Abstract
The profound characteristics of factoring problems and chaotic maps are utilized in this article to produce a new identity-based cryptographic scheme. These characteristics include random behavior and high performance (i.e., encryption and decryption) in terms of so many parameters such as computational delay, rate of security, and speed. To illustrate the performance of the proposed cryptographic scheme, some cryptographic attacks are proposed. The mathematical analysis have confirmed that the combined factoring problems and chaotic maps scheme has a high rate of security which satisfy the cryptographic requirements. To the best of our knowledge, this is the first time an ID-based cryptography based on chaotic maps and factoring problems has been proposed.