I'm trying to better understand RSA and Diffie-Hellman exchange and the modulus math that they are base on, there are some questions I have about there properties for which I am unable to find concise explanations about. I'm generally interested in how the commutative, associative, distributive, etc.. properties apply. Questions 1. About Fermat's Little Theorem. MP-1 ≡ 1 (mod P) which I'm told implies that... MP ≡ M (mod P) Is this essentially multiplying by M on both sides?? So if X ≡ Y ( mod P) then aX ≡ aY (mod P) ? Does. a⋅[ X (mod P)] = aX (mod P) is it a⋅[ X (mod P)] = the remainder of X/P times a ? Also in the Diffie Hellman exchange I'm told that... (ga mod p)b (mod p) = gab (mod p) which i think means in general that... [ g (mod p)]a (mod p)= ga ( mod p ) but i'm not sure what property that uses. Can that be derived from the multiplication property where... ab ( mod p ) = [ a (mod p) ⋅ b (mod p) ] (mod p) Thanks a lot for any explanation you can give to point me on the right track.