Hardware circuitry defines logic for both Sbox generation and inverse Sbox generation via generating a multiplicative inverse matrix as a truth table for data. The hardware circuitry receives input plain text to be encrypted. The hardware circuitry divides the input plain text to be encrypted. The hardware circuitry feeds multiplicative inverse values generated from the input plain text to a transformer module for performing affine to encrypt the plain text data. The hardware circuitry receives encrypted data to be decrypted. The hardware circuitry divides the encrypted data to be decrypted. The hardware circuitry feeds multiplicative inverse generated from the encrypted data to the transformer module for performing inverse affine to decrypt the encrypted data.

A computing device (e.g., an FPGA or integrated circuit) processes an incoming packet comprising data to compute a Galois hash. The computing device includes a plurality of circuits, each circuit providing a respective result used to determine the Galois hash, and each circuit including: a first multiplier configured to receive a portion of the data; a first exclusive-OR gate configured to receive an output of the first multiplier as a first input, and to provide the respective result; and a second multiplier configured to receive an output of the first exclusive-OR gate, wherein the first exclusive-OR gate is further configured to receive an output of the second multiplier as a second input. In one embodiment, the computing device further comprises a second exclusive-OR gate configured to output the Galois hash, wherein each respective result is provided as an input to the second exclusive-OR gate.

Embodiments are directed to aggregate GHASH-based message authentication code (MAC) over multiple cachelines with incremental updates. An embodiment of a system includes a controller comprising circuitry, the controller to generate an error correction code for a memory line, the memory line comprising a plurality of first data blocks, generate a metadata block corresponding to the memory line, the metadata block comprising the error correction code for the memory line and at least one metadata bit, generate an aggregate GHASH corresponding to a region of memory comprising a cacheline set comprising at least the memory line, encode the first data blocks and the metadata block, encrypt the aggregate GHASH as an aggregate message authentication code (AMAC), provide the encoded first data blocks and the encoded metadata block for storage on a memory module comprising the memory line, and provide the AMAC for storage on a device separate from the memory module.

A recording medium stores a program causing a computer to execute a process including: setting, for each order having a condition that a contract count is designated, a polynomial having a contract count under the condition; representing an order status in which the orders are combined, with a polynomial on a finite field having a remainder obtained by dividing a coefficient of each term in a polynomial obtained by multiplying the polynomials corresponding to the orders; updating the polynomial on the finite field to a polynomial on a finite field representing an order status after a first order is combined, by multiplying the polynomial by a polynomial corresponding to the first order; and detecting an error in the polynomial after the update when a coefficient which is not 0 of a term in the polynomial before the update is 0 in the polynomial.

Technologies for scrambling functions in a column-addressable memory architecture includes a device having a memory and a circuitry. The memory includes a matrix storing individually addressable bit data, and the matrix is formed by rows and columns. The circuitry is to receive a request to perform a write operation of one or more bit values to one of the columns. The circuitry is further to determine a scrambler state at each location of the column, the location corresponding to a respective row and column index. The scrambler state is indicative of a function used to determine a value at the respective column location. Each of the bit values is scrambled as a function of the scrambler state for the respective column location and written thereto.

According to an embodiment, an arithmetic device outputting an arithmetic result on a finite field with characteristic P includes a hardware processor. The hardware processor performs readout processing of a plurality of input values. The hardware processor performs, for each word, arithmetic operations with respect to the plurality of input values by using a value being based on the characteristic P and a comparison value between each input value of the plurality of input values and the characteristic P. The hardware processor outputs a first output value resulting from computing a value being based on each input value of the plurality of input values, the comparison value, and the characteristic P. The hardware processor outputs a second output value resulting from comparing the first output value and the characteristic P.

Operational n-state digital circuits and n-state switching operations with n and integer greater than 2 execute Finite Lab-transformed (FLT) n-state switching functions to process n-state signals provided on at least 2 inputs to generate an n-state signal on an output. The FLT is an enhancement of a computer architecture. Cryptographic apparatus and methods apply circuits that are characterized by FLT-ed addition and/or multiplication over finite field GF(n) or by addition and/or multiplication modulo-n that are modified in accordance with reversible n-state inverters, and are no longer known operations. Cryptographic methods processed on FLT modified machine instructions include encryption/decryption, public key generation, and digital signature methods including Post-Quantum methods. They include modification of isogeny based, NTRU based and McEliece based cryptographic machines.

A computing device (e.g., an FPGA or integrated circuit) processes an incoming packet comprising data to compute a Galois hash. The computing device includes a plurality of circuits, each circuit providing a respective result used to determine the Galois hash, and each circuit including: a first multiplier configured to receive a portion of the data; a first exclusive-OR gate configured to receive an output of the first multiplier as a first input, and to provide the respective result; and a second multiplier configured to receive an output of the first exclusive-OR gate, wherein the first exclusive-OR gate is further configured to receive an output of the second multiplier as a second input. In one embodiment, the computing device further comprises a second exclusive-OR gate configured to output the Galois hash, wherein each respective result is provided as an input to the second exclusive-OR gate.

A parallel finite field multiplication device is disclosed. The device comprises M cascaded logic processing modules, each of which comprises four input ends and two output ends for carrying out different finite multiplication in different length. The device is calculated step by step through M cascaded logic processing modules according to the number of cascaded logic processing modules. In this device, M cascaded logic processing modules may be used, according to different numbers of the cascaded logic processing modules, in finite field multiplication of different lengths, without needing to carry out polynomial multiplication.

Disclosed herein is an apparatus for calculating a cryptographic component R.sup.2 mod n for a cryptographic function, where n is a modulo number and R is a constant greater than n. The apparatus comprises an arithmetic logic unit configured to iteratively perform Montgomery multiplication of a first operand with a second operand to produce an intermediate result, wherein the first operand and the second operand are set to the intermediate result after each iteration, responsive to a termination condition being met, determine an adjustment parameter indicative of a difference between the intermediate result and the cryptographic component, and perform Montgomery multiplication of the intermediate result with the adjustment parameter, to calculate the cryptographic component for the cryptographic function.