Speeding up Demytko’s decryption with Chinese Remainder Theorem (CRT)

Elliptic curve cryptography (ECC) has gained popularity over the RSA cryptosystem as it preserves the same security level with lower key sizes. In ECC-based encryption, it involves using the most common method such as Koblitz’s embedding method to embed the message into points on an elliptic curve. This paper focuses on Demytko’s cryptosystem which uses the points on an elliptic curve represented as y2 ≡ x3 + ax + b (mod n). Demytko’s cryptosystem is known to have a slower decryption speed compared to other cryptosystems such as RSA and KMOV cryptosystem, motivating the need for speeding up the cryptosystem. In this paper, we present the implementation of the Chinese Remainder Theorem (CRT) during the decryption process of Demytko’s cryptosystem. The numerical tests demonstrate that the execution time for decryption is decreased by approximately 1.10 times when CRT is used.