An Improvement of ID-Based IPKC Utilizing DIDLP

The identity-based cryptosystem (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathfrak{J D}\mathcal{C}$</tex>) framework was proposed by Shamir [1] in 1984. Within this framework, consumers is required to inquiry a key authentication center (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{K} \mathcal{A C}$</tex>) to confirm their identity prior to accessing a transmission network. Once the verification is complete, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{K} \mathcal{A C}$</tex> provides the consumer with a classified key. To communicate, a consumer simply must to recognize the “identity” of the other party and the communal key of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{K} \mathcal{A C}$</tex>, removing the necessity for a communal key directory. Although Shamir was unable to create a practical identity-based cryptosystem, he successfully developed a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathfrak{J} \mathfrak{D}$</tex> signature technique. Subsequently, Meshram and Agrawal [2] introduced a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathfrak{J} \mathfrak{D}$</tex> cryptosystem that is grounded in the double discrete logarithm problem, utilizing a communal key system that also relies on this problem. In this paper, we suggest enhancements to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathfrak{J} \mathfrak{D}$</tex> cryptosystem that is established on the double isodiscrete logarithm problem. We assess the system's preservation in the context of possible collusion between certain parties and illustrate opportunities for improving its overall security.