Saber:module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM

© Springer International Publishing AG, part of Springer Nature 2018. In this paper, we introduce Saber, a package of cryptographic primitives whose security relies on the hardness of the Module Learning With Rounding problem (Mod-LWR). We first describe a secure Diffie-Hellman type key exchangeprotocol, which is then transformed into an IND-CPA encryption scheme and finally into an IND-CCA secure key encapsulation mechanism using a post-quantum version of the Fujisaki-Okamoto transform. The design goals of this package were simplicity, efficiency and flexibility resulting in the following choices: all integer moduli are powers of 2 avoiding modular reduction and rejection sampling entirely; the use of LWR halves the amount of randomness required compared to LWE-based schemes and reduces bandwidth; the module structure provides flexibility by reusing one core component for multiple security levels. A constant-time AVX2 optimized software implementation of the KEM with parameters providing more than 128 bits of post-quantum security, requires only 101K, 125K and 129K cycles for key generation, encapsulation and decapsulation respectively on a Dell laptop with an Intel i7-Haswell processor

Looking at the NIST Lightweight Candidates from a Masking Point-of-View

Cryptographic primitives have been designed to be secure against mathematical attacks in a black-box model. Such primitives can be implemented in a way that they are also secure against physical attacks, in a grey-box model. One of the most popular techniques for this purpose is masking. The increased security always comes with a high price tag in terms of implementation cost. In this work, we look at how the traditional design principles of symmetric primitives can be at odds with the optimization of the implementations and how they can evolve to be more suitable for embedded systems. In particular, we take a comparative look at the round 2 candidates of the NIST lightweight competition and their implementation properties in the world of masking

A Generic Construction of an Anonymous Reputation System and Instantiations from Lattices

With an anonymous reputation system one can realize the process of rating sellers anonymously in an online shop. While raters can stay anonymous, sellers still have the guarantee that they can be only be reviewed by raters who bought their product.We present the first generic construction of a reputation system from basic building blocks, namely digital signatures, encryption schemes, non-interactive zero-knowledge proofs, and linking indistinguishable tags. We then show the security of the reputation system in a strong security model. Among others, we instantiate the generic construction with building blocks based on lattice problems, leading to the first module lattice-based reputation system

Fully Collision-Resistant Chameleon-Hashes from Simpler and Post-Quantum Assumptions

Chameleon-hashes are collision-resistant hash-functions parametrized by a public key. If the corresponding secret key is known, arbitrary collisions for the hash can be found. Recently, Derler et al. (PKC \u2720) introduced the notion of fully collision-resistant chameleon-hashes. Full collision-resistance requires the intractability of finding collisions, even with full-adaptive access to a collision-finding oracle. Their construction combines simulation-sound extractable (SSE) NIZKs with perfectly correct IND-CPA secure public-key encryption (PKE) schemes. We show that, instead of perfectly correct PKE, non-interactive commitment schemes are sufficient. For the first time, this gives rise to efficient instantiations from plausible post-quantum assumptions and thus candidates of chameleon-hashes with strong collision-resistance guarantees and long-term security guarantees. On the more theoretical side, our results relax the requirement to not being dependent on public-key encryption

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

LAC: Practical Ring-LWE Based Public-Key Encryption with Byte-Level Modulus

We propose an instantiation of public key encryption scheme based on the ring learning with error problem, where the modulus is at a byte level and the noise is at a bit level, achieving one of the most compact lattice based schemes in the literature. The main technical challenges are a) the decryption error rates increases and needs to be handled elegantly, and b) we cannot use the Number Theoretic Transform (NTT) technique to speed up the implementation. We overcome those limitations with some customized parameter sets and heavy error correction codes. We give a treatment of the concrete security of the proposed parameter set, with regards to the recent advance in lattice based cryptanalysis. We present an optimized implementation taking advantage of our byte level modulus and bit level noise. In addition, a byte level modulus allows for high parallelization and the bit level noise avoids the modulus reduction during multiplication. Our result shows that \LAC~is more compact than most of the existing (Ring-)LWE based solutions, while achieving a similar level of efficiency, compared with popular solutions in this domain, such as Kyber

