as “constant-time” software and typically involves following three rules: 1) never branch on a secret-dependent condition, 2) never access memory at a secret-dependent location, and 3) avoid variable-time arithmetic operations on secret data. The third rule requires knowledge about such variable-time arithmetic instructions, or vice versa, which operations are safe to use on secret inputs. For a long time, this knowledge was based on either documentation or microbenchmarks, but critically, there were never any guarantees for future microarchitectures. This changed with the introduction of the data-operand-independent-timing (DOIT) mode on Intel CPUs and, to some extent, the data-independent-timing (DIT) mode on Arm CPUs. Both Intel and Arm document a subset of their respective instruction sets that are intended to leak no information about their inputs through timing, even on future microarchitectures if the CPU is set to run in a dedicated DOIT (or DIT) mode. In this paper, we present a principled solution that leverages DOIT to enable cryptographic software that is future-proof constant-time, in the sense that it ensures that only instructions from the DOIT subset are used to operate on secret data, even during speculative execution after a mispredicted branch or function return location. For this solution, we build on top of existing security type systems in the Jasmin framework for high-assurance cryptography. We then use our solution to evaluate the extent to which existing cryptographic software built to be “constant-time” is already secure in this stricter paradigm implied by DOIT and what the performance impact is to move from constant-time to future-proof constant-time.

We propose a hybrid formal verification approach that combines high-level deductive reasoning and circuit-based reasoning and apply it to highly optimized cryptographic assembly code. Our approach permits scaling up formal verification in two complementary directions: 1) it reduces the proof effort required for low-level functions where the computation logics are obfuscated by the intricate use of architecture-specific instructions and 2) it permits amortizing the effort of proving one implementation by using equivalence checking to propagate the guarantees to other implementations of the same computation using different optimizations or targeting different architectures. We demonstrate our approach via an extension to the EasyCrypt proof assistant and by revisiting formally verified implementations of ML-KEM in Jasmin. As a result, we obtain the first formally verified implementation of ML-KEM that offers performance comparable to the fastest non-verified implementation in x86-64 architectures.

In this paper we revisit the problem of erasing sensitive data from memory and registers during return from a cryptographic routine. While the problem and related attacker model is fairly easy to phrase, it turns out to be surprisingly hard to guarantee security in this model when implementing cryptography in common languages such as C/C++ or Rust. We revisit the issues surrounding zeroization and then present a principled solution in the sense that it guarantees that sensitive data is erased and it clearly defines when this happens. We implement our solution as extension to the formally verified Jasmin compiler and extend the correctness proof of the compiler to cover zeroization. We show that the approach seamlessly integrates with state-of-the-art protections against microarchitectural attacks by integrating zeroization into Libjade, a cryptographic library written in Jasmin with systematic protections against timing and Spectre-v1 attacks. We present benchmarks showing that in many cases the overhead of zeroization is barely measurable and that it stays below 2% except for highly optimized symmetric crypto routines on short inputs.

We present a formally verified proof of the correctness and IND-CCA security of ML-KEM, the Kyber-based Key Encapsulation Mechanism (KEM) undergoing standardization by NIST. The proof is machine-checked in EasyCrypt and it includes: 1) A formalization of the correctness (decryption failure probability) and IND-CPA security of the Kyber base public-key encryption scheme, following Bos et al. at Euro S&P 2018; 2) A formalization of the relevant variant of the Fujisaki-Okamoto transform in the Random Oracle Model (ROM), which follows closely (but not exactly) Hofheinz, Hovelmanns and Kiltz at TCC 2017; 3) A proof that the IND-CCA security of the ML-KEM specification and its correctness as a KEM follows from the previous results; 4) Two formally verified implementations of ML-KEM written in Jasmin that are provably constant-time, functionally equivalent to the ML-KEM specification and, for this reason, inherit the provable security guarantees established in the previous points. The top-level theorems give self-contained concrete bounds for the correctness and security of ML-KEM down to (a variant of) Module-LWE. We discuss how they are built modularly by leveraging various EasyCrypt features.

In this paper we present the first formally verified implementations of Kyber and, to the best of our knowledge, the first such implementations of any post-quantum cryptosystem. We give a (readable) formal specification of Kyber in the EasyCrypt proof assistant, which is syntactically very close to the pseudocode description of the scheme as given in the most recent version of the NIST submission. We present high-assurance open-source implementations of Kyber written in the Jasmin language, along with machine-checked proofs that they are functionally correct with respect to the EasyCrypt specification. We describe a number of improvements to the EasyCrypt and Jasmin frameworks that were needed for this implementation and verification effort, and we present detailed benchmarks of our implementations, showing that our code achieves performance close to existing hand-optimized implementations in C and assembly.

