Space and Time-Efficient Quantum Multiplier in Post Quantum Cryptography Era

This paper examines the asymptotic performance of multiplication and cost quantum implementation for Naive schoolbook, Karatsuba, Toom-Cook methods in classical cases provides insights into roles post-quantum cryptography (PQC) era. Further, considering that lattice-based PQC algorithm is based on polynomial algorithms, including 4-way multiplier as its fundamental building block, we propose a higher-degree multiplier, 8-way which has lowest cost. Additionally, designed will include additional sub-operations to complete large integers order prevent side-channel attacks. To design our detail, employ detailed step computations such splitting, evaluation, point-wise multiplication, interpolation, recomposition, well several strategies reduce space time requirements. Existing multipliers are compared with 2-way, 4-way, designs. Our analysis or qubit count terms efficiency, n ( 15/8 ) log 15 /(2 log 15–log 8) log8 n asymptotically xmlns:xlink="http://www.w3.org/1999/xlink">O xmlns:xlink="http://www.w3.org/1999/xlink">1.245 ). The logical Toffoli counts bound at 112 xmlns:xlink="http://www.w3.org/1999/xlink">log8 15 – 128 depth xmlns:xlink="http://www.w3.org/1999/xlink">1– , close xmlns:xlink="http://www.w3.org/1999/xlink">1.0569 ), corresponds space- time-efficient multiplication.