Diffie Hellman calculator in Python and my first story. Paper key lists transported by a trusted courier. The Diffie - Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using. The Diffie-Hellman key exchange algorithm was first published in 1976 by Whitfield Diffie and Martin Hellman, although the algorithm had been invented a few years earlier by the British government intelligence agency GCHQ but was kept classified. The Diffie-Hellman method works best if p = 2q+1 where q is also a prime. (For example, 5 and 11 are prime and 11 = 2 x 5 + 1.) Then half the integers 1,2.,p-1 are generators, and it is possible to check whether g is a. Back Diffie-Hellman is a standard method of Alice and Bob being able to communicate, and end up with the same secret encryption key. It is used in many applications, and uses two numbers (G and N) for the first part of the calculation (of which N must be a prime number). The Diffie-Hellman key exchange uses a large prime pand a primitive root gof this prime. These numbers are both public. To start the key exchange process, Alice chooses a secret number aless than the large prime, and computes ga(mod p). Alice sends this answer, call it A, to Bob.

You already use modulo computation when you look at the clock and e.g. needs to figure out what time it's 3 hours after 11 o'clock, which is 2 o'clock. In math we write that as:

( (11 + 3) : mod : 12 = 2 )

where 12 is the modulus because we want the time as an integer between 0 and 11 (12 o'clock is in this case denoted by 0). In words we say 11 plus 3 modulo 12 is equal 2. The result of a modulo computation is an integer between 0 and the modulus minus 1. E.g. with the modulus 3 we have that:

( 1 : mod : 3 = 1 )
( 2 : mod : 3 = 2 )
( 3 : mod : 3 = 0 )
( 4 : mod : 3 = 1 )
( 5 : mod : 3 = 2 )
( 6 : mod : 3 = 0 )
etc.

If we e.g. look at ( 27 : mod : 5 ) then modulo computes the number of times 5 divides 27 and then returns the remainder of the result which is 2 in this case, i.e. ( 27 : mod : 5 = 2 ). But how did we get this result?

First we compute the number of times it's possible to multiply 5 with the number ( x ) such that we get an integer as close as possible to 27 without exceeding it, i.e. we have to find the maximun value of ( x ) such that ( 5 cdot x leq 27 ). In this case we have that ( x = 5 ) because ( 5 cdot 5 = 25 leq 27 ). Then by subtracting 27 with 25 we get the answer ( 27 - 25 = 2).

Diffie-hellman Calculator

If the integer is negative e.g. ( -27 : mod : 5 ) we have to do it slightly different and the answer is ( -27 : mod : 5 = 3 ). In this case the integer ( x ) is negative and should be the closest integer that exceed -27, i.e. we have to find the minimum value of ( -x ) such that ( 5 cdot -x geq -27 ). Now we have that ( -x = -6 ) because ( 5 cdot -6 = -30 geq -27 ). Then by subtracting -27 with -30 we get the answer ( -27 - (-30) = -27 + 30 = 3).

It's important that ( x ) or ( -x ) is an integer such as ( -14, 3, 17 ) etc. and NOT a fraction or float such as ( frac{1}{4}, frac{-3}{7}, 2.5, 5.1 ) etc.

Diffie-hellman Calculator

If two integers ( a ) and ( b ) modulo the same modulus ( c ) returns the same remainder ( r ), then we say that ( a ) and ( b ) are congruent modulo ( c ). I.e. if ( a : mod : c = r ) and ( b : mod : c = r ) then ( a equiv b : (mod : c) ). Also, notice that if the modulus ( c ) is greater than the integer ( a ), i.e. ( c > a ), the result will always be equal ( a : mod : c = a ).

Diffie Hellman Calculator