In order to protect electronic data, pseudorandom cryptographic keys generated by a standard function known as a key derivation function play an important role. The inputs to the function are known as initial keying materials, such as passwords, shared secret keys, and non-random strings. Existing standard secure functions for the key derivation function are based on stream ciphers, block ciphers, and hash functions. The latest secure and fast design is a stream cipher-based key derivation function (SCKDF2). The security levels for key derivation functions based on stream ciphers, block ciphers, and hash functions are equal. However, the execution time for key derivation functions based on stream ciphers is faster compared to the other two functions. This paper proposes an improved design for a key derivation function based on stream ciphers, namely I−SCKDF2. We simulate instances for the proposed I−SCKDF2 using Trivium. As a result, I−SCKDF2 has a lower execution time compared to the existing SCKDF2. The results show that the execution time taken by I−SCKDF2 to generate an n-bit cryptographic key is almost 50 percent lower than SCKDF2. The security of I−SCKDF2 passed all the security tests in the Dieharder test tool. It has been proven that the proposed I−SCKDF2 is secure, and the simulation time is faster compared to SCKDF2.