Demonstrating BB84 Quantum Key Distribution in the Physical Layer of an Optical Fiber Based System

Nowadays, widely spread encryption methods (e.g., RSA) and protocols enabling digital signatures (e.g., DSA, ECDSA) are an integral part of our life. Although recently developed quantum computers have low processing capacity, huge dimensions and lack of interoperability, we must underline their practical significance – applying Peter Shor’s quantum algorithm (which makes it possible to factorize integers in polynomial time) public key cryptography is set to become breakable. As an answer, symmetric key cryptography proves to be secure against quantum based attacks and with it quantum key distribution (QKD) is going through vast development and growing to be a hot topic in data security. This is due to such methods securely generating symmetric keys by protocols relying on laws of quantum physics.

Speed improvement of the quantum factorization algorithm of P. Shor by upgrade its classical part

This report discusses Shor’s quantum factorization algorithm and ρ–Pollard’s factorization algorithm. Shor’s quantum factorization algorithm consists of classical and quantum parts. In the classical part, it is proposed to use Euclidean algorithm, to find the greatest common divisor (GCD), but now exist large number of modern algorithms for finding GCD. Results of calculations of 8 algorithms were considered, among which algorithm with lowest execution rate of task was identified, which allowed the quantum algorithm as whole to work faster, which in turn provides greater potential for practical application of Shor’s quantum algorithm. Standard quantum Shor’s algorithm was upgraded by replacing the binary algorithm with iterative shift algorithm, canceling random number generation operation, using additive chain algorithm for raising to power. Both Shor’s algorithms (standard and upgraded) are distinguished by their high performance, which proves much faster and insignificant increase in time in implementation of data processing. In addition, it was possible to modernize Shor’s quantum algorithm in such way that its efficiency turned out to be higher than standard algorithm because classical part received an improvement, which allows an increase in speed by 12%.

Accelerating Shor’s factorization algorithm on GPUs

Shor’s quantum algorithm is very important for cryptography, because it can factor large numbers much faster than classical algorithms. In this study, we implement a simulator for Shor’s quantum algorithm on graphic processor units (GPU) and compare our results with Liquid, which is a Microsoft quantum simulation platform, and two classical CPU implementations. We evaluate 10 benchmarks for comparing our GPU implementation with Liquid and single-core implementation. The analysis shows that GPU vector operations are more suitable for Shor’s quantum algorithm. Our GPU kernel function is compute-bound, due to all threads in a block reaching the same element of the state vector. Our implementation has 52.5× speedup over single-core algorithm and 20.5× speedup over Liquid.

Factoring using 2n+2 qubits with Toffoli based modular multiplication

We describe an implementation of Shor’s quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in O(n 3 ) and O(n 3 log n), respectively. We thus achieve the same space and time costs as Takahashi et al. [1], while using a purely classical modular multiplication circuit. As a consequence, our approach evades most of the cost overheads originating from rotation synthesis and enables testing and localization of some faults in both, the logical level circuit and an actual quantum hardware implementation. Our new (in-place) constant-adder, which is used to construct the modular multiplication circuit, uses only dirty ancilla qubits and features a circuit size and depth in O(n log n) and O(n), respectively.