Abstract
Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law–Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR's scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.
Highlights
IntroductionInformation theoretic (i.e., unconditional) security [1] means that the stated security level—either perfect or imperfect, as in any physical system [2]—holds even for cases when the abilities of an eavesdropper (generally called ‘‘Eve’’) are limited only by the laws of physics
Information theoretic security [1] means that the stated security level—either perfect or imperfect, as in any physical system [2]—holds even for cases when the abilities of an eavesdropper are limited only by the laws of physics
We show there that none of these ways of cracking work against the KLJN scheme, which proves that thermodynamics is essential for the security of KLJN
Summary
Information theoretic (i.e., unconditional) security [1] means that the stated security level—either perfect or imperfect, as in any physical system [2]—holds even for cases when the abilities of an eavesdropper (generally called ‘‘Eve’’) are limited only by the laws of physics. Alice and Bob know essential parameters that Eve does not have access to: they know their own resistance value and the exact amplitude of their noise fed into the line They do not need to utilize the non-ideality-based miniscule differences seen by Eve or the even smaller differences that Eve may generate by active (invasive) attack while staying hidden; they only need to monitor the channel voltage/current and identify which one of the three significantly different levels of the mean-square noise takes place. In nonideal cases involving an information leak, and when the parameters are sufficiently close to the ideal limit, p can be given as p~0:5zq, ð12Þ where 0vqvv0:5; here q~0 would mean a perfectly secure key The reason for this behavior is easy to see if one realizes that Eve’s small DC signal component offsets the center (mean value) of the probability density burying the large Gaussian noise. This ability of Alice and Bob is another indication that they are in full control of the maximum of statistical information Eve is able to access
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