Computer verification of gao assumption, related with obtaining of high order elements in finite fields
We have performed computer calculations in Maple environment for verification of Gao assumption for finite fields of characteristic 2, 3, 5 and presented correspondent results. If the assumption is true, then it is possible to construct explicitly in these fields in polynomial time elements of high multiplicative order that are used in cryptography (Diffie-Hellman protocol, El-Gamal public key cryptosystem, El-Gamal digital signature).