Paper 2026/616 Original: eprint.iacr.org/2026/616 ↗

On the properties of arithmetic crosscorrelation for sequences with coprime periods

Abstract

Arithmetic correlation is a critical performance measure for pseudorandom sequences generated by feedback with carry shift registers (FCSRs), extending classical correlation by accounting for carry propagation. Chen et al. proved that for binary sequences with coprime periods, the arithmetic crosscorrelation is constant, and established bounds for Legendre sequences and $m$-sequences. In this paper, we further investigate the arithmetic crosscorrelation of sequences with coprime periods. We derive upper bounds for sequences constructed from the Legendre symbol, which generalize classical Legendre sequences, and for sequences generated by trace functions. In addition, we show that the constant property of arithmetic crosscorrelation extends to non-binary sequences with coprime periods.