Lecture 2 Flashcards
What makes a key exchange protocol secure?
If, in the presence of an eavesdropper, for all probabilistic polynomial-time adversaries, their success probability is only negligibly better than 1/2
What is the best way to break Diffie-Hellman algorithm?
The “General Number Field Sieve”.
What attacks is Diffie-Hellman vulnerable to?
Though it is secure from eavesdroppers, it is completley insecure against man-in-the-middle attacks. The adversary can intercept the chosen exponents and then swap them out for their own.
What is the definition of a Key Exchange?
A probabilistic protocol dependent on random bits.
A security parameter 1n is input.
A session key ka and kb from {0,1}n is output.
In an honest execution of the protocol: ka = kb = k
When is a key exchange secure?
A key exchange protocol is only secure in the presence of an eavesdropper if, for all probabilistic polynomial-time adversaries A, their success probability is only negligibly* better than 1/2.
What does key exchange rely on more than computation?
Indistinguishability - this is much stronger than requiring that the adversary be unable to compute the session K key,
What is the “Merkle Puzzle Key Exchange”?
Choose random P in {0,1}^32
Choose random x, k in {0, 1}^128
puzzle <- E(({0}^96}||P), “puzzle” x, k)
E(({0}^96}||P) = Random encryption key.
“puzzle || x = Random ID.
k) = random session key.
Why is the “Merkle Puzzle Exchange” not acceptable?
There is only a quadratic gap in terms of computation for the authorised receiver vs the adversary, which is not great.
What is Zp? How is it structured?
A cyclic group which is generated by g.
It is structured: {1, g, g2, g3, …, gp-2} = (Zp)*
Example:
p=5: {1, 3, 3^2, 3^3} = {1, 3, 4, 2} = (Z5)*
What is the “order” of a generator?
It is the size of the generated group <g>.</g>
Or, ord(g) := |<g>|.</g>
