The key exchange scheme (KES) is considered an essential component of many encryption algorithms. Several versions of KES have previously been proposed by numerous researchers in the cryptographic research community. In this work, a new version of KES is proposed over the binary extension field F₂ᵐ. The public and private parameters of the proposed KES are represented as binary representation strings (BRSs) over F₂ᵐ. The users’ private keys are computed as series of BRSs through random selection of binary element strings with different lengths. The public keys are also computed as BRS series over F₂ᵐ. In addition, a new algorithm for generating the shared secret key as a BRS series (BRSs-KES) is presented. Some experimental results of the proposed BRSs-KES are implemented using Python programming language. The random generation of BRSs determines the security level of the proposed scheme. By using the proposed BRSs-KES algorithm, more suitable and secure communication is achieved in practice.
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