Ensuring integrity and authentication for data transfer are essential security goals that will be achieved using cryptography. In this context, the cryptographic hash algorithm was employed in many cryptographic applications and protocols such as digital signature, message authentication code, data source authentication, Secure Socket Layer and Pretty Good Privacy. An efficient security algorithm requires continuous maintenance to fix the vulnerability exploited by an attacker to launch an actualized threat. The prefix collision attack was a successful attack against SHA-1 that took place in January 2020 which exploited the weak point in the algorithm design. As a consequence of this attack, some authentication protocols rejected the certificates that were signed with SHA-1. This paper introduces a randomization principle to control the threats against SHA-1. Randomization is achieved by a pseudo-random sequence generator which consists of Linear Feed Back Register and Best Resilient Function. The pseudo-random sequence operation of the improved algorithm receives an input binary sequence of length 128-bit and produces an arbitrary binary output with good randomness properties. The proposed algorithm works in two modes. The SHA1-Tight in which the proposed operation is utilized in the message expansion stage, and the compression function. While in the SHA1-Light, the SRS is implemented in the message expansion step only. In the test scenarios, SHA1-Tight passes tests with the optimal value and demonstrates the algorithm efficiency for signing a certificate on the authentication protocol. The SHA1-Light passes tests with a result close to the optimal value and ensures message integrity. On the other hand, the obtained results from SHA-1 are disappointing The proposed works imply the effectiveness of utilizing randomness in designing hash algorithms to provide collision resistance.