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The unique remainder r, 0£ r £ (n – 1), when integer x is divided by positive integer n. For example, 23 mod 7 = 2.
NIST SP 800-106
The modular reduction of the (arbitrary) integer x by the positive integer n (the modulus). For the purposes of this Recommendation, y = x mod n is the unique integer satisfying the following two conditions: 1) 0 £ y < n, and 2) x - y is divisible by n.
NIST SP 800-56B Rev. 2