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• W2022231844 abstract "We introduce a binary erasure wiretap channel of type II in which the number of eavesdropped bits μ becomes available a posteriori. We aim at achieving perfect secrecy over such a channel model. The most appropriate application is a secret key agreement scheme. We present a secret key agreement scheme that adopts the formulation S = HX of Wyner-Ozarows's linear coset coding. The scheme is based on the following simple observation: even if some information on a secret message leaked out, I(S; X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>μ</sub> ) >; 0, where X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>μ</sub> is a binary sequence of length μ, it is still possible to have perfect secrecy I(S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>J</sub> ; X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>μ</sub> ) = 0 for some subsequence S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>J</sub> of S. Our secret key agreement scheme achieves perfect secrecy by taking only those subsequences S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>J</sub> that are independent of the eavesdropped bits X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>μ</sub> . Our secret key agreement scheme naturally leads to defining a security measure D <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>H</sub> (μ) for parity-check matrices such that the eavesdropper gets zero information on S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>J</sub> as long as the length of S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>J</sub> is less than D <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>H</sub> (μ). We study basic properties of D <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>H</sub> (μ) and prove the perfect secrecy of our key agreement scheme. For parity-check matrices of small sizes, we perform an exhaustive search for matrices maximizing D <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>H</sub> (μ)." @default.
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• W2022231844 date "2012-08-01" @default.
• W2022231844 modified "2023-09-23" @default.
• W2022231844 title "Perfect Secrecy Over Binary Erasure Wiretap Channel of Type II" @default.
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• W2022231844 doi "https://doi.org/10.1109/tifs.2012.2199629" @default.
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