  We present a new construction of a One Time Pad (OTP) with inherent diffusive
properties and a redundancy injection mechanism that benefits from them. The
construction is based on interpreting the plaintext and key as members of a
permutation group in the Lehmer code representation after conversion to
factoradic. The so constructed OTP translates any perturbation of the
ciphertext to an unpredictable, metrically large random perturbation of the
plaintext. This allows us to provide unconditional integrity assurance without
extra key material. The redundancy is injected using Foata's "pun": the reading
of the one-line representation as the cyclic one; we call this Pseudo Foata
Injection. We obtain algorithms of quadratic complexity that implement both
mechanisms.
