Daneshbeh et al., 2005 - Google Patents

A class of unidirectional bit serial systolic architectures for multiplicative inversion and division over GF (2/sup m/)

Daneshbeh et al., 2005

Document ID: 13630894316694568713
Author: Daneshbeh A; Hasan M
Publication year: 2005
Publication venue: IEEE Transactions on Computers

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A class of universal unidirectional bit serial systolic architectures for multiplicative inversion and division over Galois field GF (2/sup m/) is presented. The field elements are represented with polynomial (standard) basis. These systolic architectures have no carry propagation …

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Classifications

- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
- G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
- G06F7/724—Finite field arithmetic
- G06F7/726—Inversion; Reciprocal calculation; Division of elements of a finite field
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
- G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
- G06F7/724—Finite field arithmetic
- G06F7/725—Finite field arithmetic over elliptic curves
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/52—Multiplying; Dividing
- G06F7/523—Multiplying only
- G06F7/53—Multiplying only in parallel-parallel fashion, i.e. both operands being entered in parallel
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/50—Adding; Subtracting
- G06F7/505—Adding; Subtracting in bit-parallel fashion, i.e. having a different digit-handling circuit for each denomination
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F2207/00—Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F2207/38—Indexing scheme relating to groups G06F7/38 - G06F7/575
- G06F2207/3804—Details
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/50—Computer-aided design
- G06F17/5009—Computer-aided design using simulation
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/58—Random or pseudo-random number generators
- H—ELECTRICITY
- H03—BASIC ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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- G06F2207/72—Indexing scheme relating to groups G06F7/72 - G06F7/729
- G06F2207/7219—Countermeasures against side channel or fault attacks
- H—ELECTRICITY
- H03—BASIC ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/65—Purpose and implementation aspects
- H03M13/6508—Flexibility, adaptability, parametrability and configurability of the implementation

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