In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case NP search problem of finding a solution to a system of (underdetermined) constant degree multivariate equations over the finite field \(\mathbb{F}_2\) drawn from a specified distribution. In particular, for any \(d \ge 2\), we design a distribution of degree up to \(d\) polynomials \(\{p_i(x_1,\ldots,x_n)\}_{i\in[m]}\) for \(m \lt n\) over \(\mathbb{F}_2\) for which we show that there is an expected polynomial-time quantum algorithm that provably simultaneously solves \(\{p_i(x_1,\ldots,x_n) = y_i\}_{i\in[m]}\) for a random vector \((y_1,\ldots,y_m)\). On the other hand, while solutions exist with high probability, we conjecture that for constant \(d \gt 2\), it is classically hard to find one based on a thorough review of existing classical cryptanalysis. Our work thus posits that degree three functions are enough to instantiate the random oracle to obtain non-relativized quantum advantage.

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto’2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Suppose there exists any set of constants \(\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)\) such that the sub-exponential security of the following assumptions hold: — the Learning With Errors ( \(\mathsf {LWE}\) ) assumption with subexponential modulus-to-noise ratio \(2^{k^\epsilon }\) and noises of magnitude polynomial in k , where k is the dimension of the \(\mathsf {LWE}\) secret, — the Learning Parity with Noise ( \(\mathsf {LPN}\) ) assumption over general prime fields \(\mathbb {Z}_p\) with polynomially many \(\mathsf {LPN}\) samples and error rate \(1/\ell ^\delta\) , where \(\ell\) is the dimension of the \(\mathsf {LPN}\) secret, — the existence of a Boolean Pseudo-Random Generator ( \(\mathsf {PRG}\) ) in \(\mathsf {NC}^0\) with stretch \(n^{1+\tau }\) , where n is the length of the \(\mathsf {PRG}\) seed, — the Decision Linear ( \(\mathsf {DLIN}\) ) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists. Furthermore, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.

There is a growing body of work on proving hardness results for average-case estimation problems by bounding the low-degree advantage (LDA) — a quantitative estimate of the closeness of low-degree moments — between a null distribution and a related planted distribution. Such hardness results are now ubiquitous not only for foundational average-case problems but also central questions in statistics and cryptography. This line of work is supported by the low-degree conjecture of Hopkins [1], which postulates that a vanishing degree-D LDA implies the absence of any noise-tolerant distinguishing algorithm with runtime ${n^{\tilde {\mathcal{O}}(D)}}$ whenever 1) the null distribution is product on ${\{ 0,1\} ^{\binom{n}{k}}}$, and 2) the planted distribution is permutation invariant, that is, invariant under any relabeling [n] → [n].In this paper, we disprove this conjecture. Specifically, we show that for any fixed ε > 0 and k ⩾ 2, there is a permutation-invariant planted distribution on ${\{ 0,1\} ^{\binom{n}{k}}}$ that has a vanishing degree-n1−O(ε)LDA with respect to the uniform distribution on ${\{ 0,1\} ^{\binom{n}{k}}}$, yet the corresponding ε-noisy distinguishing problem can be solved in ${n^{O\left( {{{\log }^{1/(k - 1)}}(n)} \right)}}$ time. Our construction relies on algorithms for list-decoding for noisy polynomial interpolation in the high-error regime.We also give another construction of a pair of planted and (non-product) null distributions on ℝn×nwith a vanishing nΩ(1)-degree LDA while the largest eigenvalue serves as an efficient noise-tolerant distinguisher.Our results suggest that while a vanishing LDA may still be interpreted as evidence of hardness, developing a theory of average-case complexity based on such heuristics requires a more careful approach.

