Year: 2025
Type: article
Abstract: is a family of compression and hash functions over finite fields $$\mathbb {F}_q$$ F q for efficient Zero-Knowledge applications. Its round function is based on a novel permutation $$\mathcal {H}: \mathbb {F}_q^2 \rightarrow \mathbb {F}_q^2$$ H : F q 2 → F q 2 , called the open , which is parametrized by a permutation $$E: \mathbb {F}_q \rightarrow \mathbb {F}_q$$ E : F q → F q and two functions $$Q_\gamma , Q_\delta : \mathbb {F}_q \rightarrow \mathbb {F}_q$$ Q γ , Q δ : F q → F q . Over a prime field $$\mathbb {F}_p$$ F p with E a power permutation and $$Q_\gamma $$ Q γ , $$Q_\delta $$ Q δ quadratic functions with identical leading coefficient, the designers conjectured for the absolute value of the Walsh transform that $$\max _{\textbf{a} \in \mathbb {F}_p^2,\ \textbf{b} \in \mathbb {F}_p^2 {\setminus } \{ \textbf{0} \}} \left| \mathcal {W}_\mathcal {H} (\psi , \textbf{a}, \textbf{b}) \right| \le p \cdot \log \left( p \right) $$ max a ∈ F p 2 , b ∈ F p 2 \ { 0 } W H ( ψ , a , b ) ≤ p · log p . By exploiting that the open is CCZ-equivalent to the closed , we prove in this note that $$\max _{\textbf{a} \in \mathbb {F}_p^2,\ \textbf{b} \in \mathbb {F}_p^2 {\setminus } \{ \textbf{0} \}} \left| \mathcal {W}_\mathcal {H} (\psi , \textbf{a}, \textbf{b}) \right| \le (d - 1) \cdot p$$ max a ∈ F p 2 , b ∈ F p 2 \ { 0 } W H ( ψ , a , b ) ≤ ( d - 1 )
Source: Designs Codes and Cryptography
Author: Matthias Johann Steiner
Institution: University of Klagenfurt
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4407592430