Beating Classical Impossibility of Position Verification

Chandran et al. (SIAM J. Comput. \u2714) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS \u2718) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors. Along the way, we develop the notion of 1-of-2 non-local soundness for a natural non-local game for 1-of-2 puzzles, first introduced by Radian and Sattath (AFT \u2719), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness (and therefore the adaptive hardcore bit property), which could be of independent interest

Statistically Sender-Private OT from LPN and Derandomization

We construct a two-message oblivious transfer protocol with statistical sender privacy (SSP OT) based on the Learning Parity with Noise (LPN) Assumption and a standard Nisan-Wigderson style derandomization assumption. Beyond being of interest on their own, SSP OT protocols have proven to be a powerful tool toward minimizing the round complexity in a wide array of cryptographic applications from proofs systems, through secure computation protocols, to hard problems in statistical zero knowledge (SZK). The protocol is plausibly post-quantum secure. The only other constructions with plausible post quantum security are based on the Learning with Errors (LWE) Assumption. Lacking the geometric structure of LWE, our construction and analysis rely on a different set of techniques. Technically, we first construct an SSP OT protocol in the common random string model from LPN alone, and then derandomize the common random string. Most of the technical difficulty lies in the first step. Here we prove a robustness property of the inner product randomness extractor to a certain type of linear splitting attacks. A caveat of our construction is that it relies on the so called low noise regime of LPN. This aligns with our current complexity-theoretic understanding of LPN, which only in the low noise regime is known to imply hardness in SZK

Publicly Verifiable Proofs from Blockchains

A proof system is publicly verifiable, if anyone, by looking at the transcript of the proof, can be convinced that the corresponding theorem is true. Public verifiability is important in many applications since it allows to compute a proof only once while convincing an unlimited number of verifiers. Popular interactive proof systems (e.g., $\Sigma$-protocols) protect the witness through various properties (e.g., witness indistinguishability (WI) and zero knowledge (ZK)) but typically they are not publicly verifiable since such proofs are convincing only for those verifiers who contributed to the transcripts of the proofs. The only known proof systems that are publicly verifiable rely on a non-interactive (NI) prover, through trust assumptions (e.g., NIZK in the CRS model), heuristic assumptions (e.g., NIZK in the random oracle model),specific number-theoretic assumptions on bilinear groups or relying on obfuscation assumptions (obtaining NIWI with no setups). In this work we construct publicly verifiable witness-indistinguishable proof systems from any $\Sigma$-protocol, based only on the existence of a very generic blockchain. The novelty of our approach is in enforcing a non-interactive verification (thus guaranteeing public verifiability) while allowing the prover to be interactive and talk to the blockchain (this allows us to circumvent the need of strong assumptions and setups). This opens interesting directions for the design of cryptographic protocols leveraging on blockchain technology

Exploring NIST LWC/PQC Synergy with R5Sneik: How SNEIK 1.1 Algorithms were Designed to Support Round5

Most NIST Post-Quantum Cryptography (PQC) candidate algorithms use symmetric primitives internally for various purposes such as ``seed expansion\u27\u27 and CPA to CCA transforms. Such auxiliary symmetric operations constituted only a fraction of total execution time of traditional RSA and ECC algorithms, but with faster lattice algorithms the impact of symmetric algorithm characteristics can be very significant. A choice to use a specific PQC algorithm implies that its internal symmetric components must also be implemented on all target platforms. This can be problematic for lightweight, embedded (IoT), and hardware implementations. It has been widely observed that current NIST-approved symmetric components (AES, GCM, SHA, SHAKE) form a major bottleneck on embedded and hardware implementation footprint and performance for many of the most efficient NIST PQC proposals. Meanwhile, a separate NIST effort is ongoing to standardize lightweight symmetric cryptography (LWC). Therefore it makes sense to explore which NIST LWC candidates are able to efficiently support internals of post-quantum asymmetric cryptography. We discuss R5Sneik, a variant of Round5 that internally uses SNEIK 1.1 permutation-based primitives instead of SHAKE and AES-GCM. The SNEIK family includes parameter selections specifically designed to support lattice cryptography. R5Sneik is up to 40\% faster than Round5 for some parameter sets on ARM Cortex M4, and has substantially smaller implementation footprint. We introduce the concept of a fast Entropy Distribution Function (EDF), a lightweight diffuser that we expect to have sufficient security properties for lattice seed expansion and many types of sampling, but not for plain encryption or hashing. The same SNEIK 1.1 permutation core (but with a different number of rounds) can also be used to replace AES-GCM as an AEAD when building lightweight cryptographic protocols, halving typical flash footprint on Cortex M4, while boosting performance

Two-Message Statistically Sender-Private OT from LWE

: We construct a two-message oblivious transfer (OT) protocol without setup that guarantees statistical privacy for the sender even against malicious receivers. Receiver privacy is game based and relies on the hardness of learning with errors (LWE). This flavor of OT has been a central building block for minimizing the round complexity of witness indistinguishable and zero knowledge proof systems and multi-party computation protocols, as well as for achieving circuit privacy for homomorphic encryption in the malicious setting. Prior to this work, all candidates in the literature from standard assumptions relied on number theoretic assumptions and were thus insecure in the post-quantum setting. This work provides the first (presumed) post-quantum secure candidate and thus allows to instantiate the aforementioned applications in a post-quantum secure manner. Technically, we rely on the transference principle: Either a lattice or its dual must have short vectors. Short vectors, in turn, can be translated to information loss in encryption. Thus encrypting one message with respect to the lattice and one with respect to its dual guarantees that at least one of them will be statistically hidden

