Secure Knapsack Cryptosystem Against LLL Algorithm Based on Continued Fraction

الملخص

The Merkel-Hellman Knapsack cryptosystem is classified as a public

key cryptosystem that uses two dissimilar keys to encrypt and decrypt,

providing a high level of security to these systems. It is understood that

the key for decryption cannot be derived from the key for encryption.

Unfortunately, it is not immune to cryptosystem attacks, such as the

Lenstra, Lenstra, and Lovasz (LLL Algorithm) which can break it. In

this paper, we proposed a method to enhance the security of the

Knapsack Problem using continued fractions. This method aims to

prevent the problem from being compromised by the LLL algorithm

and reduce the size of encrypted data, thereby facilitating faster

transmission of data. The proposed method demonstrates that the

Merkel-Hellman knapsack cryptosystem enhances security as the LLL

algorithm is unbreakable, and reduces the size of encrypted data.

Moreover, the process of sending and receiving encrypted data is faster

because the size of the encrypted data becomes smaller.