A very fast method for verifying digital signatures

We consider the problem of broadcasting sensitive information to many low cost receivers when the authenticity and integrity of the received messages are the determining factors but secrecy is not important. Although several methods exist to authentify information, as a rule, they lack the asymmetry the transmission system itself exhibits. Therefore, we propose a highly non-symmetric algorithm to generate and verify digital signatures. The algorithm is based on the computation of square roots. Since valid messages have a definite structure, we address the question of choosing the factors to get around the difficulty caused by the quadratic nonresidues.<>