One-Hot Conversion: Towards Faster Table-based A2B Conversion

Arithmetic to Boolean masking (A2B) conversion is a crucial technique in the masking of lattice-based post-quantum cryptography. It is also a crucial part of building a masked comparison which is one of the hardest to mask building blocks for active secure lattice-based encryption. We first present a new method, called one-hot conversion, to efficiently convert from higher-order arithmetic masking to Boolean masking using a variant of the higher-order table-based conversion of Coron et al. Secondly, we specialize our method to perform arithmetic to 1-bit Boolean functions. Our one-hot function can be applied to masking lattice-based encryption building blocks such as masked comparison or to determine the most significant bit of an arithmetically masked variable. In our benchmarks, a speedup of 40 to 66 times is achieved over state-of-the-art table-based A2B conversions, bringing table-based A2B conversions in the performance range of the Boolean circuit-based A2B conversions by only a slowdown of factor 1.2 to 2

Multitarget decryption failure attacks and their application to Saber and Kyber

Many lattice-based encryption schemes are subject to a very small probability of decryption failures. It has been shown that an adversary can efficiently recover the secret key using a number of ciphertexts that cause such a decryption failure. In PKC~2019, D\u27Anvers~et~al. introduced `failure boosting\u27, a technique to speed up the search for decryption failures. In this work we first improve the state-of-the-art multitarget failure boosting attacks. We then improve the cost calculation of failure boosting and extend the applicability of these calculations to permit cost calculations of real-world schemes. Using our newly developed methodologies we determine the multitarget decryption failure attack cost for all parameter sets of Saber and Kyber, showing among others that the quantum security of Saber can theoretically be reduced from 172 bits to 145 bits in specific circumstances. We then discuss the applicability of decryption failure attack in real-world scenarios, showing that an attack might not be practical to execute

Error Term Checking: Towards Chosen Ciphertext Security without Re-encryption

Chosen ciphertext security for lattice based encryption schemes is generally achieved through a generic transformation such as the Fujisaki-Okamoto transformation. This method requires full re-encryption of the plaintext during decapsulation, which typically dominates the cost of the latter procedure. In this work we show that it is possible to develop alternative transformations specifically designed for lattice based encryption schemes. We propose two novel chosen ciphertext transformations, $\mathtt{ETC1}$ and $\mathtt{ETC2}$, in which re-encryption is replaced by checking the error term of the input ciphertext. We show that our new ciphertext validity check can be securely applied to lattice based encryption schemes under specific conditions. For the NIST post-quantum standardization candidate Threebears we show a speed-up for decapsulation of up to $37.4\%$. Moreover, as our method only changes the validation check during decapsulation, it is fully backwards compatible with existing implementations of the Fujisaki-Okamoto transformation

On the impact of decryption failures on the security of LWE/LWR based schemes

In this paper we investigate the impact of decryption failures on the chosen-ciphertext security of (Ring/Module)-Learning With Errors and (Ring/Module)-Learning with Rounding based primitives. Our analysis is split in three parts: First, we use a technique to increase the failure rate of these schemes called failure boosting. Based on this technique we investigate the minimal effort for an adversary to obtain a failure in 3 cases: when he has access to a quantum computer, when he mounts a multi-target attack and when he can only perform a limited number of oracle queries. Secondly, we examine the amount of information that an adversary can derive from failing ciphertexts. Finally, these techniques are combined in an attack on (Ring/Module)-LWE and (Ring/Module)-LWR based schemes with decryption failures. We provide both a theoretical analysis as well as an implementation to calculate the security impact and show that an attacker can significantly reduce the security of (Ring/Module)-LWE/LWR based schemes that have a relatively high failure rate. However, for the candidates of the NIST post-quantum standardization process that we assessed, the number of required oracle queries is above practical limits due to their conservative parameter choices

The impact of error dependencies on Ring/Mod-LWE/LWR based schemes

Current estimation techniques for the probability of decryption failures in Ring/Mod-LWE/LWR based schemes assume independence of the failures in individual bits of the transmitted message to calculate the full failure rate of the scheme. In this paper we disprove this assumption both theoretically and practically for schemes based on Ring/Mod-Learning with Errors/Rounding. We provide a method to estimate the decryption failure probability, taking into account the bit failure dependency. We show that the independence assumption is suitable for schemes without error correction, but that it might lead to underestimating the failure probability of algorithms using error correcting codes. In the worst case, for LAC-128, the failure rate is $2^{48}$ times bigger than estimated under the assumption of independence. This higher-than-expected failure rate could lead to more efficient cryptanalysis of the scheme through decryption failure attacks

Revisiting Higher-Order Masked Comparison for Lattice-Based Cryptography: Algorithms and Bit-sliced Implementations

Masked comparison is one of the most expensive operations in side-channel secure implementations of lattice-based post-quantum cryptography, especially for higher masking orders. First, we introduce two new masked comparison algorithms, which improve the arithmetic comparison of D\u27Anvers et al. and the hybrid comparison method of Coron et al. respectively. We then look into implementation-specific optimizations, and show that small specific adaptations can have a significant impact on the overall performance. Finally, we implement various state-of-the-art comparison algorithms and benchmark them on the same platform (ARM-Cortex M4) to allow a fair comparison between them. We improve on the arithmetic comparison of D\u27Anvers et al. with a factor $\approx 20\%$ by using Galois Field multiplications and the hybrid comparison of Coron et al. with a factor $\approx 25\%$ by streamlining the design. Our implementation-specific improvements allow a speedup of a straightforward comparison implementation of $\approx 33\%$. We discuss the differences between the various algorithms and provide the implementations and a testing framework to ease future research

