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Patent

Table matching for multiplication of elements in Galois Field

TLDR
A table matching method for multiplication of elements in Galois field is presented in this paper, where the byte value is the product of the two elements in the Galois Field, and the two exponents are then added up to obtain a sum.
Abstract
A table matching method for multiplication of elements in Galois Field. First, a table of the byte value in Galois Field and the corresponding exponent is formed in the hardware. To perform the multiplication between two elements in the Galois Field, the corresponding exponents of the two elements are found out in advance. The two exponents are then added up to obtain a sum. Then, by using the table, a corresponding byte value of the sum can be obtained. The byte value is the product of the two elements in the Galois Field.

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Patent

Modular multiplication method with precomputation using one known operand

TL;DR: In this article, a modular multiplication method implemented in an electronic digital processing system takes advantage of the case where one of the operands W is known in advance or used multiple times with different second operands V to speed calculation.
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Optimized multiplicative inverse

TL;DR: In this paper, a method, device and cipher for performing an optimized multiplicative inverse on received data in substantially real-time and without use of a look-up table is presented.
References
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Patent

Modular arithmetic operation system

TL;DR: In this paper, a modular arithmetic unit consisting of an input register, a multiple computing section, an adder, and a correcting section is presented, where the adder adds the modulo N retrieved from the multiple table and the contents of the input register.
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TL;DR: In this paper, a method and device for calculating syndromes used in forward error correction codes is presented, where the polynomial equation C(X) is divided by a generator polynomials G(X), to form a remainder poynomial R(X).
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High speed calculation of cyclical redundancy check sums

TL;DR: In this article, a frame of data is partitioned into a plurality of sub-frames and a look-up table containing pre-computed CRC values is stored in computer memory and accessed during the CRC calculation of the sub-frame.
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High-speed evaluation of polynomials

TL;DR: In this paper, the polynomial equation is split into a plurality of sub-polynomials and the results of the sub-nomials can be simultaneously evaluated using Horner's rule.
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Bit-serial division method and apparatus

TL;DR: In this paper, a bit-serial division method is disclosed for computing the value v/u, where v and u represent vectors in a canonical basis constituting elements in a finite field consisting of 2n elements.