Non-Interactive Zero-Knowledge Proof Without Bilinear Pairing

The patent extracts the bilinear pairing operation from the verification process and replaces it with alternative cryptographic primitives. Specifically, the invention uses commitment schemes and zero-knowledge proofs that do not rely on bilinear pairings, thereby eliminating the computational burden while maintaining verification capability. The core verification logic is separated from the pairing operation and reimplemented using more efficient mathematical foundations.

The patent changes the underlying cryptographic parameters and assumptions. Instead of relying on the mathematical properties of bilinear pairings (such as the pairing-friendly curve parameters), the invention transitions to parameter sets compatible with commitment schemes and zk-SNARKs, such as different elliptic curve parameters or hash function parameters. This parameter change fundamentally alters the verification mechanism to be more computationally efficient.

The patent substitutes the mechanical computation of bilinear pairings with a different computational mechanism. The verification process is replaced using commitment schemes where the verifier checks consistency of commitments rather than performing pairing operations. For multiplication verification, the patent uses product proof mechanisms that rely on homomorphic properties of commitments rather than pairing-based arithmetic, dramatically reducing computational steps.

The patent performs preliminary actions during the proof generation phase that simplify subsequent verification. Commitments are pre-computed and embedded in the proof structure, allowing the verifier to check validity without performing expensive operations. The heavy computational lifting is shifted to the prover side during proof generation, while verification becomes a lightweight consistency check, thereby improving overall productivity.

The patent performs the trusted third party initialization as a preliminary action that occurs once during system setup, rather than requiring it for each proof generation. The common reference string (CRS) or public parameters are generated in advance and cached, allowing subsequent proof generations to proceed without re-invoking the trusted third party. This preliminary setup phase separates the one-time initialization complexity from the repeated proof operations.

The patent creates reusable copies of the initialization parameters and commitment structures. The public parameters and commitment keys generated during setup are copied and stored for multiple use across different proof instances. This copying mechanism allows the system to maintain the security properties of trusted third party initialization while eliminating the need to repeat the complex initialization process for each new proof, thereby improving ease of use.