Abstract: The concept of batch verifying multiple digital signatures is to find a method by which multiple digital signatures can be verified simultaneously in a lower time complexity than separately verifying all the signatures. In this article, we analyze the complexity of the batch verifying schemes defined by Li, Hwang and Chen in 2010, and propose a new batch verifying multiple digital signature scheme, in two variants: one for RSA - by completing the Harn’s schema with an identifying illegal signatures algorithm, and the other adapted for a modified Elliptic Curve Digital Signature Algorithm protocol.