Subject Cryptography Chapter is about DiffieHellman Alice an

Subject Cryptography Chapter is about Diffie-Hellman

Alice and Bob wish to agree on a 256-bit AES key. They are trying to decide between using 256-bit, 512-bit, or some other length DH public keys g^x and g^y. What would be your recommendation to them?

Solution

Assuming that \"p\" is a prime number and \"g\" is a primitive root of \"p\".

Bob could generate a secret value x and find (g^x mod p), call this value as A. This A will be sent to Alice.

Similarly Alice could generate a secret value y and find (g^y mod p), call this value as B. This B will be sent to Bob.

Now, Alice will calculate (A^y mod p) and Bob will calculate (B^x mod p).

If we clearly see   [(g^x mod p)^y mod p] and [(g^y mod p)^x mod p] are same as (A^y mod p) and (B^x mod p) respectively and also both will generate a same result.

This algorithm of sharing a secret key will be very strong for larger P values. Larger the value of P the larger will be the value of g^x and g^y. Thus, for higher security it is always recommended to got with 512 bit keys.