Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $SZK$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $BPP^{SZK}$. This poses a barrier for building advanced primitives from code-based assumptions, as the only known such assumption is Learning Parity with Noise (LPN) with an extremely low noise rate $\frac{\log^2 n}{n}$, which is broken in quasi-polynomial time.
In this work, we propose a new code-based assumption: Dense-Sparse LPN, that falls in the complexity class $BPP^{SZK}$ and is conjectured to be secure against subexponential time adversaries. Our assumption is a variant of LPN that is inspired by McEliece's cryptosystem and random $k\mbox{-}$XOR in average-case complexity.
We leverage our assumption to build lossy trapdoor functions (Peikert-Waters STOC 08). This gives the first post-quantum alternative to the lattice-based construction in the original paper. Lossy trapdoor functions, being a fundamental cryptographic tool, are known to enable a broad spectrum of both lossy and non-lossy cryptographic primitives; our construction thus implies these primitives in a generic manner. In particular, we achieve collision-resistant hash functions with plausible subexponential security, improving over a prior construction from LPN with noise rate $\frac{\log^2 n}{n}$ that is only quasi-polynomially secure.
Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through intensive Monte Carlo simulations. However, several applications, like code-based cryptography, need guaranteed low values of the error rate, which are infeasible to assess through simulations, thus requiring the development of theoretical models for the error rate of these codes under iterative decoding. Some models of this type already exist, but become computat…
In line with advances in recent years about realizing cryptographic functionalities in an information-theoretically secure way from physical phenomena and laws, we propose here to obtain useful tasks from the sole assumption of limited free energy. Specifically, based on that assumption -- resulting in a setting loosely related to Maurer's bounded-storage model -- we derive protocols for unconditional proofs-of-thermodynamical-work, secret sharing of free energy, unforgeable money, and proofs-of-position. While our schemes can be considered classical and not quantum per se, they are resistant …
Starting from the one-way group action framework of Brassard and Yung (Crypto '90), we revisit building cryptography based on group actions. Several previous candidates for one-way group actions no longer stand, due to progress both on classical algorithms (e.g., graph isomorphism) and quantum algorithms (e.g., discrete logarithm). We propose the general linear group action on tensors as a new candidate to build cryptography based on group actions. Recent works (Futorny--Grochow--Sergeichuk, Lin. Alg. Appl., 2019) suggest that the underlying algorithmic problem, the tensor isomorphism problem,…
We present the Foundational Cryptography Framework (FCF) for developing and checking complete proofs of security for cryptographic schemes within a proof assistant. This is a general-purpose framework that is capable of modeling and reasoning about a wide range of cryptographic schemes, security definitions, and assumptions. Security is proven in the computational model, and the proof provides concrete bounds as well as asymptotic conclusions. FCF provides a language for probabilistic programs, a theory that is used to reason about programs, and a library of tactics and definitions that are us…
The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to extend the maximum reconciliation distance between the two remote parties. Key reconciliation over multiple dimensions has been shown to further improve the error-correction performance of multi-edge LDPC …
Post-Quantum Cryptography from Quantum Stabilizer Decoding
Massachusetts Institute of Technology（麻省理工学院）；Boston University（波士顿大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；California Institute of Technology（加州理工学院）
Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable,…
We initiate the study of Access Control Encryption (ACE), a novel cryptographic primitive that allows fine-grained access control, by giving different rights to different users not only in terms of which messages they are allowed to receive, but also which messages they are allowed to send. Classical examples of security policies for information flow are the well known Bell-Lapadula [BL73] or Biba [Bib75] model: in a nutshell, the Bell-Lapadula model assigns roles to every user in the system (e.g., public, secret and top-secret). A users' role specifies which messages the user is allowed to re…
From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；NTT Social Informatics Laboratories（NTT社会信息学实验室）；NTT Research Center for Theoretical Quantum Information（NTT理论量子信息中心）
Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasona…
The impossibility of creating perfect identical copies of unknown quantum systems is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. This limitation imposed by quantum mechanics, famously known as the no-cloning theorem, has played a central role in quantum cryptography as a key component in the security of quantum protocols. In this thesis, we look at Unclonability in a broader context in physics and computer science and more specifically through the lens of cryptography, learnability and hardware assumptions. We introduce new notio…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable t…
