We propose a new key sharing protocol executed through any constant parameter noiseless public channel (as Internet itself) without any cryptographic assumptions and protocol restrictions on SNR in the eavesdropper channels. This protocol is based on extraction by legitimate users of eigenvalues from randomly generated matrices. A similar protocol was proposed recently by G. Qin and Z. Ding. But we prove that, in fact, this protocol is insecure and we modify it to be both reliable and secure using artificial noise and privacy amplification procedure. Results of simulation prove these statements.