The Iso-ElGamal Cryptographic Scheme

Abstract

In this paper, we use Santilli’s isonumber theory of the first kind to add a new degree of freedom of unit to the ElGamal cryptographic system leading to a new encryption scheme. In this scheme, the key generation, encryption, and decryption steps are performed in an isofield with an isounit replacing unit one of normal arithmetic. This isounit is used as a shared secret isokey for encryption and decryption as is the case in a symmetric cryptographic system. In addition, our proposed cryptographic system is asymmetric with a public isokey used for encryption and a private isokey used for decryption. We thus obtain a hybrid public-key private-key cryptographic system with a substantial increase in security due to this additional freedom of unit. The private isokeys and ciphertexts produced by this scheme are highly secure. In addition, the ability to use isokeys of ten thousand bits or more with minimum additional computational cost makes this cryptographic scheme produce highly secure encrypted information. Also, applications and implementations of the Iso-ElGamal scheme on messages represented by positive integers and data or information encoded into binary digits or bits are presented. A wide range of other applications in security services and security mechanisms, which include authentication, data confidentiality, data integrity, digital signature, and others can be implemented using our proposed scheme.