**An import concept in [[Public Key Encryption]]** Primitive Root is a thing one number can be of another number. This deals with [[Prime Numbers]] and [[Modular Arithmetic]]. When used in the context of [[Public Key Encryption]], the Primitive Root of the Modular operation is called the '**generator**'. The definition of "primitive root" is a bit to opaque for me to glean without the examples below, but it's: > A primitive root mod n is **an integer g such that every integer [[Relatively Prime]] to n is congruent to a power of g mod n**. This makes a lot more sense in the examples below, from the source video: ![[IMG_9429.jpeg]] 2 is a primitive root of 5 because 2^1 mod 5 all the way through 2^(5-1) mod 5 give **unique values**. Same can be said for 3 is a primitive root of 7: ![[IMG_9430.jpeg]] And, to show that not all primes are primitive roots of each other - 2 is NOT a primitive root of 7: ![[IMG_9431.jpeg]] # So what With a Primitive Root, you get a uniform distribution when raising the "**generator**" to any integer power (X) modulus the prime number. ![[IMG_9432.jpeg]] Given the congruent result, finding the exponent is computationally _hard_ to do. It is a [[One-Way Function]]: ![[IMG_9434.jpeg]] **** ## Source -  ## Related - [[Public Key Encryption]]