Quantum modular multiplication circuit is one of the basic quantum computation circuits which are basic functions in quantum algorithms. However, since quantum-quantum modular multipliers require a high cost reversible modular inversion routine for modular multiplication, researchers have been unable to propose a feasible quantum-quantum modular multiplier. In this paper, we proposed efficient quantum-classical modular multipliers and the first quantum-quantum modular multipliers that do not require a reduction stage by transforming the partial product used in multiplication utilizing bit-shift operation. Then, we calculated quantum resource complexity and analyzed it compared to other quantum modular multipliers and utilized ETRI (Electronics and Telecommunications Research Institute) Qcrypton to analyze quantum resource complexity in the practical quantum computing situation. The proposed quantum modular multipliers show an improvement of 50% in terms of gates and circuit depth compared to the most recently proposed high-performance quantum modular multipliers.

In recent years, drones have been widely used in many areas such as farming, movie making, surveillance and delivery. So, there is a need to protect these drones against security attacks including hijacking, spying and theft of stored data through the utilization of security mechanisms. Cryptographic keys are needed to operate these security mechanisms, and they must be generated by using random number generators which create unpredictable and non-regenerable random numbers. However, existing random number generators used in drones are not tailored for drones specifically as they use random sources generated on a desktop, not a drone. Recently, random number generators utilizing sensors in mobile phones and IoT (Internet of Things) devices have been studied, but are not appropriate for drones. In this paper, considering that drone sensors must be applied to flight and stationary modes, we proposed a drone specific random number generator called DroneRNG and implemented it. Then, we showed that our DroneRNG passed all of the NIST randomization tests and possesses better statistical properties and unpredictability than random number generators that are currently used in drones.

Addition is the most basic operation of computing based on a bit system. There are various addition algorithms considering multiple number systems and hardware, and studies for a more efficient addition are still ongoing. Quantum computing based on qubits as the information unit asks for the design of a new addition because it is, physically, wholly different from the existing frequency-based computing in which the minimum information unit is a bit. In this paper, we propose an efficient quantum circuit of modular addition, which reduces the number of gates and the depth. The proposed modular addition is for the Galois Field $GF(2^n-1)$, which is important as a finite field basis in various domains, such as cryptography. Its design principle was from the ripple carry addition (RCA) algorithm, which is the most widely used in existing computers. However, unlike conventional RCA, the storage of the final carry is not needed due to modifying existing diminished-1 modulo $2^n-1$ adders. Our proposed adder can produce modulo sum within the range $\left\{0,2^n-2\right\}$ by fewer qubits and less depth. For comparison, we analyzed the proposed quantum addition circuit over $GF(2^n-1)$ and the previous quantum modular addition circuit for the performance of the number of qubits, the number of gates, and the depth, and simulated it with IBM’s simulator ProjectQ.

Quantum squaring circuits have been used as helpful arithmetic modules in various quantum algorithms for calculating series expansions or distances of vectors, etc. Quantum multipliers can replace quantum squaring circuits, but squaring with quantum multipliers is inefficient because it involves using quantum gates for unnecessary bitwise multiplication. In this paper, we propose a depth-optimized quantum circuit dedicated to squaring by eliminating these unnecessary quantum gates and implementing quantum gates in parallel. We also discuss the optimal distribution of the partial products to reduce further the gate cost of the quantum adder used for the sum of the partial products. The proposed partial product distribution method lowers the quantum adder’s number of gates and depth by half. Our quantum squaring circuit is the most efficient, with an average improvement of 68% and 79.7% in T-count and T-depth, respectively, compared to existing quantum squaring circuits. Despite the increased qubit counts caused by the depth optimization, we demonstrate that the proposed circuit has the smallest \(\hbox {KQ}_\textrm{T}\).

The security of lattice-based cryptography relies on the computational complexity of solving the Shortest Vector Problem (SVP) on a high-dimensional lattice. Due to its efficacy in addressing SVP, lattice-based cryptographic systems have so far used the sieve algorithm to analyze their security. Previous works have analyzed the theoretical complexity improvement of the sieve algorithm in quantum computing environments, noting that Grover’s algorithm provides a quadratic speed-up for search problems. However, these works have solely focused on the theoretical analysis of query complexity, neglecting to present quantum circuit designs for sieves. Quantum circuit design and quantum resource estimation are necessary for practical analysis of the complexity of quantum sieves. Additionally, the cost of quantum error correction must also be considered, as quantum computation has a large number of errors. In this paper, we present quantum circuit designs for the sieve algorithm and provide estimates of the quantum resources required, including the number of gates and their depth. Furthermore, we evaluate the quantum sieve’s impact on the security level of ML-KEM and ML-DSA, comparing it to the classical sieve algorithm. We do this by evaluating the classical processing cost for quantum error correction using these estimates. Our results show that the quantum sieve algorithm does not break ML-KEM and ML-DSA, but it reduces their security level by 15 to 27 bits compared to the classical sieve.

The development of quantum computers has led to the possibility of solving problems intractable to deal with in clas-sical computers. That threatens the current standard of public-key cryptography based on factoring or discrete-log problem. As a result, it is necessary to use a secure cryptosystem even in a quantum computing environment. NIST has been conducting a Post-Quantum Cryptography (PQC) standardization process. Recently, there have been attempting to design binary MQ solver with the Grover's algorithm to solve the binary Multivariate Quadratic (MQ) problem. However, most PQC candidates based on the MQ problem do not select a small security parameter and are over GF(16) and above. In this paper, we design the Grover's oracle circuit to solve the MQ problem over GF(31) that can be used to analyze the quantum security of PQC candidates such as Rainbow and MQDSS.