A new method is proposed to design short signature schemes based on difficulty of factorizing a composite number n = qr, where q and r are two large primes. Using the method new digital signature schemes (DSS) with the 320-bit and 240-bit signature size are developed. The characteristic feature of the 240-bit signature DSS is the use of ”three-level” verification equation, for example, R = ¯® kgH mod n mod p, where k = ¡R®g mod n mod p¢mod ±. The (k; g) signature corresponds to the H hash value and represents a pair of natural numbers having the size of 80 and 160 bits, respectively. The ± modulus is a prime number. The public key is the triple (®; ¯; p), where p = 2n 1 is prime, ¯ is the q order element modulo p, ® is the° order element modulo q. The private key is represented by the pair of two prime numbers (q; °).