A technique for efficient encryption for use with devices such as smartcards restricted in memory resource, including a calculation unit for reconstructing a large number of small primes, a sieving unit for checking the divisibility of an integer by small primes, a recoding unit for changing the representation of an integer, and a primality testing unit. The sieving unit eliminates “bad” candidates by checking their divisibility by small primes reconstructed by the calculation unit. The primality of the remaining candidates is tested using the primality testing unit. The primality testing unit uses the recoding unit to change the representation of prime candidates. The primality testing unit performs a primality test using the representation after change.