- Page 1. Wiretap Channels with Random States Paul Cuff (Princeton University), Ziv Golfeld, Haim Permuter Page 2. Wiretap Channel Xn Yn PY,Z|X Zn Memoryless Dec Enc M (nR bits) - Reliable communication - Zn contains no information about M Secrecy Capacity: Page 3. Solution PY,Z|X PX|U U X Y Z Cs = max PX,UI(U;Y ) - I(U;Z) Page 4. Solutions 1975: Wyner introduced the problem and gave solution for degraded channels (U=X is sufficient) 1978: Csiszár and Körner gave solution for all channels Page 5. Encoding Random Codebook Pad with random garbage bits 01001011010111100100 011001010 Message Padding Transmitted together in one block Page 6. Encoding Diagram Xn Yn PY,Z|X Zn Memoryless Dec Enc M (nR bits) M' (nR' bits) Given M, can decode M'. R' ≈ I(X;Z) ⟹ Page 7. Wyner's security argument I(M,M';Zn) = I(M;Zn) + I(M';Zn|M) I(Xn;Zn) ≈ nI(X;Z) H(M') = nR' Decodable if R'