Mathematical Model of QBFT Consensus GAS Efficiency Based on RIP-7212 / EIP-7951 Elliptic Curve Precompiles on EVM Smart Contracts

Verifying secp256r1 (NIST P-256) elliptic curve digital signatures on the Ethereum Virtual Machine (EVM) conventionally incurs high computational complexity requiring up to 348,120 gas per verification. This execution overhead presents a severe bottleneck for adopting WebAuthn/Passkey biometric authentication and Account Abstraction (ERC-4337) across enterprise blockchain networks running Quorum Byzantine Fault Tolerance (QBFT) consensus. This theoretical study formulates a deterministic mathematical model to evaluate verification gas efficiency and analyze its impact on the upper bound of block transaction capacity (N_max) and QBFT consensus latency dynamics. The model evaluates a baseline pure Solidity implementation against the P256VERIFY precompile (address 0x0100) under RIP-7212 (3,450 gas) and EIP-7951 (6,900 gas) specifications. Mathematical formulation and simulation demonstrate theoretical gas reduction efficiencies of 99.01% (RIP-7212) and 98.02% (EIP-7951). Reducing verification overhead expands the gas-based upper bound of block capacity by 15.20x under a 30M block gas limit scenario, mitigating block validation latency delays across QBFT networks.