Short signatures from the difficulty of factoring problem

For some practical applications there is a need of digital signature schemes (DSSes) with short signatures. The paper presents some new DSSes based on the difficulty of the factorization problem, the signature size of them being equal to 160 bits. The signature size is significantly reduced against the known DSS. The proposed DSSes are based on the multilevel exponentiation procedures. Three type of the exponentiation operations are used in the DSSes characterized in performing multiplication modulo different large numbers. As modulus prime and composite numbers are used. The latters are difficult for factoring and have relation with the prime modulus.