Discrete exponential function

The discrete exponential function (also modular exponentiation or modular exponentiation )

${\displaystyle b^{x}\ {\bmod {\ }}m}$

returns the remainder when dividing by . The inverse of the discrete exponential function is called the discrete logarithm . ${\displaystyle b^{x}}$ ${\displaystyle m}$

The discrete exponential function can also be calculated efficiently for large exponents . For the inversion, i.e. the calculation of the exponent , given the basis , module and desired result, no fast algorithm is known to date. The discrete exponential function is therefore used as a one-way function in asymmetric cryptosystems . ${\displaystyle x}$ ${\displaystyle b}$ ${\displaystyle m}$

Euler's theorem and the Square & Multiply method can be used to efficiently compute the discrete exponential function .

Web links

• Fast Modular Exponentiation applet