Hash functions are the most widespread among all cryptographic primitives, and are currently used in multiple cryptographic schemes and in security protocols. Cryptographic hash function plays an important role in the world of cryptography. They are employed in many applications for digital signatures, message authentication data integrity and key derivation. A hash function is a map from variable-length input bit strings to fixed-length output bit strings. Digital Signature is a way for secure and authentic data transmission This paper is proposed a method to provide a digital signature (16 byte) from random generator based on hash function (SHA1). Security of this signature based on strength of the function that is used to generate a key (160 bit) because the SHA-1 has been designed to satisfy the different level of enhanced security and to resist the attacks. Then the (160 bit) are inputted to random key function to produce a (100) random keys. After that compressed the key from 20 byte to 16 byte then using this key as a digital signature to sign the encrypted message. The generated key is passing from some randomness test so the time needed to encrypt a message by key (20 byte) is 16.3143 Msec and (16 byte) is 9.5998 Msec. Choosing the SHA-1 based improve random key generator to improve time, security and ensure data integrity.