A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key e and system parameters p, q where p and q are primes and ed=1 mod (p-1) (q-1). The method comprises the steps of obtaining a value r, and exponentiating the value r to the power e to obtain an exponent r.sup.e mod p, combining said exponent r.sup.e with the message m to obtain a combined value r.sup.e m and mod p; selecting a value s and obtaining a difference (d-s), exponentiating the combined value with said difference to obtain an intermediate exponent (r.sup.em).sup.d-s, multiplying the intermediate exponent by a value m.sup.s to obtain a resultant value equivalent to r.sup.1-es m.sup.d and multiplying the resultant value by a value corresponding to r.sup.1-es to obtain an exponent corresponding to m.sup.d mod p.