Randomness is an imperative component in every cryptographic algorithm to guarantee secret keys are unpredictable and secured against all forms of attacks. Speck generated sequence is non-random, a clear sign that it falls beyond the acceptable success rate when tested in statistical analysis. Thus, this study resolves the non-randomness by integrating a novel key derivation function that uses elementary operators designed for lightweight application. This design aims not to compromise performance when implemented on software and hardware. As a result, the modified Speck successfully passed the NIST SP 800 - 22 and Dieharder v3.31.0 Statistical Test Analysis as no p-value is flagged as failed during testing. Hence, making modified Speck cryptographically secured. Nevertheless, a 1.06% decrease in the figure of merit of the modified Speck still makes it worthier in a resource-constrained Internet of Things application as contrasted to Speck because it is proven to be beyond cryptographically secured.