D-H is a key exchange mechanism , a way to exchange cryptographic keys over public channels, that is , I want to agree a number with my buddy Simon but i don’t want to tell him what the number is. Agreeing in Prime and Base Numbers So there is a few requirements for this to work , and also a bunch of rules that have to be applied to the values we gonna communicate over an open space: Agree a Prime Number Agree a Base Number 1 secret exponent each So all these numbers are communicated to each other over public transport , and this is the requirement: . So here’s some code to make this up Each user will generate a “secret exponent” that can’t have any common factors between them def giveMePrimes():primeList = list()for num in range(1000,10001):if all(num%i!=0 for i in range(2,int(math.sqrt(num))+1)):primeList.append(num)return primeList This appends the the prime numbers in the range() to a list. For the Base and Secret Exponents we pick numbers just randomzingin a range: secure_random.choice = random.SystemRandom()secure_random.choice(range(1,10001)) Let’s assume we have these numbers: P (prime) = N (base) = J(Jerry's Secret exponent) = S(Simon's Secret exponent) = 2833 3667 6531 8249 Only the secret exponent are the ones we want to keep private , Jerry and Simon know only their “secret exponent” ,P and N , in short only P and N have been communicated over public channels. Now each party will compute a number with the values they have (P , N and each individual “secret exponent”) Jerry will compute: (N(base) to the J(secret exponent) modulus P (prime)) JC = N ** J % P ( ) 2642 and Simon: SC = N ** S % P ( ) 1037 And they will pass each other these values (Jerry passes JC to Simon , and Simon passes SC to Jerry). Good ! so now to Recap , let’s see what values each individual knows: : Prime , Base , Jerry’s secret exponent , JC and SC Jerry : Prime , Base , Simon’s secret exponent , JC and SC Simon : Prime , Base , JC and SC Random So now is when the magic happens , both of them apply the following function: ( peer’s computed number to the “secret exponent” modulus Prime) Jerry: SC ** J % P Simon JC ** S % P And if you do the math this translates to: Jerry 1037 ** 6531 % 2833 = 1747L Simon 2642 ** 8249 % 2833 = 1747L Great ( == Python’s literal ) , now we have have a number( ) that Simon and Jerry know that derived of a bunch of numbers that were transmitted publicly. L 1747L With this number as a “key” Simon and Jerry can start communicating privately using a cipher. I’ve put an example of the code that i’ve used for this , it kind of works:
