International Association
for Cryptologic Research

This paper describes an ECC implementation computing the X25519 keyexchange protocol on the Arm Cortex-M4 microcontroller. For providing protections against various side-channel and fault attacks we first review known attacks and countermeasures, then we provide software implementations that come with extensive mitigations, and finally we present a preliminary side-channel evaluation. To our best knowledge, this is the first public software claiming affordable protection against multiple classes of attacks that are motivated by distinct real-world application scenarios. We distinguish between X25519 with ephemeral keys and X25519 with static keys and show that the overhead to our baseline unprotected implementation is about 37% and 243%, respectively. While this might seem to be a high price to pay for security, we also show that even our (most protected) static implementation is at least as efficient as widely-deployed ECC cryptographic libraries, which offer much less protection.

We present efficient and compact hardware/software co-design implementations of the Supersingular Isogeny Key Encapsulation (SIKE) protocol on field-programmable gate arrays (FPGAs). In order to be better equipped for different post-quantum scenarios, our architectures were designed to feature high-flexibility by covering all the currently available parameter sets and with support for primes up to 1016 bits. In particular, any of the current SIKE parameters equivalent to the post-quantum security of AES-128/192/256 and SHA3-256 can be selected and run on-the-fly. This security scalability property, together with the small footprint and efficiency of our architectures, makes them ideal for embedded applications in a post-quantum world. In addition, the proposed implementations exhibit regular, constant-time execution, which provides protection against timing and simple sidechannel attacks. Our results demonstrate that supersingular isogeny-based primitives such as SIDH and SIKE can indeed be deployed for embedded applications featuring competitive performance. For example, our smallest architecture based on a 128-bit MAC unit takes only 3415 slices, 21 BRAMs and 57 DSPs on a Virtex 7 690T and can perform key generation, encapsulation and decapsulation in 14.4, 24.4 and 26.0 milliseconds for SIKEp434 and in 52.3, 86.4 and 93.2 milliseconds for SIKEp751, respectively.

In this work we present a duplex-based authenticated encryption scheme Friet based on a new permutation called Friet-P. We designed Friet-P with a novel approach for cryptographic permutations and block ciphers that takes fault-attack resistance into account and that we introduce in this paper. In this method, we build a permutation f_C to be embedded in a larger one f. First, we define f as a sequence of steps that all abide a chosen error-correcting code C, i.e., that map C-codewords to C-codewords. Then, we embed f_C in f by first encoding its input to an element of C, applying f and then decoding back from C. This last step detects a fault when the output of f is not in C. We motivate the design of the permutation we use in Friet and report on performance in soft- and hardware. We evaluate the fault-detection capabilities of the software and simulated hardware implementations with attacks. Finally, we perform a leakage evaluation. Our code is available at https://github.com/thisimon/Friet.git.

To mitigate side-channel attacks, real-world implementations of public-key cryptosystems adopt state-of-the-art countermeasures based on randomization of the private or ephemeral keys. Usually, for each private key operation, a “scalar blinding” is performed using 32 or 64 randomly generated bits. Nevertheless, horizontal attacks based on a single trace still pose serious threats to protected ECC or RSA implementations. If the secrets learned through a single-trace attack contain too many wrong (or noisy) bits, the cryptanalysis methods for recovering remaining bits become impractical due to time and computational constraints. This paper proposes a deep learning-based framework to iteratively correct partially correct private keys resulting from a clustering-based horizontal attack. By testing the trained network on scalar multiplication (or exponentiation) traces, we demonstrate that a deep neural network can significantly reduce the number of wrong bits from randomized scalars (or exponents).When a simple horizontal attack can recover around 52% of attacked multiple private key bits, the proposed iterative framework improves the private key accuracy to above 90% on average and to 100% for at least one of the attacked keys. Our attack model remains fully unsupervised and excludes the need to know where the error or noisy bits are located in each separate randomized private key.

The Residue Number System (RNS) arithmetic is gaining grounds in public key cryptography, because it offers fast, efficient and secure implementations over large prime fields or rings of integers. In this paper, we propose a generic, thorough and analytic evaluation approach for protected scalar multiplication implementations with RNS and traditional Side Channel Attack (SCA) countermeasures in an effort to assess the SCA resistance of RNS. This paper constitutes the first robust evaluation of RNS software for Elliptic Curve Cryptography against electromagnetic (EM) side-channel attacks. Four different countermeasures, namely scalar and point randomization, random base permutations and random moduli operation sequence, are implemented and evaluated using the Test Vector Leakage Assessment (TVLA) and template attacks. More specifically, variations of RNS-based Montgomery Powering Ladder scalar multiplication algorithms are evaluated on an ARM Cortex A8 processor using an EM probe for acquisition of the traces. We show experimentally and theoretically that new bounds should be put forward when TVLA evaluations on public key algorithms are performed. On the security of RNS, our data and location dependent template attacks show that even protected implementations are vulnerable to these attacks. A combination of RNS-based countermeasures is the best way to protect against side-channel leakage.

Near-field microprobes have the capability to isolate small regions of a chip surface and enable precise measurements with high spatial resolution. Being able to distinguish the activity of small regions has given rise to the location-based side-channel attacks, which exploit the spatial dependencies of cryptographic algorithms in order to recover the secret key. Given the fairly uncharted nature of such leakages, this work revisits the location side-channel to broaden our modeling and exploitation capabilities. Our contribution is threefold. First, we provide a simple spatial model that partially captures the effect of location-based leakages. We use the newly established model to simulate the leakage of different scenarios/countermeasures and follow an information-theoretic approach to evaluate the security level achieved in every case. Second, we perform the first successful location-based attack on the SRAM of a modern ARM Cortex-M4 chip, using standard techniques such as difference of means and multivariate template attacks. Third, we put forward neural networks as classifiers that exploit the location side-channel and showcase their effectiveness on ARM Cortex-M4, especially in the context of single-shot attacks and small memory regions. Template attacks and neural network classifiers are able to reach high spacial accuracy, distinguishing between 2 SRAM regions of 128 bytes each with 100% success rate and distinguishing even between 256 SRAM byte-regions with 32% success rate. Such improved exploitation capabilities revitalize the interest for location vulnerabilities on various implementations, ranging from RSA/ECC with large memory footprint, to lookup-table-based AES with smaller memory usage.