Fully Invisible Protean Signatures Schemes

Protean Signatures (PS), recently introduced by Krenn et al. (CANS \u2718), allow a semi-trusted third party, named the sanitizer, to modify a signed message in a controlled way. The sanitizer can edit signer-chosen parts to arbitrary bitstrings, while the sanitizer can also redact admissible parts, which are also chosen by the signer. Thus, PSs generalize both redactable signature (RSS) and sanitizable signature (SSS) into a single notion. However, the current definition of invisibility does not prohibit that an outsider can decide which parts of a message are redactable - only which parts can be edited are hidden. This negatively impacts on the privacy guarantees provided by the state-of-the-art definition. We extend PSs to be fully invisible. This strengthened notion guarantees that an outsider can neither decide which parts of a message can be edited nor which parts can be redacted. To achieve our goal, we introduce the new notions of Invisible RSSs and Invisible Non-Accountable SSSs (SSS\u27), along with a consolidated framework for aggregate signatures. Using those building blocks, our resulting construction is significantly more efficient than the original scheme by Krenn et al., which we demonstrate in a prototypical implementation

Policy-Based Sanitizable Signatures

Sanitizable signatures are a variant of signatures which allow a single, and signer-defined, sanitizer to modify signed messages in a controlled way without invalidating the respective signature. They turned out to be a versatile primitive, proven by different variants and extensions, e.g., allowing multiple sanitizers or adding new sanitizers one-by-one. However, existing constructions are very restricted regarding their flexibility in specifying potential sanitizers. We propose a different and more powerful approach: Instead of using sanitizers\u27 public keys directly, we assign attributes to them. Sanitizing is then based on policies, i.e., access structures defined over attributes. A sanitizer can sanitize, if, and only if, it holds a secret key to attributes satisfying the policy associated to a signature, while offering full-scale accountability

Improved Circuit Synthesis with Amortized Bootstrapping for FHEW-like Schemes

In recent years, the research community has made great progress in improving techniques for privacy-preserving computation such as fully homomorphic encryption (FHE). Despite the progress, there remain open challenges, mostly in the areas of performance and usability, to further advance the adoption of these technologies. This work provides multiple contributions to improve the current state-of-the-art in both areas. More specifically, we significantly simplify the bootstrapping idea by Carpov, Izabach`ene, and Mollimard [1] for Boolean-based FHE schemes such as FHEW or TFHE, making the concept usable in practice. Based on our simplifications, we provide an easy-to-use interface for amortized bootstrapping implementing our improvements in the open-source library FHE-Deck and provide new parameter sets for multi-bit encryptions with state-of-the-art security. We build a toolset that compiles high-level code such as C++ to code that executes operations on encrypted data. For this toolset, we propose the first non-trivial FHE-specific optimizations in synthesizing privacy-preserving circuits from high-level code, namely look-up table (LUT) grouping and adder substitution. Using LUT grouping, we reduce the number of bootstrapping required by almost 35 % on average, while for adder substitution, we reduce the number of required bootstrapping by up to 80 % for certain use cases. Overall, the execution time is up to 3.8× faster using our optimizations compared to previous state-of-the-art circuit synthesis

Do Not Bound to a Single Position: Near-Optimal Multi-Positional Mismatch Attacks Against Kyber and Saber

Misuse resilience is an important security criterion in the evaluation of the NIST Post-quantum cryptography standardization process. In this paper, we propose new key mismatch attacks against Kyber and Saber, NIST\u27s selected scheme for encryption and one of the finalists in the third round of the NIST competition, respectively. Our novel idea is to recover partial information of multiple secret entries in each mismatch oracle call. These multi-positional attacks greatly reduce the expected number of oracle calls needed to fully recover the secret key. They also have significance in side-channel analysis. From the perspective of lower bounds, our new attacks falsify the Huffman bounds proposed in [Qin et al. ASIACRYPT 2021], where a one- positional mismatch adversary is assumed. Our new attacks can be bounded by the Shannon lower bounds, i.e., the entropy of the distribution generating each secret coefficient times the number of secret entries. We call the new attacks near-optimal since their query complexities are close to the Shannon lower bounds