In a short 2012 preprint, an unconventional cipher was introduced, now in this note we take that representational core, formalize it, and use it as the basis for a clean generalization of the one-time pad to non-uniform bases, which we call the Mixed-Radix One-Time Pad (MR-OTP). And we prove that the MR-OTP achieves Shannon perfect secrecy, show that the classical binary OTP is exactly the all-bases-equal-2 special case, and that fixed-base variants recover OTPs over arbitrary alphabets. We then examine whether secret bases can lower the key entropy required for perfect secrecy (they cannot). We close with a usable session protocol based on key rolling that preserves perfect secrecy, and with an honest account of the open problems.
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References (10)
06iv) We describe a usable session protocol based on key rolling that preserves perfect secrecythe mixed bases provide encoding efficiency and adaptivity rather than a reduction in key length (Section 5)
07Encoding efficiency (always safe)The gain is representational convenience
08Entropy reduction (conditional, and dangerous)ciphers
09i) We formalize the mixed-radix representation underlying [2] and define the Mixed-Radix One-Time Pad (MR-OTP), the natural one-time pad over a mixed-radix digit system(Section 2)
10iii) We state and resolve a tempting conjecture: that secret bases might let the message-covering key be shorter than the message while retaining perfect secrecystrong