The welch-gong stream cipher-evolutionary path

This survey presents the rich history of the Welch-Gong (WG) Stream cipher family. It has been a long journey that lead the WG stream ciphers to become practical. The evolutionary path is a combination of mathematical endeavour and engineering striving to transfer pure mathematical functions to practical encryption algorithms for various applications. This path began as the pioneering work on WG transformation sequences with 2-level autocorrelation, leading to important breakthroughs in the early 2000's, such as the submission of the first WG stream cipher to the eSTREAM competition in 2005 and the subsequent introduction of the WG stream cipher family WG(m, l), followed by extensive work on particular instances proposed for various (mostly lightweight) applications. A recent construction using a WG permutation is the authenticated encryption WAGE, submitted to the NIST LWC competition in 2019. The story of the WG stream cipher is by far not finished. The future opens numerous possibilities for WG stream ciphers and WAGE, with applications in both lightweight environments and in high-performance computing. We conclude the survey with new ideas and open problems.