The paper evaluates the performances of the Secure Remote Password (SRP) authentication protocol computations. The software implementations are written in C with the MIRACL and OpenSSL libraries utilized and evaluated on Pentium III and ARM9TDMI microprocessors. Accelerating the performance of the critical computational parts with dedicated hardware is discussed. The measurements show that with a prime modulus of length 2048 bits the SRP computations take 80.5 ms on 700 MHz Pentium III and 503 ms on 200 MHz ARM9TDMI with the highest software optimizations within the libraries. With maximal precomputation the execution times can be decreased down to 30.6 ms and 194 ms respectively. By adding appropriate hardware support for the SHA-1 hash computation and exponentiation their cycle counts can be reduced at least by factors of 10 and 20.