Efficient implementation of a CCA2-secure variant of McEliece using generalized Srivastava codes

International audienceIn this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device

Automatic Search of Bit-Based Division Property for ARX Ciphers and Word-Based Division Property

Division property is a generalized integral property proposed by Todo at Eurocrypt 2015. Previous tools for automatic searching are mainly based on the Mixed Integer Linear Programming (MILP) method and trace the division property propagation at the bit level. In this paper, we propose automatic tools to detect ARX ciphers\u27 division property at the bit level and some specific ciphers\u27 division property at the word level. For ARX ciphers, we construct the automatic searching tool relying on Boolean Satisfiability Problem (SAT) instead of MILP, since SAT method is more suitable in the search of ARX ciphers\u27 differential/linear characteristics. The propagation of division property is translated into a system of logical equations in Conjunctive Normal Form (CNF). Some logical equations can be dynamically adjusted according to different initial division properties and stopping rule, while the others corresponding to r-round propagations remain the same. Moreover, our approach can efficiently identify some optimized distinguishers with lower data complexity. As a result, we obtain a 17-round distinguisher for SHACAL-2, which gains four more rounds than previous work, and an 8-round distinguisher for LEA, which covers one more round than the former one. For word-based division property, we develop the automatic search based on Satisfiability Modulo Theories (SMT), which is a generalization of SAT. We model division property propagations of basic operations and S-boxes by logical formulas, and turn the searching problem into an SMT problem. With some available solvers, we achieve some new distinguishers. For CLEFIA, 10-round distinguishers are obtained, which cover one more round than the previous work. For the internal block cipher of Whirlpool, the data complexities of 4/5-round distinguishers are improved. For Rijndael-192 and Rijndael-256, 6-round distinguishers are presented, which attain two more rounds than the published ones. Besides, the integral attacks for CLEFIA are improved by one round with the newly obtained distinguishers

EnCounter: On Breaking the Nonce Barrier in Differential Fault Analysis with a Case-Study on PAEQ

This work exploits internal differentials within a cipher in the context of Differential Fault Analysis (DFA). This in turn overcomes the nonce barrier which acts as a natural counter-measure against DFA. We introduce the concept of internal differential fault analysis which requires only one faulty ciphertext. In particular, the analysis is applicable to parallelizable ciphers that use the counter-mode. As a proof of concept we develop an internal differential fault attack called EnCounter on PAEQ which is an AES based parallelizable authenticated cipher presently in the second round of on-going CAESAR competition. The attack is able to uniquely retrieve the key of three versions of full-round PAEQ of key-sizes 64, 80 and 128 bits with complexities of about $2^{16}$, $2^{16}$ and $2^{50}$ respectively. Finally, this work addresses in detail the instance of fault analysis with varying amounts of partial state information and also presents the first analysis of PAEQ

A Transform for NIZK Almost as Efficient and General as the Fiat-Shamir Transform Without Programmable Random Oracles

The Fiat-Shamir (FS) transform is a popular technique for obtaining practical zero-knowledge argument systems. The FS transform uses a hash function to generate, without any further overhead, non-interactive zero-knowledge (NIZK) argument systems from public-coin honest-verifier zero-knowledge (public-coin HVZK) proof systems. In the proof of zero knowledge, the hash function is modeled as a programmable random oracle (PRO). In TCC 2015, Lindell embarked on the challenging task of obtaining a similar transform with improved heuristic security. Lindell showed that, for several interesting and practical languages, there exists an efficient transform in the non-programmable random oracle (NPRO) model that also uses a common reference string (CRS). A major contribution of Lindell’s transform is that zero knowledge is proved without random oracles and this is an important step towards achieving efficient NIZK arguments in the CRS model without random oracles. In this work, we analyze the efficiency and generality of Lindell’s transform and notice a significant gap when compared with the FS transform. We then propose a new transform that aims at filling this gap. Indeed our transform is almost as efficient as the FS transform and can be applied to a broad class of public-coin HVZK proof systems. Our transform requires a CRS and an NPRO in the proof of soundness, similarly to Lindell’s transform

