Quantum Dot Cellular Automata (QCA) for the Efficient Design of Cube Architecture With Lower Power Dissipation Compared to the Square Architecture

Cube calculations using finite-field arithmetic are crucial in cryptography and error-correcting codes. Finite fields, also known as Galois fields <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(GF(p^{n}))$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> represents a prime number and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> is a positive integer, support essential operations for various applications, including elliptic curve cryptography (ECC), cryptographic Hash functions, Reed-Solomon codes, and polynomial irreducibility testing. Understanding cube computations in finite fields is crucial for developing secure and reliable digital systems. Conventional multiplication techniques for cube calculations often result in complex designs that increase power consumption and latency. To address these issues, a QCA-based cubing circuit is developed. The 2-bit cube circuit, utilizing coplanar technology, employs a three-input majority gate (MV3) and XOR gate, while a QCA-based 2-bit square circuit reduces circuit complexity. This design achieves significant reductions in cell count, size and latency compared to a 2-bit QCA-based square circuit. The power dissipation for the 2-bit cube circuit measures <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.991 nW$</tex>.