Abstract 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 $$\mathcal {SZK}$$ SZK (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $$\mathcal {BPP}^{\mathcal {SZK}}$$ BPP SZK . This poses a barrier for building advanced cryptography from code-based assumptions such as Learning Parity with Noise (LPN), as LPN is only known to be in $$\mathcal {BPP}^{\mathcal {SZK}}$$ BPP SZK under an extremely low noise rate $$\frac{\log ^2 n}{n}$$ log 2 n n , for which it 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 $$\mathcal {BPP}^{\mathcal {SZK}}$$ BPP SZK and we conjecture to be secure against subexponential time adversaries. Our assumption is a variant of LPN that is inspired by McEliece’s cryptosystem and the random $$k\text{- }$$ k - XOR problem in average-case complexity. Roughly, the assumption states that $$\begin{aligned}({\textbf{T}}\, {\textbf{M}}, {\textbf{s}} \,{\textbf{T}}\, {\textbf{M}} + {\textbf{e}}) \quad \text {is indistinguishable from}\quad ({\textbf{T}} \,{\textbf{M}}, {\textbf{u}}),\end{aligned}$$ ( T M , s T M + e ) is indistinguishable from ( T M , u ) , for a random (dense) matrix $${\textbf{T}}$$ T , random sparse matrix $${\textbf{M}}$$ M , and sparse noise vector $${\textbf{e}}$$ e drawn from the Bernoulli distribution with inverse polynomial noise rate. 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 $$\frac{\log ^2 n}{n}$$ log 2 n n

The random oracle model (ROM) allows us to opti-mistically reason about security properties of cryptographic hash functions, and has been hugely influential in designing practical cryptosystems. But it is overly optimistic against non-uniform adversaries, and often suggests security properties and security levels unachievable by any real hash function. To reconcile with this discrepancy, Unruh [CRYPTO '07] proposed the auxiliary-input random oracle model (AI-ROM), where a non-uniform attacker additionally gets a bounded amount of advice about the random oracle. Proving security in the AI-ROM is often much more difficult, but a series of works starting with Unruh provided useful technical tools to do so. Although these tools lead to good results in the information-theoretic setting, they are unsatisfactory in the computational setting, where the random oracle is used alongside other computational hardness assumptions. At the most basic level, we did not even know whether it is possible to efficiently simulate random oracle queries given auxiliary input, which has remained as an explicit open problem since the work of Unruh. In this work, we resolve the above open problem and show how to efficiently simulate auxiliary-input random oracles. Moreover, the simulation has low concrete overhead, leading to small losses in exact security. We use it to prove the security of a broad class of computational schemes in the AI-ROM, including the first non-interactive zero-knowledge (NIZK) scheme in the AI-ROM. As a tool of independent interest, we develop a new notion of ultra-secure pseudorandom functions with fast RAM evaluation, which can achieve$2^{\lambda}$security while having sublinear$\mathrm{o}(\lambda)$evaluation time.

Recently, the question of adversarially robust streaming, where the stream is allowed to depend on the randomness of the streaming algorithm, has gained a lot of attention. In this work, we consider a strong white-box adversarial model (Ajtai et al. PODS 2022), in which the adversary has access to all past random coins and the parameters used by the streaming algorithm. We focus on the sparse recovery problem and extend our result to other tasks such as distinct element estimation and low-rank approximation of matrices and tensors. The main drawback of previous work is that it requires a *random oracle*, which is especially problematic in the streaming model since the amount of randomness is counted in the space complexity of a streaming algorithm. Also, the previous work suffers from large update time. We construct a near-optimal solution for the sparse recovery problem in white-box adversarial streams, based on the subexponentially secure Learning with Errors assumption. Importantly, our solution does not require a random oracle and has a polylogarithmic per item processing time. We also give results in a related white-box adversarially robust distributed model. Our constructions are based on homomorphic encryption schemes satisfying very mild structural properties that are currently satisfied by most known schemes.

