Millis Function in Due

Hardware Arduino Due
15

SysTick->CTRL &= ~SysTick_CTRL_ENABLE_Msk ; ---- > this corresponds to noInterrupts();
and SysTick->CTRL |= SysTick_CTRL_ENABLE_Msk; -----> this corresponds to interrupts();

Those ONLY disable the timer used for millis(); other interrupts (serial, perhaps?) can still occur.

Due DOES include it's own version of interrupts() and noInterrupts()
Maybe you should just use those?