Enhancing the security of public key cryptographic model based on integrated ElGamal-Elliptic Curve Diffe Hellman (EG-ECDH) key exchange technique
Kshitish Kumar Mohanta, Deena Sunil Sharanappa, Vishnu Narayan Mishra · 2023
This chapter proposes an integrated technique to create the key matrices using multi-key exchange algorithm based on the combination of the ElGamal algorithm and the Elliptic Curve Diffe Hellman (ECDH) algorithm. The generalized Fibonacci matrix modulo https://www.w3.org/1998/Math/MathML" display="inline"> p https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003460169/12a01f1c-4677-4b79-9b86-8256557baaa3/content/C006_equ_0001.tif "/> and the inverse of the generalized Fibonacci matrix modulo https://www.w3.org/1998/Math/MathML" display="inline"> p https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003460169/12a01f1c-4677-4b79-9b86-8256557baaa3/content/C006_equ_0002.tif "/> are used as the key matrix for encryption and decryption. These matrices are generated using generalized Fibonacci sequences. Instead of sending the whole key matrix, we need to send only the order and the power of the generalized Fibonacci matrix and the seeds of the generalized Fibonacci sequence using the proposed combined algorithm. In this public key cryptographic model, the Affine Hill Cipher technique is used for the encryption of the plain text and also for the decryption of the cipher text. The proposed method increases the security strength of the public key cryptographic model due to the use of four secret integers https://www.w3.org/1998/Math/MathML" display="inline"> a , b , ( n , m ) https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003460169/12a01f1c-4677-4b79-9b86-8256557baaa3/content/C006_equ_0003.tif "/> .