Swin.del - Primitive.Root flac album

In modular arithmetic, a branch of number theory, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root mod n if for every integer a coprime to n, there is an integer k such that gk ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. Note that g is a primitive root mod n if and only if g is a generator of the multiplicative group of integers modulo n.

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g is a primitive root mod. p p. p, the quadratic residues mod. p are precisely the even powers of the primitive root. Primitive roots are also important in cryptological applications involving the discrete log problem, most notably the Diffie-Hellman key exchange protocol. Terminology and a Formal Definition. Background and Motivation. Existence of Primitive Roots. Finding Primitive Roots. Once one primitive root. g g. g has been found, the others are easy to construct: simply take the powers. a a. a is relatively prime to. ϕ(n) phi(n). But finding a primitive root efficiently is a difficult computational problem in general.