On the pseudorandom properties of filtered Legendre symbol sequences using three polynomials

Gyarmati, Katalin and Müllner, Károly (2026) On the pseudorandom properties of filtered Legendre symbol sequences using three polynomials. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA. ISSN 0081-6906 (In Press)

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Abstract

This paper presents a further development of a well-known construction that relies on polynomials and the Legendre symbol. To address theoretical security concerns regarding the original method, which used a single polynomial, we introduce a new approach that combines three different polynomials to generate the sequence, thereby enhancing its security. We prove that the sequences produced by this new construction also exhibit strong pseudorandom properties with respect to the pseudorandom measures introduced by Mauduit and Sárközy.

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