In some applications, such as randomization and cryptography, remainder computation for a number is required. The remainder computation is also used in modulo arithmetic. The remainder computation can be simplified when the divisor belongs to a certain class of numbers. A method and apparatus are disclosed that enable low complexity implementation of remainder computation of any number when the divisor belongs to a type of numbers that can be represented as 2.sup.k+1.

Various embodiments include a modulo operation generator associated with a cache memory in a computer-based system. The modulo operation generator generates a first sum by performing an addition and/or a subtraction function on an input address. A first portion of the first sum is applied to a lookup table that generates a correction value. The correction value is then added to a second portion of the first sum to generate a second sum. The second sum is adjusted, as needed, to be less than the divisor. The adjusted second sum forms a residue value that identifies a cache memory slice in which the input data value corresponding to the input address is stored. By generating the residue value in this manner, the cache memory efficiently distributes input data values among the slices in a cache memory even when the number of slices is not a power of two.

A method and compression unit for compressing a block of image data to satisfy a target level of compression, wherein the block of image data comprises a plurality of image element values, each image element value comprising one or more data values relating to a respective channel. For each of the channels: (i) an origin value for the channel for the block is determined, (ii) difference values are determined representing differences between the data values and the determined origin value for the channel for the block, and (iii) a first number of bits for losslessly representing a maximum difference value of the difference values for the channel for the block is determined. The determined first number of bits for each of the channels is used to determine a respective second number of bits for each of the channels, the second number of bits being determined such that representing each of the difference values for the channels with the respective second number of bits satisfies the target level of compression for compressing the block of image data. Compressed data is formed, having for each of the one or more channels an indication of the determined origin value for the channel, an indication of the determined first number of bits for the channel, and representations of the determined difference values for the channel, wherein each of the representations of the determined difference values for the channel uses the determined second number of bits for the channel, such that the target level of compression is satisfied.

Aspects of the present disclosure involve a method and a system to execute the method to perform a cryptographic operation involving a modulo N computation, the method comprising loading a first integer number and a second integer number, wherein the first integer number and the second integer number are within an interval of 2N integer numbers, and performing an arithmetic operation involving the first integer number and the second integer number, wherein the arithmetic operation is to produce a third integer number, and wherein the arithmetic operation comprises a shifting operation to ensure that the third integer number is inside the interval of 2N integer numbers.

A secure digital communications method is provided in which a Certificate Authority generates an improved RSA key pair having a modulus, a public key exponent, a public key, and a private key. The public key exponent can contain descriptive attributes and a digital signature. The digital signature can be responsive to the descriptive attributes and the modulus. A secure session can be established between a first system and a second system, within a secure digital communication protocol. The second system can verify the digital signature to authenticate the public key.

This disclosure relates to data encryption and decryption. In one aspect, a method includes receiving, by a second peer end computing device, first data from a first peer end computing device. The second end computing device generates a random term based on a result range pre-agreed upon with the first peer end computing device. The result range includes a minimum result value and a maximum result value. The random term is a product of a random number and an agreed upon constant. The agreed upon constant is greater than a difference between the maximum result value and the minimum result value. The second peer end computing device performs a homomorphic operation based on the first data, local private second data, and the random term to obtain an encryption result. The second peer end computing device returns the encryption result to the first peer end computing device.

Various embodiments include a modulo operation generator associated with a cache memory in a computer-based system. The modulo operation generator generates a first sum by performing an addition and/or a subtraction function on an input address. A first portion of the first sum is applied to a lookup table that generates a correction value. The correction value is then added to a second portion of the first sum to generate a second sum. The second sum is adjusted, as needed, to be less than the divisor. The adjusted second sum forms a residue value that identifies a cache memory slice in which the input data value corresponding to the input address is stored. By generating the residue value in this manner, the cache memory efficiently distributes input data values among the slices in a cache memory even when the number of slices is not a power of two.

A post-quantum, public key cryptosystem is described which is polynomial based and where the private key polynomial has coefficients from a sub-set of Galois field elements and plain text message polynomials have coefficients from a second sub-set of Galois field elements. The public key polynomial is constructed using the inverse of the private key polynomial and a randomly chosen polynomial having coefficients chosen from a third sub-set of Galois field elements. Cipher texts are constructed using the public key and randomly chosen session key polynomials. Other more complicated embodiments are described. For implementation a small prime base field such as 2, 3 or 5 will usually be used in constructing the prime power Galois field. The system has the advantage of relatively small public key sizes.

Disclosed herein are an apparatus and method for calculating a multiplicative inverse. The apparatus for calculating a multiplicative inverse includes a data input unit for receiving input data, a multiplicative inverse calculation unit for dividing an input degree-8 finite field corresponding to the input data into two first degree-4 finite fields so as to perform Advanced Encryption Standard (AES) encryption on the input data, and for performing a multiplicative inverse calculation on the first degree-4 finite fields in consideration of a circuit depth value (T-Depth) and qubit consumption of quantum gates in a quantum circuit, and a data output unit for outputting result data obtained by performing the multiplicative inverse calculation.

This disclosure relates to data encryption and decryption. In one aspect, a method includes receiving, by a second peer end computing device, first data from a first peer end computing device. The second end computing device generates a random term based on a result range pre-agreed upon with the first peer end computing device. The result range includes a minimum result value and a maximum result value. The random term is a product of a random number and an agreed upon constant. The agreed upon constant is greater than a difference between the maximum result value and the minimum result value. The second peer end computing device performs a homomorphic operation based on the first data, local private second data, and the random term to obtain an encryption result. The second peer end computing device returns the encryption result to the first peer end computing device.