Card-based cryptography enables the execution of cryptographic protocols such as secure multiparty computation, by using a deck of physical cards. To facilitate statistical analysis with card-based cryptography, we have previously presented protocols for integer-based arithmetic operations. These protocols utilize integer commitments, which are face-down card sequences encoding integers, and consist of simple operations. However, in statistical applications, they suffer from poor scalability, as the required number of cards increases significantly as the number of data points increases. To address this issue, this paper introduces a new representation of commitments, named floating-point number (FPN) commitments, which are face-down card sequences encoding floating-point numbers. These FPN commitments allow us to represent a wide range of numbers, including negative and arbitrary-precision values, with fewer cards. We then propose protocols for converting a conventional integer commitment to an FPN commitment and for performing arithmetic operations using FPN commitments. We also demonstrate that our new representation and protocols enhance the applicability of card-based cryptography to statistical processing.
In the past few decades, quantum computation has become increasingly attractive due to its remarkable performance. Quantum image scaling is considered a common geometric transformation in quantum image processing, however, the quantum floating-point data version of which does not exist. Is there a corresponding scaling for 2-D and 3-D floating-point data? The answer is yes. In this paper, we present a quantum scaling up and down scheme for floating-point data by using trilinear interpolation method in 3-D space. This scheme offers better performance (in terms of the precision of floating-point numbers) for realizing the quantum floating-point algorithms than previously classical approaches. The Converter module we proposed can solve the conversion of fixed-point numbers to floating-point numbers of arbitrary size data with [Formula: see text] qubits based on IEEE-754 format, instead of 32-bit single-precision, 64-bit double-precision and 128-bit extended-precision. Usually, we use nearest-neighbor interpolation and bilinear interpolation to achieve quantum image scaling algorithms, which are not applicable in high-dimensional space. This paper proposes trilinear interpolation of floating-point data in 3-D space to achieve quantum algorithms of scaling up and down for 3-D floating-point data. Finally, the quantum scaling circuits of 3-D floating-point data are designed.
There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around
90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.