vokoyo said:May I know how to solve the equation as below:
(1) y2 = x3 + x + 1 mod 17
Finding Inverses
Finding Points on the Curve
Elliptic Curve Cryptography (ECC) is a type of public key encryption that is based on the algebraic structure of elliptic curves over finite fields. It is used for secure communication and data encryption in various applications such as online banking, e-commerce, and digital signatures.
ECC uses a mathematical equation in the form of an elliptic curve to generate public and private key pairs. The public key can be shared with anyone, while the private key is kept secret. Messages are encrypted using the recipient's public key and can only be decrypted using their private key, ensuring secure communication.
ECC offers several advantages over other types of public key cryptography, such as RSA. It allows for shorter key lengths while maintaining the same level of security, making it more efficient in terms of storage and processing. Additionally, ECC is more resistant to quantum computing attacks, making it a more future-proof option.
One potential drawback of ECC is its relatively new and complex nature, which can make it more difficult to implement and manage compared to other forms of encryption. Additionally, there have been concerns about the potential for backdoors in ECC algorithms, although these have not been proven.
ECC is used in a variety of applications, including secure communication protocols like HTTPS and SSH, digital signatures for document and software authentication, and even in cryptocurrency systems such as Bitcoin. It is also becoming more widely adopted in mobile devices due to its efficient use of resources.