In blockchain systems with privacy protection,cryptographic algorithms such as digital signatures and zero-knowledge proofs are often used to protect data security and user privacy.However,many cryptographic algo-rithms,including range proofs,have become performance bottlenecks of blockchain systems due to their heavy reliance on operations of large numbers and elliptic curves.Moreover,the GPU optimization of cryptographic algorithms has gained extensive attention and research in recent years.We make full use of the advantages of GPU as many-core proc-essors and design a GPU-based elliptic curve operation library.In the library,we implement and optimize the common operations of elliptic curves and large numbers on GPU,and design different implementations and interfaces to ac-commodate various requirements.To maximize the throughput and performance of the library,we carefully allocate storage such as registers and constant memory,and use optimization methods such as precomputation to reduce the amount of calculation.For testing the usability and effectiveness of the library,we use it to implement the proxy re-encryption algorithm and the verification algorithm of Bulletproofs range proofs.We further optimize them by mak-ing full use of the intrinsic parallelism of the algorithms.Experiments show that the operation library achieves a per-formance that far exceeds that of commonly used CPU-side libraries such as OpenSSL in each operation.Compared with the CPU-side implementation,the proxy re-encryption algorithm implemented with the library achieves up to 145 times speedup.The Bulletproofs range proof verification algorithm implemented with the library achieves a speedup of about 5.57 times as well.The average verification time of GPU-based Bulletproofs is within 1 millisecond,which meets the performance requirement of privacy protection for over 2000 digital currency transactions per second.Therefore,the operation library provides a solid foundation for applications requiring high throughput of cryptographic calcula-tions,such as the privacy protection of blockchain systems.
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