Cloud-based Quadratic Optimization with Partially Homomorphic Encryption

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party's inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs

Cloud-Based Quadratic Optimization with Partially Homomorphic Encryption

This article develops a cloud-based protocol for a constrained quadratic optimization problem involving multiple parties, each holding private data. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure communication techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy. We show the implementation results of the protocol and discuss its computational and communication complexity. We conclude this article with a discussion on privacy notions

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

On UC-Secure Range Extension and Batch Verification for ECVRF

Verifiable random functions (Micali et al., FOCS\u2799) allow a key-pair holder to verifiably evaluate a pseudorandom function under that particular key pair. These primitives enable fair and verifiable pseudorandom lotteries, essential in proof-of-stake blockchains such as Algorand and Cardano, and are being used to secure billions of dollars of capital. As a result, there is an ongoing IRTF effort to standardize VRFs, with a proposed ECVRF based on elliptic-curve cryptography appearing as the most promising candidate. In this work, towards understanding the general security of VRFs and in particular the ECVRF construction, we provide an ideal functionality in the Universal Composability (UC) framework (Canetti, FOCS\u2701) that captures VRF security, and show that ECVRF UC-realizes this functionality. We further show how the range of a VRF can generically be extended in a modular fashion based on the above functionality. This observation is particularly useful for protocols such as Ouroboros since it allows to reduce the number of VRF evaluations (per slot) and VRF verifications (per block) from two to one at the price of additional (but much faster) hash-function evaluations. Finally, we study batch verification in the context of VRFs. We provide a UC-functionality capturing a VRF with batch-verification capability, and propose modifications to ECVRF that allow for this feature. We again prove that our proposal UC-realizes the desired functionality. We provide a performance analysis showing that verification can yield a factor-two speedup for batches with 1024 proofs, at the cost of increasing the proof size from 80 to 128 bytes