Every time you send a text, pay for groceries with your phone, or use your health site, you are relying on encryption.

Oracle-based quantum algorithms cannot use deep loops because quantum states exist only as mathematical amplitudes in Hilbert space with no physical substrate. Criticall ...

Those that solve artificially simplified problems where quantum advantage is meaningless. Those that provide no genuine quantum advantage when all costs are properly accounted for. This critique is ...

Scroll through social media long enough and a pattern emerges. Pause on a post questioning climate change or taking a hard line on a political issue, and the platform is quick to respond—serving up ...

Today, PKC forms the foundation for e-commerce, allowing more than US$1 trillion per day in foreign exchange transactions in North America alone. 10 This technology also allows electronic banking, ...

Abstract: In the paper, a method of fast modular multiplication by a constant number, the length of which significantly exceeds the processor bit capacity has been proposed and investigated. The ...

Multiplication is working out how many groups of something you have altogether. Division is working how many you get, after sharing a number between another number. You can use place value charts to ...

Abstract: This paper describes a comparison of two FPGA Montgomery modular multiplication architectures: a fully systolic array and a parallel implementation. The modular multiplication is employed in ...

Core discovery / 核心发现: A model can maintain 100% test accuracy while its internal representation undergoes complete reorganization. The "brain" changes but ...