Nonlinear Mapping for Fair Secure Real Number Comparison

The patent replaces traditional cryptographic computation mechanisms (homomorphic encryption, secret sharing) with a cryptographic protocol based on cryptographic hash functions and bit manipulation operations. This substitution reduces computational complexity from O(n^2) to O(n) while maintaining security through the use of cryptographic primitives like SHA-256 hash functions and secure bit-wise operations.

The patent changes the computational parameters by transforming the numerical comparison problem into a bit-level manipulation problem. Instead of performing complex cryptographic computations on full precision numbers, the protocol operates on binary representations using hash function outputs, changing the parameter space from continuous real numbers to discrete bit sequences, thereby reducing computational burden.

The patent introduces cryptographic hash function outputs as intermediary values that both parties can independently verify. Instead of one party directly receiving the comparison result, both parties compute hash-based verification values that serve as intermediaries, ensuring that neither party can unilaterally determine or manipulate the final result without the other party's corresponding verification value.

The patent employs asymmetric computation paths where each party performs different but complementary operations. Party A computes verification value V1 = H(x ⊕ k) and Party B computes V2 = H(y ⊕ k), where the asymmetric operations ensure that neither party can derive the comparison result alone, yet both contribute equally to the final fair outcome through their respective asymmetric computational roles.

The patent extracts only the essential security requirement (protecting the comparison result) from the broader goal of protecting all intermediate values. Instead of obfuscating the entire difference value with random values, the protocol extracts and protects only the critical comparison outcome through hash function outputs, discarding unnecessary obfuscation layers that would increase computational overhead.

The patent inverts the traditional approach of adding obfuscation to protect data. Instead of obfuscating the input difference and then comparing, the protocol inverts the process by directly computing cryptographic verification values from the inputs and comparing those hash outputs, thereby eliminating the need for intermediate obfuscation values and reducing computational overhead.

The patent enables the two parties to perform secure comparison computations themselves without relying on third-party cloud services. Each party independently computes their respective verification values using the protocol, and the comparison result is determined through their mutual interaction, making the system self-sufficient and eliminating security risks associated with untrustworthy external platforms.

The patent uses cryptographic hash functions as trusted intermediaries that both parties can independently execute. Instead of trusting a third-party cloud platform, the protocol introduces mathematical hash functions as impartial mediators that both parties can compute locally, ensuring fairness and security without requiring trust in external service providers.