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“secp256r1” elliptic curve is a standardized curve by NIST which has the same calculations by different input parameters with “secp256k1” elliptic curve used by the “ecrecover” precompiled contract. The cost of combined attacks and the security conditions are almost the same for both curves. Adding a precompiled contract which is similar to “ecrecover” can provide signature verifications using the “secp256r1” elliptic curve in the smart contracts and multi-faceted benefits can occur. One important factor is that this curve is widely used and supported in many modern devices such as Apple’s Secure Enclave, Webauthn, Android Keychain which proves the user adoption. Additionally, the introduction of this precompiled contract could enable valuable features in the account abstraction which allows more efficient and flexible management of accounts by transaction signs in mobile devices. Most of the modern devices and applications rely on the “secp256r1” elliptic curve. The addition of this precompiled contract enables the verification of device native transaction signing mechanisms. For example:
Apple’s Secure Enclave: There is a separate “Trusted Execution Environment” in Apple hardware which can sign arbitrary messages and can only be accessed by biometric identification.
Webauthn: Web Authentication (WebAuthn) is a web standard published by the World Wide Web Consortium (W3C). WebAuthn aims to standardize an interface for authenticating users to web-based applications and services using public-key cryptography. It is being used by almost all of the modern web browsers.
Android Keystore: Android Keystore is an API that manages the private keys and signing methods. The private keys are not processed while using Keystore as the applications’ signing method. Also, it can be done in the “Trusted Execution Environment” in the microchip.
Passkeys: Passkeys is utilizing FIDO Alliance and W3C standards. It replaces passwords with cryptographic key-pairs which is also can be used for the elliptic curve cryptography.
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Citing from: https://eips.ethereum.org/EIPS/eip-7212
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