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Binary Finite Fields In a binary finite field numbers are actually polynomial equations. If you represent the number as a sequence of bits you get a sequence of 1's or 0's. These 1's or 0's represent the coefficients of the x**n, where n is the location of the given bit. When you add numbers over a binary finite field the result should have a coefficient of 1 or 0 as well. Hence addition and subtraction become the same operation as XOR. eg. 1 + 1 + 1 == 3 % 2 == 1 or 0 - 1 == -1 % 2 == 1
| Author: | Jim Wigginton |
| Copyright: | 2017 Jim Wigginton |
| License: | http://www.opensource.org/licenses/mit-license.html MIT License |
| File Size: | 516 lines (14 kb) |
| Included or required: | 0 times |
| Referenced: | 0 times |
| Includes or requires: | 0 files |
Integer:: (26 methods):
__construct()
setModulo()
setRecurringModuloFunction()
checkInstance()
equals()
compare()
deg()
polynomialDivide()
regularPolynomialMultiply()
polynomialMultiply()
subMultiply()
subAdd2()
subAdd3()
add()
subtract()
multiply()
modInverse()
divide()
negate()
getModulo()
toBytes()
toHex()
toBits()
toBigInteger()
__toString()
__debugInfo()
| __construct($instanceID, $num = '') X-Ref |
| Default constructor |
| setModulo($instanceID, $modulo) X-Ref |
| Set the modulo for a given instance param: int $instanceID param: string $modulo |
| setRecurringModuloFunction($instanceID, callable $function) X-Ref |
| Set the modulo for a given instance |
| checkInstance(self $x, self $y) X-Ref |
| Tests a parameter to see if it's of the right instance Throws an exception if the incorrect class is being utilized |
| equals(self $x) X-Ref |
| Tests the equality of two numbers. return: bool |
| compare(self $x) X-Ref |
| Compares two numbers. return: int |
| deg($x) X-Ref |
| Returns the degree of the polynomial return: int param: string $x |
| polynomialDivide($x, $y) X-Ref |
| Perform polynomial division link: https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Euclidean_division return: string[] |
| regularPolynomialMultiply($x, $y) X-Ref |
| Perform polynomial multiplation in the traditional way link: https://en.wikipedia.org/wiki/Finite_field_arithmetic#Multiplication return: string |
| polynomialMultiply($x, $y) X-Ref |
| Perform polynomial multiplation Uses karatsuba multiplication to reduce x-bit multiplications to a series of 32-bit multiplications link: https://en.wikipedia.org/wiki/Karatsuba_algorithm return: string |
| subMultiply($x, $y) X-Ref |
| Perform polynomial multiplication on 2x 32-bit numbers, returning a 64-bit number link: https://www.bearssl.org/constanttime.html#ghash-for-gcm return: string param: string $x param: string $y |
| subAdd2($x, $y) X-Ref |
| Adds two numbers return: string param: string $x param: string $y |
| subAdd3($x, $y, $z) X-Ref |
| Adds three numbers return: string param: string $x param: string $y |
| add(self $y) X-Ref |
| Adds two BinaryFieldIntegers. return: static |
| subtract(self $x) X-Ref |
| Subtracts two BinaryFieldIntegers. return: static |
| multiply(self $y) X-Ref |
| Multiplies two BinaryFieldIntegers. return: static |
| modInverse() X-Ref |
| Returns the modular inverse of a BinaryFieldInteger return: static |
| divide(self $x) X-Ref |
| Divides two PrimeFieldIntegers. return: static |
| negate() X-Ref |
| Negate A negative number can be written as 0-12. With modulos, 0 is the same thing as the modulo so 0-12 is the same thing as modulo-12 return: object |
| getModulo($instanceID) X-Ref |
| Returns the modulo return: string |
| toBytes() X-Ref |
| Converts an Integer to a byte string (eg. base-256). return: string |
| toHex() X-Ref |
| Converts an Integer to a hex string (eg. base-16). return: string |
| toBits() X-Ref |
| Converts an Integer to a bit string (eg. base-2). return: string |
| toBigInteger() X-Ref |
| Converts an Integer to a BigInteger return: string |
| __toString() X-Ref |
| __toString() magic method |
| __debugInfo() X-Ref |
| __debugInfo() magic method |