This question is from Understanding Cryptography (Applied cryptography) In pract

Question

This question is from Understanding Cryptography (Applied cryptography)

In practice, it is sometimes desirable that both communication parties influence the
selection of the session key. For instance, this prevents the other party from choosing a key which
is a weak key for a symmetric algorithm. Many block ciphers such as DES have weak keys.
Messages encrypted with weak keys can be recovered relatively easily from the cipher-text.
Develop a protocol in which both parties influence the key. Assume that both Alice and Bob have
a pair of public/private keys for the RSA cryptosystem. Please note that there are several valid
approaches to this problem. Show just one.

Explanation / Answer

Alice and Bob then work independently:

Alice

Bob

Although Alice and Bob will really choose large values for N and G, I will use small values for example only; let's use N=7 and G=3.

Alice

Bob

In this example, then, Alice and Bob will both find the secret key 1 which is, indeed, 36 mod 7 (i.e., GXAXB = 323). If an eavesdropper (Mallory) was listening in on the information exchange between Alice and Bob, he would learn G, N, YA, and YB which is a lot of information but insufficient to compromise the key; as long as XA and XB remain unknown, K is safe. As said above, calculating Y = GX is a lot easier than finding X = logG Y.

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