Optimizing the Complexity of Time in the Process of Multiplying Matrices in the Hill Cipher Algorithm Using the Strassen Algorithm

Abstract

Hill Cipher is one of the symmetric key cryptographic algorithms that have several advantages in data encryption. To avoid key invertible matrices, key matrices are generated using Newton's binomial coefficients. Hill Cipher is one of the symmetric key cryptographic algorithms. The Hill Cipher algorithm uses a matrix measuring m x m as a key for encryption and decryption. The basic matrix theory used in Hill Cipher includes multiplication between matrices and inverses the matrix. Hill Cipher uses mathematical calculations called Linear Algebra and specifically requires users to understand the basis of the matrix. During this time the matrix multiplication used to encrypt and decrypt this method is only done by Divide and Conquer. This is less effective in minimizing the processing time. A good algorithm must not only be correct but also efficient in its use. In addition, an algorithm must also have low complexity. Algorithms like this must be able to optimize its performance, especially in data processing which is getting more and more in number. An algorithm with low complexity is an algorithm that is able to minimize the use of time and memory space even though more and more data is used. Therefore the author applies the Strassen method in optimizing the matrix multiplication process to encrypt and decrypt it. However, this algorithm will only apply to use of keys and plaintexts of the same order size, which is nxn where n = 2a(a> 0). Then the encryption and decryption process will be done by matrix multiplication using the Strassen method. The final results show that by using the Strassen algorithm the encryption and decryption process in the Hill Cipher method can be optimized. Where every time the data to be processed increases the complexity of the time required will not be too high an increase. And this shown that Strassen more effective than the Divide and Conquer method.