Paper 2026/829

Beyond Binary: crosscorrelation of Cubic, Quartic and Quintic Character Sequences

, Ramakrishna Mission Vivekananda Educational and Research Institute, Kokata, Institute for Advancing Intelligence (IAI), TCG CREST, Kolkata

Sampa Dey, Indian Statistical Institute, Kolkata

Sampurna Pal, Indian Institute of Technology Kanpur

Subhabrata Samajder, Institute for Advancing Intelligence (IAI), TCG CREST, Kolkata

Rana Barua, Institute for Advancing Intelligence (IAI), TCG CREST, Kolkata

Abstract

The arithmetic crosscorrelation of pseudorandom sequences is a fundamental measure of their suitability for applications in cryptography and communications. While prior works have studied this quantity for binary sequences, the non-binary setting has remained largely open. In this paper, we initiate a systematic study of arithmetic crosscorrelation for non-binary pseudorandom sequences constructed from higher-order multiplicative characters over finite fields. For two quartic sequences of co-prime periods $P$ and $Q$ defined via polynomials of degree $d$, we establish that $$\left|C^{A}_{\mathcal{S},\mathcal{T}}(\tau)\right| \ \ll \ dP^{1/2}Q(\log P)^{2},$$ for all shifts $\tau$, using character orthogonality, joint pattern distribution and the Weil bound. An analogous bound is also derived for cubic and quintic character sequences. To the best of our knowledge, these are the first nontrivial upper bounds on the arithmetic crosscorrelation of non-binary pseudorandom sequences, generalizing prior works of Chen et al. (IEEE IT, 2022) and Yan and Ke (eprint archive, 2026).

@misc{cryptoeprint:2026/829,
      author = {Mriganka Dey and Sampa Dey and Sampurna Pal and Subhabrata Samajder and Rana Barua},
      title = {Beyond Binary: crosscorrelation of Cubic, Quartic and Quintic Character Sequences},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/829},
      year = {2026},
      url = {https://eprint.iacr.org/2026/829}
}