In contrast to Symmetric Key schemes such as AES<\/a> (Advanced Encryption Standard), the asymmetric key scheme contains a key pair, the public key, and the private key. This is also known as public key cryptography.<\/p>\n\n\n\n <\/p>\n\n\n\n Asymmetric Key<\/strong><\/p>\n\n\n\n Complex mathematical problems underpin the asymmetric key construction, which allows the private key to derive a corresponding public key easily while keeping reverse computation infeasible. Several popular cryptographic schemes have been constructed using the mathematical relation between the public and private keys, such as a digital signature or a key agreement.<\/p>\n\n\n\n <\/p>\n\n\n\n ECC Standards<\/strong><\/p>\n\n\n\n The elliptic curve cryptography (ECC) is an asymmetric key tool based on the elliptic curve discrete logarithm problem (ECDLP). SEC 1 presents the ECC-based signature scheme, encryption and key transport scheme, and key agreements scheme. To assist others with adopting the ECC, SEC 2 proposed 15 domain parameters categorized into five security levels: 80-bit, 112-bit, 128-bit, 192-bit, and 256-bit.<\/p>\n\n\n\n <\/p>\n\n\n\n Classical Public key Cryptography<\/strong><\/p>\n\n\n\n RSA and Diffie-Hellman-Merkle are the first two public key constructions. RSA is based on the integer factorization problem, and Diffie-Hellman-Merkle is based on the finite field discrete logarithm problem (DLP). Due to the existence of sub-exponential time algorithms solving these problems, the key size of these two public key systems is longer than the ECC key size. The ECC cryptography therefore is considered a natural modern successor of RSA and Diffie-Hellman-Merkle, due to the smaller keys and signatures producing the same level of security, while also providing faster key generation, key agreement, and signatures.<\/p>\n\n\n\n <\/p>\n\n\n\n SM2<\/strong><\/p>\n\n\n\n SM2 is a bunch of ECC standards proposed by China. It defines an ECC-based digital signature scheme, an encryption scheme, and a Key exchange scheme. In addition, it also presents its own domain parameters of security level 128-bit, which is different from those in SEC 2.<\/a><\/p>\n\n\n\n <\/p>\n\n\n\n