fuzzy extractor design

This paper addresses the fundamental question of whether cryptography can reduce algorithmic time complexity. We propose the first framework that systematically leverages cryptographic trapdoor mechanisms to accelerate deterministic computation. Our core method constructs a provably secure trapdoor matrix distribution: under standard assumptions (LWE or DDH), it is computationally indistinguishable from a random matrix distribution, yet a holder of the trapdoor key can compute an $n imes n$ matrix–vector product in nearly linear time $ ilde{O}(n)$, breaking the classical $Omega(n^2)$ lower bound. The construction supports both finite fields and the real domain, integrating randomness elimination and efficient key derivation techniques. In canonical applications such as dimensionality reduction, it achieves asymptotic speedup while preserving exact correctness. Both the formal security guarantees and the asymptotic acceleration are rigorously proven.

This work addresses the overreliance of conventional cryptography on one-way functions by proposing a generic algebraic-invariant-based cryptographic framework that replaces one-way functions with structural identities for key encapsulation and message authentication. Methodologically, it systematically extends the four-point algebraic invariant scheme, introducing novel symmetric constructions—including shift polynomial roots, discriminants, and multilinear identities—integrated with polynomial root encoding, functional equation constraints, and structural consistency verification. The framework achieves balanced guarantees in recoverability, integrity binding, and forgery resistance, attaining security strength comparable to the oscillation model while substantially reducing computational and storage overhead. Its primary contribution is establishing an “invariant-driven” paradigm for lightweight symmetric cryptography, yielding compact, provably secure, and structurally grounded cryptographic primitives tailored for resource-constrained environments.

Traditional symmetric encryption relies on algebraic hardness assumptions and lacks intrinsic structural self-verifiability. Method: This paper proposes a novel symmetric encryption scheme based on functional invariants of discrete oscillatory functions. It constructs a four-point algebraic identity with hidden parameters, encoding secret integers as structurally consistent functional invariants; security stems from the inherent geometric and algebraic consistency of the identity—not invertibility or computational assumptions. Contribution/Results: It introduces functional invariants as a new cryptographic primitive, enabling keyless ciphertext validity verification—a first for self-verifying encryption. The scheme features modular parameter design, an index recovery algorithm, hash-binding analysis, and a rigorously provable security framework. Experiments demonstrate lightweight implementation, forgery resistance, compactness, high efficiency, and strong verifiability.

Motivated by the urgent need for high-security, large-scale randomness extraction in cryptography and related fields, this paper proposes and implements an efficient Python-based randomness extractor library. Methodologically: (i) we design novel two-source, seeded, and deterministic extractor constructions whose theoretical parameters surpass those of existing schemes; (ii) we introduce the first number-theoretic transform (NTT)-based convolution implementation, eliminating floating-point rounding errors inherent in FFT-based approaches and thereby enhancing cryptographic robustness; (iii) the library supports automatic parameter computation and efficient processing of inputs up to 2⁴⁰ bits. Experimental evaluation demonstrates stable operation and throughput exceeding one trillion bits per second—significantly outperforming mainstream tools. The project is open-sourced, accompanied by comprehensive documentation, reproducible examples, and benchmark datasets.

This work addresses the communication complexity asymmetry in one-shot information-theoretic key agreement. It establishes a fundamental connection between bipartite graph mixing properties and extractable mutual information. Leveraging spectral graph theory, one-shot information theory, and cryptographic modeling, we derive the first rigorous correspondence: strong mixing—specifically, well-mixed bipartite graphs—implies mutual information non-extractability; that is, no protocol can reliably extract shared mutual information from endpoints of a random edge. This yields a tight lower bound showing that communication load must be inherently unbalanced—dominated by one party—in any one-shot key-agreement protocol. The result fundamentally explains the unavoidable severe communication asymmetry in the one-shot setting. Our framework introduces a novel graph-theoretic analytical paradigm for information-theoretic cryptography and provides a critical theoretical boundary on achievable communication efficiency.

Hardware benchmarking often suffers from limited verifiability, hindering reproducibility and auditability, and is vulnerable to silent computational errors. This work proposes the first end-to-end verifiable measurement logging system, which integrates transparent logs, probabilistic verification (e.g., Freivalds’ algorithm), and an adversarial-aware Fiat-Shamir challenge mechanism to bind all observations into an append-only hash chain via content-based hashing, enabling offline auditing. The system incorporates algebraic checks, floating-point error tolerance calibration, and di/dt power and thermal stress testing to effectively distinguish physical faults from malicious tampering. Experiments on Blackwell and Hopper GPUs demonstrate that the approach accurately characterizes residual noise floors across varying precisions and scales, detects no undetected silent errors, and thereby validates its effectiveness and robustness.

This work addresses the lack of generic, CCA-secure steganographic encryption schemes in the standard model, a gap that undermines the security of covert channels under key exposure. The authors formally define an adaptive key encapsulation mechanism (AKEM) and propose a generic construction based on recoverable randomness and injective KEMs, seamlessly integrating steganography into the KEM-DEM paradigm. Their scheme is the first to achieve sIND-CCA security for general-purpose steganographic encryption in the standard model, supporting both public-key and symmetric-key variants. Notably, it remains secure even against a “dictator” adversary who possesses the decapsulation key, thereby significantly enhancing the practicality and robustness of covert communication within real-world cryptographic infrastructures.

This work addresses the dual challenges of preserving computational privacy in untrusted cloud environments and enabling plausible deniability under coercion. To this end, it presents the first fully homomorphic computation framework with deniability support (PD-FHC). The framework embeds both genuine and multiple decoy computations into RGB images via steganography and processes them uniformly using Fredkin gate circuits. It formally defines medium-agnostic Deniable Computation Media (DCM) and Deniable Computation Schemes (DCS). Maintaining performance comparable to TFHE, the system demonstrates feasibility across image sizes from 128² to 512² and circuit complexities ranging from 5 to 289 gates, thereby achieving—for the first time—a fully homomorphic computation scheme that simultaneously guarantees computational privacy and provable plausible deniability.

In cryptography, short keys or certificates that cannot be generated or verified within bounded time fail to meet protocols’ demands for resource predictability and immediate verifiability. This work introduces the notion of witness complexity, denoted γ(x), defined as the minimal runtime required on a universal Turing machine to produce a near-shortest description of a string x, thereby capturing the practical feasibility of succinct representations. Distinct from both Shannon entropy and Kolmogorov complexity, γ(x) is intrinsically linked to the P≠NP conjecture and polynomial-time tractability. We establish that γ(x) is invariant up to polynomial factors, provide conditional separation results, derive a biconditional characterization of P=NP, and demonstrate polynomial-time solvability for structured families of NP problems.