Generalized Triangular Dynamical System: An Algebraic System for Constructing Cryptographic Permutations over Finite Fields Article Swipe

MAKE IMPACT

Arnab Roy , Matthias Steiner · YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2204.01802

In recent years a new class of symmetric-key primitives over $\mathbb{F}_p$ that are essential to Multi-Party Computation and Zero-Knowledge Proofs based protocols have emerged. Towards improving the efficiency of such primitives, a number of new block ciphers and hash functions over $\mathbb{F}_p$ were proposed. These new primitives also showed that following alternative design strategies to the classical Substitution-Permutation Network (SPN) and Feistel Networks leads to more efficient cipher and hash function designs over $\mathbb{F}_p$ specifically for large odd primes $p$. In view of these efforts, in this work we build an \emph{algebraic framework} that allows the systematic exploration of viable and efficient design strategies for constructing symmetric-key (iterative) permutations over $\mathbb{F}_p$. We first identify iterative polynomial dynamical systems over finite fields as the central building block of almost all block cipher design strategies. We propose a generalized triangular polynomial dynamical system (GTDS), and based on the GTDS we provide a generic definition of an iterative (keyed) permutation over $\mathbb{F}_p^n$. Our GTDS-based generic definition is able to describe the three most well-known design strategies, namely SPNs, Feistel networks and Lai--Massey. Consequently, the block ciphers that are constructed following these design strategies can also be instantiated from our generic definition. Moreover, we find that the recently proposed \texttt{Griffin} design, which neither follows the Feistel nor the SPN design, can be described using the generic GTDS-based definition. We also show that a new generalized Lai--Massey construction can be instantiated from the GTDS-based definition. We further provide generic analysis of the GTDS including an upper bound on the differential uniformity and the correlation.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2204.01802

PDF

https://arxiv.org/pdf/2204.01802

OA Status

green

Cited By

2

Related Works

10

OpenAlex ID

https://openalex.org/W4224310057

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W4224310057

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.2204.01802

Digital Object Identifier

Title

Generalized Triangular Dynamical System: An Algebraic System for Constructing Cryptographic Permutations over Finite Fields

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2022

Year of publication

Publication date

2022-04-04

Full publication date if available

Authors

Arnab Roy, Matthias Steiner

List of authors in order

Landing page

https://arxiv.org/abs/2204.01802

Publisher landing page

PDF URL

https://arxiv.org/pdf/2204.01802

Direct link to full text PDF

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://arxiv.org/pdf/2204.01802

Direct OA link when available

Concepts

Block cipher, Symmetric-key algorithm, Mathematics, Hash function, Cryptography, Discrete mathematics, Permutation (music), Block (permutation group theory), Combinatorics, Theoretical computer science, Computer science, Encryption, Algorithm, Public-key cryptography, Acoustics, Operating system, Computer security, Physics

Top concepts (fields/topics) attached by OpenAlex

Cited by

2

Total citation count in OpenAlex

Citations by year (recent)

2023: 2

Per-year citation counts (last 5 years)

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload