Traditional cryptographic methods for software integrity verification rely on validating cryptographic signatures attached to software binaries. However, these methods primarily focus on load-time measurements and may be circumvented by an attacker interfering with the boot process. To address this limitation, we propose a novel approach that uses side-channel data collected during software execution to generate a proof of software integrity. Through a side-channel trace encoder, we generate cryptographic keys derived from the unique side-channel profiles of software processes. This ensures that only the processes with expected side-channel characteristics can produce the valid key, effectively linking software integrity verification to runtime behavior. We demonstrate the feasibility of this approach in a secure boot setting compliant with the TCG DICE framework. The presented solution provides holistic boot protection while enhancing resilience against attacks such as fault injection, misconfiguration, and downgrading of security algorithms.