FIELD: communication, in particular, verification of authenticity of messages which are sent through telecommunication lines. SUBSTANCE: method involves generation of digital signature B by means of raising digital signal of source message A to secret power s by modulo m which is product of two secret primes p and q: B = Asmod m.. Then digital signals of source message and signature are sent to receiver and authenticity is checked by means of public key. In contrast to RSA method, secret power s conforms to condition ((s+x)•y)mod((p-1)•(q-1)) = z,, and authenticity is checked by means of two test integers C and D: 
, where e is public exponent, x, y, z are given integers, At and Bt are message and signature which are sent through communication line. Final check involves comparison of these test integers. EFFECT: in comparison with RSA speed of signature generation is doubled for equal bit-length of key and safety. 3 cl, 1 dwg