Set It and Forget It! Turnkey ECC for Instant Integration

Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations. While there are a handful of outliers where all these concepts join and land in real-world deployments, these are generally on a case-by-case basis: e.g.\ a library may feature such X25519 or P-256 code, but not for all curves. In this work, we propose and implement a methodology that fully automates the implementation, testing, and integration of ECC stacks with the above properties. We demonstrate the flexibility and applicability of our methodology by seamlessly integrating into three real-world projects: OpenSSL, Mozilla's NSS, and the GOST OpenSSL Engine, achieving roughly 9.5x, 4.5x, 13.3x, and 3.7x speedup on any given curve for key generation, key agreement, signing, and verifying, respectively. Furthermore, we showcase the efficacy of our testing methodology by uncovering flaws and vulnerabilities in OpenSSL, and a specification-level vulnerability in a Russian standard. Our work bridges the gap between significant applied cryptography research results and deployed software, fully automating the process

Efficient 4-way Vectorizations of the Montgomery Ladder

We propose two new algorithms for 4-way vectorization of the well known Montgomery ladder over elliptic curves of Montgomery form. The first algorithm is suitable for variable base scalar multiplication. In comparison to the previous work by Hisil et al. (2020), it eliminates a number of non-multiplication operations at the cost of a single multiplication by a curve constant. Implementation results show this trade-off to be advantageous. The second algorithm is suitable for fixed base scalar multiplication and provides clear speed improvement over a previous vectorization strategy due to Costigan and Schwabe (2009). The well known Montgomery curves Curve25519 and Curve448 are part of the TLS protocol, version~1.3. For these two curves, we provide constant time assembly implementations of the new algorithms. Additionally, for the algorithm of Hisil et al. (2020), we provide improved implementations for Curve25519 and new implementation for Curve448. Timings results on the Haswell and Skylake processors indicate that in practice the new algorithms are to be preferred over previous methods for scalar multiplication on these curves

Folding Alternant and Goppa Codes with Non-Trivial Automorphism Groups

The main practical limitation of the McEliece public-key encryption scheme is probably the size of its key. A famous trend to overcome this issue is to focus on subclasses of alternant/Goppa codes with a non trivial automorphism group. Such codes display then symmetries allowing compact parity-check or generator matrices. For instance, a key-reduction is obtained by taking quasi-cyclic (QC) or quasi-dyadic (QD) alternant/Goppa codes. We show that the use of such symmetric alternant/Goppa codes in cryptography introduces a fundamental weakness. It is indeed possible to reduce the key-recovery on the original symmetric public-code to the key-recovery on a (much) smaller code that has not anymore symmetries. This result is obtained thanks to a new operation on codes called folding that exploits the knowledge of the automorphism group. This operation consists in adding the coordinates of codewords which belong to the same orbit under the action of the automorphism group. The advantage is twofold: the reduction factor can be as large as the size of the orbits, and it preserves a fundamental property: folding the dual of an alternant (resp. Goppa) code provides the dual of an alternant (resp. Goppa) code. A key point is to show that all the existing constructions of alternant/Goppa codes with symmetries follow a common principal of taking codes whose support is globally invariant under the action of affine transformations (by building upon prior works of T. Berger and A. D{\"{u}}r). This enables not only to present a unified view but also to generalize the construction of QC, QD and even quasi-monoidic (QM) Goppa codes. All in all, our results can be harnessed to boost up any key-recovery attack on McEliece systems based on symmetric alternant or Goppa codes, and in particular algebraic attacks.Comment: 19 page

On the susceptibility of Texas Instruments SimpleLink platform microcontrollers to non-invasive physical attacks

We investigate the susceptibility of the Texas Instruments SimpleLink platform microcontrollers to non-invasive physical attacks. We extracted the ROM bootloader of these microcontrollers and then analysed it using static analysis augmented with information obtained through emulation. We demonstrate a voltage fault injection attack targeting the ROM bootloader that allows to enable debug access on a previously locked microcontroller within seconds. Information provided by Texas Instruments reveals that one of our voltage fault injection attacks abuses functionality that is left over from the integrated circuit manufacturing process. The demonstrated physical attack allows an adversary to extract the firmware (i.e. intellectual property) and to bypass secure boot. Additionally, we mount side-channel attacks and differential fault analysis attacks on the hardware AES co-processor. To demonstrate the practical applicability of these attacks we extract the firmware from a Tesla Model 3 key fob. This paper describes a case study covering Texas Instruments SimpleLink microcontrollers. Similar attack techniques can be, and have been, applied to microcontrollers from other manufacturers. The goal of our work is to document our analysis methodology and to ensure that system designers are aware of these vulnerabilities. They will then be able to take these into account during the product design phase. All identified vulnerabilities were responsibly disclosed