Cryptography secures our online interactions, transactions, and trust. To achieve this goal, not only do the cryptographic primitives and protocols need to be secure in theory, they also need to be securely implemented by cryptographic library developers in practice. However, implementing cryptographic algorithms securely is challenging, even for skilled professionals, which can lead to vulnerable implementations, especially to side-channel attacks. For timing attacks, a severe class of side-channel attacks, there exist a multitude of tools that are supposed to help cryptographic library developers assess whether their code is vulnerable to timing attacks. Previous work has established that despite an interest in writing constant-time code, cryptographic library developers do not routinely use these tools due to their general lack of usability. However, the precise factors affecting the usability of these tools remain unexplored. While many of the tools are developed in an academic context, we believe that it is worth exploring the factors that contribute to or hinder their effective use by cryptographic library developers [61]. To assess what contributes to and detracts from usability of tools that verify constant-timeness (CT), we conducted a two-part usability study with 24 (post) graduate student participants on 6 tools across diverse tasks that approximate real-world use cases for cryptographic library developers. We find that all studied tools are affected by similar usability issues to varying degrees, with no tool excelling in usability, and usability issues preventing their effective use. Based on our results, we recommend that effective tools for verifying CT need usable documentation, simple installation, easy to adapt examples, clear output corresponding to CT violations, and minimal noninvasive code markup. We contribute first steps to achieving these with limited academic resources, with our documentation, examples, and installation scripts(1).

X-Wing is a hybrid key-encapsulation mechanism based on X25519 and ML-KEM-768. It is designed to be the sensible choice for most applications. The concrete choice of X25519 and ML-KEM-768 allows X-Wing to achieve improved efficiency compared to using a generic KEM combiner. In this paper, we introduce the X-Wing hybrid KEM construction and provide a proof of security. We show (1) that X-Wing is a classically IND-CCA secure KEM if the strong Diffie-Hellman assumption holds in the X25519 nominal group, and (2) that X-Wing is a post-quantum IND-CCA secure KEM if ML-KEM-768 is itself an IND-CCA secure KEM and SHA3-256 is secure when used as a pseudorandom function. The first result is proved in the ROM, whereas the second one holds in the standard model. Loosely speaking, this means X-Wing is secure if either X25519 or ML-KEM-768 is secure. We stress that these security guarantees and optimizations are only possible due to the concrete choices that were made, and it may not apply in the general case.

How will future microarchitectures impact the security of existing cryptographic implementations? As we cannot keep reducing the size of transistors, chip vendors have started developing new microarchitectural optimizations to speed up computation. A recent study (Sanchez Vicarte et al., ISCA 2021) suggests that these optimizations might open the Pandora's box of microarchitectural attacks. However, there is little guidance on how to evaluate the security impact of future optimization proposals. To help chip vendors explore the impact of microarchitectural optimizations on cryptographic implementations, we develop (i) an expressive domain-specific language, called LmSpec, that allows them to specify the leakage model for the given optimization and (ii) a testing framework, called LmTest, to automatically detect leaks under the specified leakage model within the given implementation. Using this framework, we conduct an empirical study of 18 proposed microarchitectural optimizations on 25 implementations of eight cryptographic primitives in five popular libraries. We find that every implementation would contain secret-dependent leaks, sometimes sufficient to recover a victim's secret key, if these optimizations were realized. Ironically, some leaks are possible only because of coding idioms used to prevent leaks under the standard constant-time model.

The advent of quantum computers has sparked significant interest in post-quantum cryptographic schemes, as a replacement for currently used cryptographic primitives. In this context, lattice-based cryptography has emerged as the leading paradigm to build post-quantum cryptography. However, all existing viable replacements of the classical Diffie-Hellman key exchange require additional rounds of interactions, thus failing to achieve all the benefits of this protocol. Although earlier work has shown that lattice-based Non-Interactive Key Exchange (NIKE) is theoretically possible, it has been considered too inefficient for real-life applications. In this work, we challenge this folklore belief and provide the first evidence against it. We construct an efficient lattice-based NIKE whose security is based on the standard module learning with errors (M-LWE) problem in the quantum random oracle model. Our scheme is obtained in two steps: (i) A passively-secure construction that achieves a strong notion of correctness, coupled with (ii) a generic compiler that turns any such scheme into an actively-secure one. To substantiate our efficiency claim, we provide an optimised implementation of our passively-secure construction in Rust and Jasmin. Our implementation demonstrates the scheme's applicability to real-world scenarios, yielding public keys of approximately 220 KBs. Moreover, the computation of shared keys takes fewer than 12 million cycles on an Intel Skylake CPU, offering a post-quantum security level exceeding 120 bits.

In this work, we assess the real-world practicality of CSIDH, an isogeny-based non-interactive key exchange. We provide the first thorough assessment of the practicality of CSIDH in higher parameter sizes for conservative estimates of quantum security, and with protection against physical attacks. This requires a three-fold analysis of CSIDH. First, we describe two approaches to efficient high-security CSIDH implementations, based on SQALE and CTIDH. Second, we optimize such high-security implementations, on a high level by improving several subroutines, and on a low level by improving the finite field arithmetic. Third, we benchmark the performance of high-security CSIDH. As a stand-alone primitive, our implementations outperform previous results by a factor up to 2.53×. As a real-world use case considering network protocols, we use CSIDH in TLS variants that allow early authentication through a NIKE. Although our instantiations of CSIDH have smaller communication requirements than post-quantum KEM and signature schemes, even our highly-optimized implementations result in too-large handshake latency (tens of seconds), showing that CSIDH is only practical in niche cases.

