Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages

Alex Shafarenko

doi:10.3390/cryptography9020027

Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages

Alex Shafarenko

Research output: Contribution to journal › Article › peer-review

1 Downloads (Pure)

Abstract

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.

Original language	English
Article number	27
Pages (from-to)	1-23
Number of pages	23
Journal	Cryptography
Volume	9
Issue number	2
Early online date	29 Apr 2025
DOIs	https://doi.org/10.3390/cryptography9020027
Publication status	E-pub ahead of print - 29 Apr 2025

Access to Document

10.3390/cryptography9020027Licence: CC BY

Final_Version
© 2025 The Author(s). Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/
Final published version, 471 KBLicence: CC BY

Cite this

@article{355012a087db47bcb128a198af883f16,

title = "Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages",

abstract = "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{\textquoteright}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.",

author = "Alex Shafarenko",

note = "{\textcopyright} 2025 The Author(s). Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/ ",

year = "2025",

month = apr,

day = "29",

doi = "10.3390/cryptography9020027",

language = "English",

volume = "9",

pages = "1--23",

journal = "Cryptography",

issn = "2410-387X",

publisher = "MDPI Multidisciplinary Digital Publishing Institute",

number = "2",

}

TY - JOUR

T1 - Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages

AU - Shafarenko, Alex

N1 - © 2025 The Author(s). Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/

PY - 2025/4/29

Y1 - 2025/4/29

N2 - 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.

AB - 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.

U2 - 10.3390/cryptography9020027

DO - 10.3390/cryptography9020027

M3 - Article

SN - 2410-387X

VL - 9

SP - 1

EP - 23

JO - Cryptography

JF - Cryptography

IS - 2

M1 - 27

ER -

Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages

Abstract

Access to Document

Fingerprint

Cite this