1. A cryptographic method a) with at least one computing step containing a modular exponentiation E E&equals;x d (mod p·q ) with a first prime factor p, a second prime factor q, an exponent d and a base x, whereby b) for carrying out the modular exponentiation two natural numbers r and s are chosen with the condition that d is relatively prime to &phgr;(kgV(r,s)), and whereby the following computing steps are performed: ti x 1 &equals;x (mod p·r ) x 2 &equals;x (mod q·s ) d — 1&equals; d (mod &phgr;( p·r )) d — 2&equals; d (mod &phgr;( q·s )) z 1 &equals;x 1 d — 1 (mod p·r ) z 2 &equals;x 2 d — 2 (mod q·s ) and whereby &phgr;(.) is the Eulerian function and kgV(r,s) is the smallest common multiple of r and s, c) then a number z is calculated according to the Chinese Remainder Theorem from z 1 and z 2 with z&equals;z 1 (mod p·r); z&equals;z 2 (mod q·s); d) the result E of the exponentiation is calculated by reduction of z modulo p·q, e) the previously calculated number z and thus the result E is checked for computing errors in a checking step, f) the checking step comprises the following computing operations: f1) calculating the smallest possible natural number e with the property e·d&equals;1 (mod &phgr;(kgV(r,s))) with the aid of the Extended Euclidean Algorithm, f2) calculating the value C&equals;z e (mod kgV(r,s)), f3) comparing the values x and C modulo kgV(r,s), whereby the result of the modular exponentiation E is rejected as faulty if x≠C (mod kgV(r,s)).