Abstract: This paper presents two improved modular multiplication algorithms: variable length Interleaved modular multiplication (VLIM) algorithm and parallel modular multiplication (P_MM) method ...

Abstract: Elliptic curve cryptography (ECC) is widely used in security applications such as public key cryptography (PKC) and zero-knowledge proofs (ZKP). ECC is composed of modular arithmetic, where ...

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 ...

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