White-Box Processing of Large Prime Numbers used in the RSA algorithm
Reamogetse Kutlwano Merahe, Mnoneleli Nogwina, Phumezo Ntlatywa, Lucky Makhoere, Nthabiseng Modiba, Colin Chibaya · 2024
Cryptography is the practice and study of hiding information. A key challenge in cryptography is securely sharing keys through public channels. The RSA algorithm addresses this challenge using a public key for encryption and a private key for decryption by using very large prime numbers. These large primes make it extremely difficult to factorize the resulting product, thus securing the encryption. However, operations with these large numbers can exceed the range limits of most programming languages' data types. This study demonstrates the handling of large values in RSA implementation, aiming to provide insights for efficiently processing large primes in RSA. Results indicate that the BigInteger class in Java support the needs of the RSA algorithm at very minimal CPU time demands. The algorithm is thus strengthened and enhanced for potential use in modern cryptography.