Abstract
The random number generators (RNGs) are an indispensable tool for information security. Among various approaches, the radioactive decay has been considered as a promising candidate of RNGs for over half a century, on account of its seemingly unpredictable decay timings as quantum phenomena. However, the security of these radioactive RNGs has not been proven so far. Here we prove the security by a change of tactics, that is, by rewriting decay timings into decay directions, which allows us to ensure the secrecy with the help of the parity invariance deeply rooted in the fundamental law of nature. Our result demonstrates that the foundational properties of particle physics, such as the symmetry of interactions, can be used as a firm basis for the RNGs.
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