Mass customization and shorter manufacturing cycles are becoming more important among small and medium-sized companies. However, classical industrial robots struggle to cope with product variation and dynamic environments. In this paper, we present CoBT, a collaborative programming by demonstration framework for generating reactive and modular behavior trees. CoBT relies on a single demonstration and a combination of data-driven machine learning methods with logic-based declarative learning to learn a task, thus eliminating the need for programming expertise or long development times. The proposed framework is experimentally validated on 7 manipulation tasks and we show that CoBT achieves ≈ 93% success rate overall with an average of 7.5s programming time. We conduct a pilot study with non-expert users to provide feedback regarding the usability of CoBT. More videos and generated behavior trees are available at: https://github.com/jainaayush2006/CoBT.git.

Reinforcement Learning (RL) has progressed from simple control tasks to complex real-world challenges with large state spaces. While RL excels in these tasks, training time remains a limitation. Reward shaping is a popular solution, but existing methods often rely on value functions, which face scalability issues. This paper presents a novel safety-oriented reward-shaping framework inspired by barrier functions, offering simplicity and ease of implementation across various environments and tasks. To evaluate the effectiveness of the proposed reward formulations, we conduct simulation experiments on CartPole, Ant, and Humanoid environments, along with real-world deployment on the Unitree Go1 quadruped robot. Our results demonstrate that our method leads to 1.4-2.8 times faster convergence and as low as 50-60% actuation effort compared to the vanilla reward. In a sim-to-real experiment with the Go1 robot, we demonstrated better control and dynamics of the bot with our reward framework. We have open-sourced our code at https://github.com/Safe-RL-IISc/barrier_shaping.

Passwords remain fundamental to user authentication, including handheld devices, wearables, personal computers, and network devices. Privacy concerns have led to the development of new password guidelines and alternatives, yet these have not seen widespread adoption among users. Increasing skepticism towards the service providers has made users reluctant to share sensitive information, including passwords. While current security protocols ensure data protection in transit, assurances regarding the security and privacy of data at rest are often assumed without verification. Traditional best practices for password storage involve hashing, which still requires the original password to be shared as plaintext or as a hash. Each of these methods has its vulnerabilities. For instance, an adversary can sniff network packets to capture the original password or the hash value, potentially compromising the authentication system. To address these issues, we propose a framework for password-based authentication using graph isomorphism as a zero-knowledge proof technique. This framework aims to replace conventional authentication methods and enhance password privacy. The results demonstrate the proposed framework's effectiveness in ensuring secure and private password authentication.

Hyperspectral datasets obtained from a specific sensor can experience changes in their characteristics due to environmental noise and variations in illumination. Consequently, a segmentation model trained on one dataset may struggle to accurately predict labels and detect objects on a different dataset due to discrepancies between the two domains. To overcome this challenge, domain adaptation techniques can be employed. In the paper, we study hyperspectral domain adaptation for adapting the target domain to align with the source domain in detecting the material type of mm-scale particles from shredded electrolyzers on a conveyor belt for recycling applications. This is necessary due to the non-uniform distribution of particles, variations in material types, and changes in the imaging environment. The results show improvements compared to a pre-trained model using a 2D convolutional neural network.

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove:

An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,…,B_n) of square matrices over ?_q and a function Eval: ?_q → {0,1}, and evaluated on x ∈ {0,1}^n by computing Eval(det(A + ∑_{i∈[n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (i?) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation.

It is crucial for the police department to automatically determine if suspects are present in the criminal database, sometimes based on the informant's visual memory alone. FaceFetch [15] is a state-of-the-art face retrieval system capable of retrieving an envisioned face from a large-scale database. Although FaceFetch can retrieve images effectively, it lacks sophisticated techniques to produce results efficiently. To this end, we propose SeekSuspect, a faster interactive suspect retrieval framework, which introduces several optimization algorithms to FaceFetch's framework. We train and test our system on a real-world dataset curated in collaboration with a metropolitan police department in India. Results reveal that SeekSuspect beats FaceFetch and can be employed by law enforcement agencies to retrieve suspects.

Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control. We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization. Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width.