Side-channel and Fault-injection attacks over Lattice-based Post-quantum Schemes (Kyber, Dilithium): Survey and New Results

In this work, we present a systematic study of Side-Channel Attacks (SCA) and Fault Injection Attacks (FIA) on structured lattice-based schemes, with a focus on Kyber Key Encapsulation Mechanism (KEM) and Dilithium signature scheme, which are leading candidates in the NIST standardization process for Post-Quantum Cryptography (PQC). Through our study, we attempt to understand the underlying similarities and differences between the existing attacks, while classifying them into different categories. Given the wide variety of reported attacks, simultaneous protection against all the attacks requires to implement customized protections/countermeasures for both Kyber and Dilithium. We therefore present a range of customized countermeasures, capable of providing defenses/mitigations against existing SCA/FIA, and incorporate several SCA and FIA countermeasures within a single design of Kyber and Dilithium. Among the several countermeasures discussed in this work, we present novel countermeasures that offer simultaneous protection against several SCA and FIA-based chosen-ciphertext attacks for Kyber KEM. We implement the presented countermeasures within the well-known pqm4 library for the ARM Cortex-M4 based microcontroller. Our performance evaluation reveals that the presented custom countermeasures incur reasonable performance overheads, on the ARM Cortex-M4 microcontroller. We therefore believe our work argues for the usage of custom countermeasures within real-world implementations of lattice-based schemes, either in a standalone manner or as reinforcements to generic countermeasures such as masking

Timing attacks on Error Correcting Codes in Post-Quantum Schemes

While error correcting codes (ECC) have the potential to significantly reduce the failure probability of post-quantum schemes, they add an extra ECC decoding step to the algorithm. Even though this additional step does not compute directly on the secret key, it is susceptible to side-channel attacks. We show that if no precaution is taken, it is possible to use timing information to distinguish between ciphertexts that result in an error before decoding and ciphertexts that do not contain errors, due to the variable execution time of the ECC decoding algorithm. We demonstrate that this information can be used to break the IND-CCA security of post-quantum secure schemes by presenting an attack on two round 1 candidates to the NIST Post-Quantum Standardization Process: the Ring-LWE scheme LAC and the Mersenne prime scheme Ramstake. This attack recovers the full secret key using a limited number of timed decryption queries and is implemented on the reference and the optimized implementations of both submissions. It is able to retrieve LAC\u27s secret key for all security levels in under 2 minutes using less than $2^{16}$ decryption queries and Ramstake\u27s secret key in under 2 minutes using approximately $2400$ decryption queries. The attack generalizes to other lattice-based schemes with ECC in which any side-channel information about the presence of errors is leaked during decoding

FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) is a technique that allows computation on encrypted data. It has the potential to drastically change privacy considerations in the cloud, but high computational and memory overheads are preventing its broad adoption. TFHE is a promising Torus-based FHE scheme that heavily relies on bootstrapping, the noise-removal tool invoked after each encrypted logical/arithmetical operation. We present FPT, a Fixed-Point FPGA accelerator for TFHE bootstrapping. FPT is the first hardware accelerator to heavily exploit the inherent noise present in FHE calculations. Instead of double or single-precision floating-point arithmetic, it implements TFHE bootstrapping entirely with approximate fixed-point arithmetic. Using an in-depth analysis of noise propagation in bootstrapping FFT computations, FPT is able to use noise-trimmed fixed-point representations that are up to 50% smaller than prior implementations that prefer floating-point or integer FFTs. FPT is built as a streaming processor inspired by traditional streaming DSPs: it instantiates directly cascaded high-throughput computational stages, with minimal control logic and routing networks. We explore different throughput-balanced compositions of streaming kernels with a user-configurable streaming width in order to construct a full bootstrapping pipeline. Our proposed approach allows 100% utilization of arithmetic units and requires only a small bootstrapping key cache, enabling an entirely compute-bound bootstrapping throughput of 1 BS / 35$\mu$s. This is in stark contrast to the established classical CPU approach to FHE bootstrapping acceleration, which is typically constrained by memory and bandwidth. FPT is fully implemented and evaluated as a bootstrapping FPGA kernel for an Alveo U280 datacenter accelerator card. FPT achieves two to three orders of magnitude higher bootstrapping throughput than existing CPU-based implementations, and 2.5$\times$ higher throughput compared to recent ASIC emulation experiments

Defeating Low-Cost Countermeasures against Side-Channel Attacks in Lattice-based Encryption - A Case Study on Crystals-Kyber

In an effort to circumvent the high cost of standard countermeasures against side-channel attacks in post-quantum cryptography, some works have developed low-cost detection-based countermeasures. These countermeasures try to detect maliciously generated input ciphertexts and react to them by discarding the ciphertext or secret key. In this work, we take a look at two previously proposed low-cost countermeasures: the ciphertext sanity check and the decapsulation failure check, and demonstrate successful attacks on these schemes. We show that the first countermeasure can be broken with little to no overhead, while the second countermeasure requires a more elaborate attack strategy that relies on valid chosen ciphertexts. Thus, in this work, we propose the first chosen-ciphertext based side-channel attack that only relies on valid ciphertexts for key recovery. As part of this attack, a third contribution of our paper is an improved solver that retrieves the secret key from linear inequalities constructed using side-channel leakage from the decryption procedure. Our solver is an improvement over the state-of-the-art Belief Propagation solvers by Pessl and Prokop, and later Delvaux. Our method is simpler, easier to understand and has lower computational complexity, while needing less than half the inequalities compared to previous methods