This article describes the idea of utilizing Attested Execution Secure Processors (AESPs) that fit into building a secure Self-Sovereign Identity (SSI) system satisfying Sybil-resistance under permissionless blockchains. Today’s circumstances requiring people to be more online have encouraged us to address digital identity preserving privacy. There is a momentum of research addressing SSI, and many researchers approach blockchain technology as a foundation. SSI brings natural persons various benefits such as owning controls; on the other side, digital identity systems in the real world require Sybil-resistance to comply with Anti-Money-Laundering (AML) and other needs. The main idea in our proposal is to utilize AESPs for three reasons: first is the use of attested execution capability along with tamper-resistance, which is a strong assumption; second is powerfulness and flexibility, allowing various open-source programs to be executed within a secure enclave, and the third is that equipping hardware-assisted security in mobile devices has become a norm. Rafael Pass et al.’s formal abstraction of AESPs and the ideal functionality $\color{brown}{\mathcal{G}_\mathtt{att}}$ enable us to formulate how hardware-assisted security works for secure digital identity systems preserving privacy under permissionless blockchains mathematically. Our proposal of the AESP-based SSI architecture and system protocols, $\color{blue}{\Pi^{\mathcal{G}_\mathtt{att}}}$, demonstrates the advantages of building a proper SSI system that satisfies the Sybil-resistant requirement. The protocols may eliminate the online distributed committee assumed in other research, such as CanDID, because of assuming AESPs; thus, $\color{blue}{\Pi^{\mathcal{G}_\mathtt{att}}}$ allows not to rely on multi-party computation (MPC), bringing drastic flexibility and efficiency compared with the existing SSI systems.