The key generation of the lattice-based key-encapsulation mechanism CRYSTALS-Kyber (or short, just Kyber) involves a rejection-sampling routine to produce coefficients modulo q = 3329 that look uniformly random. The input to this rejection sampling is output of the SHAKE-128 extendable output function (XOF). If this XOF is modelled as a random oracle with infinite output length, it is easy to see that Kyber terminates with probability 1; also, in this model, for any upper bound on the running time, the probability of termination is strictly smaller than 1. In this short note we show that an (unconditional) upper bound for the running time for Kyber exists. Computing a tight upper bound, however, is (likely to be) infeasible. We remark that the result has no real practical value, except that it may be useful for computer-assisted reasoning about Kyber using tools that require a simple proof of termination.

The current gold standard of cryptographic software is to write efficient libraries with systematic protections against timing attacks. In order to meet this goal, cryptographic engineers increasingly use high-assurance cryptography tools. These tools guide programmers and provide rigorous guarantees that can be verified independently by library users. However, high-assurance tools reason about overly simple execution models that elide transient execution leakage. Thus, implementations validated by high-assurance cryptography tools remain potentially vulnerable to transient execution attacks such as Spectre or Meltdown. Moreover, proposed countermeasures are not used in practice due to performance overhead. We propose, analyze, implement and evaluate an approach for writing efficient cryptographic implementations that are protected against Spectre v1 attacks. Our approach ensures speculative constant-time, an information flow property which guarantees that programs are protected against Spectre v1. Speculative constant-time is enforced by means of a (valuedependent) information flow type system. The type system tracks security levels depending on whether execution is misspeculating. We implement our approach in the Jasmin framework for high-assurance cryptography, and use it for protecting all implementations of an experimental cryptographic library that includes highly optimized implementations of symmetric primitives, of elliptic-curve cryptography, and of Kyber, a latticebased KEM recently selected by NIST for standardization. The performance impact of our protections is very low; for example, less than 1% for Kyber and essentially zero for X25519.

The advent of quantum computers has generated a wave of interest for post-quantum cryptographic schemes, as a replacement for currently used cryptographic primitives. In this context, lattice-based cryptography has emerged as the leading paradigm to build post-quantum cryptography. However, all viable replacements of the classical Diffie-Hellman key exchange require additional rounds of interactions, thus failing to achieve all the benefits of this protocol. Although earlier work has shown that lattice-based Non-Interactive Key Exchange (NIKE) is theoretically possible, it has been considered too inefficient for real-life applications. Inthiswork, we provide the first evidence against this folklore belief. We construct a practical lattice-based NIKE whose security is based on the standard module learning with errors (M-LWE) problem in the quantum random oracle model. Our scheme is obtained in two steps: (i) A passively-secure construction that achieves a strong notion of correctness, coupled with (ii) a generic compiler that turns any such scheme into an actively-secure one. To substantiate our efficiency claim, we present an optimised implementation of our construction in Rust and Jasmin, demonstrating its applicability to real-world scenarios. For this we obtain public keys of approximately 220KBs and the computation of shared keys takes than 12 million cycles on an Intel Skylake CPU at a post-quantum security level of more than 120 bits.

A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a corresponding set of independently chosen receiver public keys. The resulting ''multi-recipient ciphertext'' can be then be reduced (by any 3rd party) to a shorter, receiver specific, ''invidual ciphertext.'' Finally, to recover the i-th message in the batch from their indvidual ciphertext the i-th receiver only needs their own decryption key. A special case of mmPKE is multi-recipient PKE (mPKE) where all receivers are sent the same message. By treating (m)mPKE and their KEM counterparts as a stand-alone primitives we allow for more efficient constructions than trivially composing individual PKE/KEM instances. This is especially valuable in the post-quantum setting, where PKE/KEM ciphertexts and public keys tend to be far larger than their classic counterparts. In this work we describe a collection of new results around mKEMs and (m)mPKEs. We provide both classic and post-quantum proofs for all results. Our results are geared towards practical constructions and applications (for example in the domain of PQ-secure group messaging). Concretely, our results include a new non-adaptive to adaptive compiler for CPA-secure mKEMs resulting in public keys roughly half the size of the previous state-of-the-art [Hashimoto et al., CCS'21]. We also prove their FO transform for mKEMs to be secure in the presence of adaptive corruptions in the quantum random oracle model. Further, we provide the first mKEM combiner. Finally, we give two mmPKE constructions. The first is an arbitrary message-length black-box construction from an mKEM (e.g. one produced by combining a PQ with a classic mKEM). The second is optimized for short messages (which is suited for several recent mmPKE applications) and achieves hybrid PQ/classic security more directly. When encrypting n short messages at 256-bits of security the mmPKE ciphertext are 144n bytes shorter than the generic construction. Finally, we provide an optimized implementation of the (CCA secure) mKEM construction based on the NIST PQC winner Kyber and report benchmarks showing a significant speedup for encapsulation and up to 79% savings in ciphertext size compared to a naive solution.