All defined Woodall primes hit the p % 4n === 3n shortcut - modular power algorithm, not really modular square root.

[esc-mhild]

Hello, Vlad!

Thank you for sharing this work.

All of the Woodall primes you define satisfy p % 4n === 3n and therefore hit the shortcut in the Tonelli-Shanks algorithm.

In this situation, the tonelliShanks function is redundant and POW algorithm degenerates into the computation of a modular power.

This may be good enough for the purpose, but we can get rid of a lot of brouhaha in the code and your package deserves an updated description of what it does.

Best wishes,

M.

[esc-mhild]

BTW, this also means that a client can cut the CPU cycles required to pass your captcha test by about half: Your tonelliShanks function checks for the existence of a solution via a modular power. For challenges generated by your library, this check must always succeed. However, it makes up about half of the computing time spent by the client (the other half is the shortcut I mentioned before).