Silent-Radix Cryptography: Exploiting the Base Ambiguity of Positional Notation as a Cryptographic Primitive

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-14
DOI
https://doi.org/10.5281/zenodo.21046733
Primary Topic
Cryptographic Implementations and Security
Type
article
Field-Weighted Citation Impact
0.00
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article

Silent-Radix Cryptography: Exploiting the Base Ambiguity of Positional Notation as a Cryptographic Primitive

Rowan Brad Quni-Gudzinas
Zenodo (CERN European Organization for Nuclear Research)
Cryptographic Implementations and Security
article

Silent-Radix Cryptography: Exploiting the Base Ambiguity of Positional Notation as a Cryptographic Primitive

Rowan Brad Quni-Gudzinas
article en

Abstract

The observation that a positional numeral cannot internally specify its own base — the "silent radix" problem identified in §1.1 of the Ultrametric Foundation — is not merely a philosophical curiosity. It is a cryptographic primitive. We formalize this as **Silent Radix Encryption (SRE)**, a key encapsulation mechanism (KEM) where the shared secret is derived from the base-$b$ interpretation of publicly transmitted decimal digits. Only a party who knows the secret base $b$ can recover the correct key. Eve, seeing the same decimal digit string $N$, must solve a variant of the integer knapsack problem where the weights ($b^i$) are unknown: given $N = \sum d_i \cdot 10^i$, find $b$ such that $K = \sum d_i \cdot b^i$ decodes the ciphertext correctly. For $b \sim 2^{128}$, brute force is infeasible. ---

Zenodo (CERN European Organization for Nuclear Research)
Q-Flex (United States) (US)
Openalex Percentile: Top 39%
Cryptographic Implementations and Security
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