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.

翻译：在2012年的一篇短预印本中，引入了一种非常规密码。现在，我们在本文中取其表示核心，将其形式化，并以此为基础，将一次性密码本干净地推广到非均匀进制上，称之为混合进制一次性密码本（MR-OTP）。我们证明MR-OTP实现了香农完美保密性，展示了经典二进制OTP恰好是所有进制均等于2的特殊情况，并且固定进制变体可恢复任意字母表上的OTP。随后，我们考察了保密进制是否能降低实现完美保密所需的密钥熵（结论为不能）。最后，我们提出一个基于密钥滚动、可保持完美保密性的可用会话协议，并诚实地阐述了尚待解决的关键问题。