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{{Short description|Operation in modular arithmetic}}
{{refimprove|date=February 2018}}
'''Modular exponentiation''' is [[exponentiation]] performed over a [[modular arithmetic|modulus]]. It is useful in [[computer science]], especially in the field of [[public-key cryptography]], where it is used in both [[Diffie-Hellman Key Exchange]] and [[RSA_(cryptosystem)|RSA public/private keys]].
Modular exponentiation is the remainder when an integer {{math|''b''}} (the base) is raised to the power {{math|''e''}} (the exponent), and divided by a [[positive integer]] {{math|''m''}} (the modulus); that is, {{math|''c'' {{=}} ''b''<sup>''e''</sup> [[Modulo operation|mod]] ''m''}}. From the definition of division, it follows that {{math|0 ≤ ''c'' < ''m''}}.
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