comparison of security for identity based signature and Hashing (SHA-1) the identities I would like to know which method can provide better security: using identity based signature or hashing the identities and message (using SHA-1) for authentication?
Of the two, identity based is more secure. In fact, unless you have left details out of the question, a SHA-1 hash (or any hash for that matter) of the sender's identity and the message content provides no source authentication (or data integrity check).

According to your comment, the way you would use SHA-1 to authenticate this is to concatenate the senders identity and the message, and compute the SHA-1 hash of that value. The problem is, anyone who knows your identifier can do this for any message. To illustrate this, consider the message I, SARA, give all my money to mikeazo.. Surely you wouldn't send this message, but, as proof that you sent it, here is the "authentication" tag: 92a7904e083e41d8667b92b7100d9d970eb0e84c. 

You can check that SHA-1(SARA I, SARA, give all my money to mikeazo.) == 92a7904e083e41d8667b92b7100d9d970eb0e84c. So that message must have come from you, so where is my money?