There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

/pdf/a-fully-programmable-100-spin-coherent-ising-machine-with-inaxlu4ff3.pdf

A fully programmable 100-spin coherent Ising machine with all-to-all connections

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Μετακβαντικοί κρυπτογραφικοί αλγόριθμοι (Post-Quantum Cryptography)

Humans rely increasingly on sensors to address grand challenges and to improve quality of life in the era of digitalization and big data. For ubiquitous sensing, flexible sensors are developed to overcome the limitations of conventional rigid counterparts. Despite rapid advancement in bench-side research over the last decade, the market adoption of flexible sensors remains limited. To ease and to expedite their deployment, here, we identify bottlenecks hindering the maturation of flexible sensors and propose promising solutions. We first analyze challenges in achieving satisfactory sensing performance for real-world applications and then summarize issues in compatible sensor-biology interfaces, followed by brief discussions on powering and connecting sensor networks. Issues en route to commercialization and for sustainable growth of the sector are also analyzed, highlighting environmental concerns and emphasizing nontechnical issues such as business, regulatory, and ethical considerations. Additionally, we look at future intelligent flexible sensors. In proposing a comprehensive roadmap, we hope to steer research efforts towards common goals and to guide coordinated development strategies from disparate communities. Through such collaborative efforts, scientific breakthroughs can be made sooner and capitalized for the betterment of humanity.

Technology Roadmap for Flexible Sensors.

We present a new proposal for a trapdoor one-way function, from which we derive public-key encryption and digital signatures. The security of the new construction is based on the conjectured computational difficulty of lattice-reduction problems, providing a possible alternative to existing public-key encryption algorithms and digital signatures such as RSA and DSS.

Public-Key Cryptosystems from Lattice Reduction Problems.

Traditional public key cryptography will become obsolete when quantum computers are able to break it The authors propose two quantum algorithms to solve the shortest-vector problem, which could play an important role in designing new cryptosystems for the postquantum era

/pdf/two-quantum-ising-algorithms-for-the-shortest-vector-problem-2jyvyr1h9o.pdf

Two quantum Ising algorithms for the shortest-vector problem

This paper describes adiabatic-inspired algorithms to solve the approximate shortest vector problem. Numerical simulations varying algorithm sweep-time suggest the existence of a Goldilocks zone for maximizing likelihood of success.

https://link.aps.org/pdf/10.1103/PhysRevResearch.2.013361

Not-so-adiabatic quantum computation for the shortest vector problem

Transitioning organizations to post-quantum cryptography

This paper presents a code-based signature scheme based on the well-known syndrome decoding (SD) problem. The scheme builds upon a recent line of research which uses the Multi-Party-Computation-in-the-Head (MPCitH) approach to construct efficient zero-knowledge proofs, such as Syndrome Decoding in the Head (SDitH), and builds signature schemes from them using the Fiat-Shamir transform. At the heart of our proposal is a new approach, Hypercube-MPCitH, to amplify the soundness of any MPC protocol that uses additive secret sharing. An MPCitH protocol with N parties can be repeated D times using parallel composition to reach the same soundness as a protocol run with $$N^D$$ parties. However, the former comes with D times higher communication costs, often mainly contributed by the usage of D ‘auxiliary’ states (which in general have a significantly bigger impact on size than random states). Instead of that, we begin by generating $$N^D$$ shares, arranged into a D-dimensional hypercube of side N containing only one ‘auxiliary’ state. We derive from this hypercube D sharings of size N which are used to run D instances of an N party MPC protocol. Hypercube-MPCitH leads to a protocol with $$1/N^D$$ soundness error, requiring $$N^D$$ offline computation, but with only $$N\cdot D$$ online computation, and only 1 ‘auxiliary’. As the (potentially offline) share generation phase is generally inexpensive, this leads to trade-offs that are superior to just using parallel composition. Our novel method of share generation and aggregation not only improves certain MPCitH protocols in general but also shows in concrete improvements of signature schemes. Specifically, we apply it to the work of Feneuil, Joux, and Rivain (CRYPTO’22) on code-based signatures, and obtain a new signature scheme that achieves a 8.1x improvement in global runtime and a 30x improvement in online runtime for their shortest signatures size (8,481 Bytes). It is also possible to leverage the fact that most computations are offline to define parameter sets leading to smaller signatures: 6,784 Bytes for 26 ms offline and 5,689 Bytes for 320 ms offline. For NIST security level 1, online signature cost is around 3 million cycles (<1 ms on commodity processors), regardless of signature size. 

The Return of the SDitH

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite (and currently small) number of qubits, however, poses the risk of finding only the optimum within the restricted space supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence of improved problem Hamiltonians converges to the desired solution. 

David Joseph

Papers

Two quantum Ising algorithms for the shortest-vector problem

Not-so-adiabatic quantum computation for the shortest vector problem

Transitioning organizations to post-quantum cryptography

The Return of the SDitH

Iterative quantum optimization with an adaptive problem Hamiltonian for the shortest vector problem