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# Computer Security Resource Center

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### exclusive-OR

Abbreviation(s) and Synonym(s):

Exclusive OR
Exclusive-or

Definition(s):

Exclusive-OR operation.
Source(s):
FIPS 197 under XOR
FIPS 197 under ⊕

Bitwise logical “exclusive-or”, where 0⊕ 0 = 0, 0⊕ 1 = 1, 1⊕ 0 = 1, and 1⊕ 1 = 0. For example: 01101⊕ 11010 = 10111.
Source(s):
NIST SP 800-106 under ⊕

Bit-wise exclusive-or. A mathematical operation that is defined as: 0⊕ 0 = 0 0⊕ 1 = 1 1⊕ 0 = 1 , and 1⊕ 1 = 0
Source(s):
NIST SP 800-133 [Superseded] under ⊕

A bitwise logical operation such that 1⊕ 1 = 0, 1⊕ 0 = 1, 0⊕ 0 = 0, and 0⊕ 1 = 1. For example, given a string A = 10 and a string B = 11, then A⊕ B = (1⊕ 1) || (0⊕ 1) = 01.
Source(s):
NIST SP 800-135 Rev. 1 under ⊕

A XOR B is equivalent to A ⊕ B. See the definition of the bitwise logical operation ⊕ above.
Source(s):
NIST SP 800-135 Rev. 1 under XOR

The bit-by-bit modulo 2 addition of binary vectors of equal length.
Source(s):
NIST SP 800-20 under Exclusive-OR
NIST SP 800-67 Rev. 2 under Exclusive-OR
NIST SP 800-67 Rev. 1 [Superseded] under Exclusive-OR

The bitwise addition, modulo 2, of two bit strings of equal length.
Source(s):
NIST SP 800-38A under Exclusive-OR
NIST SP 800-38B under Exclusive-OR
NIST SP 800-38C under Exclusive-OR
NIST SP 800-38D under Exclusive-OR
NIST SP 800-38F

Exclusive-OR.
Source(s):
NIST SP 800-38D under XOR

A mathematical operation; the symbol⊕, defined as: 0⊕ 0 = 0 1⊕ 0 = 1 0⊕ 1 = 1 1⊕ 1 = 0 Equivalent to binary addition without carry.
Source(s):
NIST SP 800-90A Rev. 1 under Exclusive-or

Exclusive-Or (XOR) operation, defined as bit-wise modulo 2 arithmetic with no carry.
Source(s):
NIST SP 800-56B Rev. 2 under Ꚛ

Bit-wise exclusive-or. A mathematical operation that is defined as: 0 ⊕ 0 = 0, 0 ⊕ 1 = 1, 1 ⊕ 0 = 1, and 1 ⊕ 1 = 0
Source(s):
NIST SP 800-133 Rev.1 [Superseded] under ⊕
NIST SP 800-133 Rev. 2 under ⊕

Exclusive-Or (XOR) operator, defined as bit-wise modulo 2 arithmetic with no carry.
Source(s):
NIST SP 800-56B Rev. 1 [Superseded] under ⊕