We present modular reduction algorithms over finite fields of large characteristic that allow the use of redundant modular arithmetic. This technique provides constant time reduction algorithms. Moreover, it can also be used to strengthen the differential side-channel resistance of asymmetric cryptosystems. We propose modifications to the classic Montgomery and Barrett reduction algorithms in order to have efficient and resistant modular reduction methods. Our algorithms are called dynamic redundant reductions as random masks are intrinsically added within each reduction for a small overhead. This property is useful in order to thwart recent refined attacks on public key algorithms.