A public key cryptosystem and signature scheme based on numerical series

A public key cryptosystem and signature scheme based on a proposed key exchange algorithm are introduced. The key exchange algorithm is based on the difficulty of calculating the nth partial sum of infinite numerical series where no exponentiation computation is required to share a secret key between two parties as in the Diffie-Hellman algorithm. With the proposed public key cryptosystem ciphering and deciphering of messages, online signing documents and verifying signatures do not require exponentiation computation while providing higher security level than the state-of-the-art cryptosystems that depend on the difficulty of discrete logarithmic problem or factorizing large prime numbers. The proposed cryptosystem and signature scheme do not depend on elliptic curve cryptography or RSA cryptography that are computationally too slow, this makes the proposed cryptosystem and signature scheme computationally faster, easier to implement and more practical to be used in online transactions. It also provides a higher level of security as it provides forward secrecy and using large size symmetric keys to encrypt and decrypt messages in a significantly short time. Moreover, the proposed signature scheme can be used as a cryptographic hash function as the hash value significantly changes when a single letter in the document is changed. In comparison with the state-of-the art the experimental results show the superiority of the proposed key exchange algorithm and public key cryptosystem.