Perfect Zero Knowledge: New Upperbounds and Relativized Separations

We investigate the complexity of problems that admit perfect zero-knowledge interactive protocols and establish new unconditional upper bounds and oracle separation results. We establish our results by investigating certain distribution testing problems: computational problems over high-dimensional distributions represented by succinct Boolean circuits. A relatively less-investigated complexity class SBP emerged as significant in this study. The main results we establish are: 1. A unconditional inclusion that NIPZK is in CoSBP. 2. Construction of a relativized world in which there is a distribution testing problem that lies in NIPZK but not in SBP, thus giving a relativized separation of NIPZK (and hence PZK) from SBP. 3. Construction of a relativized world in which there is a distribution testing problem that lies in PZK but not in CoSBP, thus giving a relativized separation of PZK from CoSBP. These results refine the landscape of perfect zero-knowledge classes in relation to traditional complexity classes

The Insecurity of Masked Comparisons: SCAs on ML-KEM’s FO-Transform

NIST has released the draft standard for ML-KEM, and ML-KEM is actively used in several widely-distributed applications. Thus, the wide-spread use of ML-KEM in the embedded worlds has to be expected in the near future. This makes security against side-channel attacks a pressing matter. Several side-channel attacks have previously been proposed, and one line of research have been attacks against the comparison step of the FO-transform. These attacks construct a decryption failure oracle using a side-channel. A recent work published at TCHES 2022 stresses the need for higher-order masked comparisons by presenting a horizontal attack and proposes a t-probing secure comparison operation. A subsequent work by D’Anvers, Van Beirendonck, and Verbauwhede improves upon the performance of several previous proposals. In this work, we show that the latter masked comparison suffers from weakness similar to those identified in the former. We first propose an approximate template attack that requires only a very low number of traces for profiling and has an exceptionally high noise tolerance. We show that the profiling phase is not necessary and can be replaced by a vertical analysis of the distribution of certain points of interest without knowledge of the targeted values. Finally, we explain how a horizontal attack may construct a decryption failure oracle from a single trace. We provide a leakage model of the targeted operations, which is based on the noisy Hamming weight model. Our evaluations are carried out on a physical device to stress the practicality of our attack. In addition, we simulate the attacks to determine the measurement noise levels that can be handled. We discuss the underlying causes for our attack, the difficulty of securing the Fujisaki-Okamoto transform in ML-KEM, and draw conclusion about the (in-)sufficiency of t-probing security in this context

Post-Quantum Authenticated Encryption against Chosen-Ciphertext Side-Channel Attacks

Over the last years, the side-channel analysis of Post-Quantum Cryptography (PQC) candidates in the NIST standardization initiative has received increased attention. In particular, it has been shown that some post-quantum Key Encapsulation Mechanisms (KEMs) are vulnerable to Chosen-Ciphertext Side-Channel Attacks (CC-SCA). These powerful attacks target the re-encryption step in the Fujisaki-Okamoto (FO) transform, which is commonly used to achieve CCA security in such schemes. To sufficiently protect PQC KEMs on embedded devices against such a powerful CC-SCA, masking at increasingly higher order is required, which induces a considerable overhead. In this work, we propose to use a conceptually simple construction, the ΕtS KEM, that alleviates the impact of CC-SCA. It uses the Encrypt-then-Sign (EtS) paradigm introduced by Zheng at ISW ’97 and further analyzed by An, Dodis and Rabin at EUROCRYPT ’02, and instantiates a postquantum authenticated KEM in the outsider-security model. While the construction is generic, we apply it to the CRYSTALS-Kyber KEM, relying on the CRYSTALSDilithium and Falcon signature schemes. We show that a CC-SCA-protected EtS KEM version of CRYSTALS-Kyber requires less than 10% of the cycles required for the CC-SCA-protected FO-based KEM, at the cost of additional data/communication overhead. We additionally show that the cost of protecting the EtS KEM against fault injection attacks, necessarily due to the added signature verification, remains negligible compared to the large cost of masking the FO transform at higher orders. Lastly, we discuss relevant embedded use cases for our EtS KEM construction

Two attacks on rank metric code-based schemes: RankSign and an Identity-Based-Encryption scheme

RankSign [GRSZ14a] is a code-based signature scheme proposed to the NIST competition for quantum-safe cryptography [AGHRZ17] and, moreover, is a fundamental building block of a new Identity-Based-Encryption (IBE) [GHPT17a]. This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits. Unfortunately we will show that all the parameters proposed for this scheme in [AGHRZ17] can be broken by an algebraic attack that exploits the fact that the augmented LRPC codes used in this scheme have very low weight codewords. Therefore, without RankSign the IBE cannot be instantiated at this time. As a second contribution we will show that the problem is deeper than finding a new signature in rank-based cryptography, we also found an attack on the generic problem upon which its security reduction relies. However, contrarily to the RankSign scheme, it seems that the parameters of the IBE scheme could be chosen in order to avoid our attack. Finally, we have also shown that if one replaces the rank metric in the [GHPT17a] IBE scheme by the Hamming metric, then a devastating attack can be found

Side-Channel Analysis of Lattice-Based Post-Quantum Cryptography: Exploiting Polynomial Multiplication

Polynomial multiplication algorithms such as Toom-Cook and the Number Theoretic Transform are fundamental building blocks for lattice-based post-quantum cryptography. In this work, we present correlation power analysis-based side-channel analysis methodologies targeting every polynomial multiplication strategy for all lattice-based post-quantum key encapsulation mechanisms in the final round of the NIST post-quantum standardization procedure. We perform practical experiments on real side-channel measurements demonstrating that our method allows to extract the secret key from all lattice-based post-quantum key encapsulation mechanisms. Our analysis demonstrates that the used polynomial multiplication strategy can significantly impact the time complexity of the attack