Key-Dependent Symmetric Encryption over GF(2 ⁵²¹ -1) Without S-boxes for Big Data Security

This paper proposes a novel symmetric block cipher over the large prime field GF (2521-1) for secure and efficient big data encryption. Unlike traditional cryptosystems using fixed S-boxes, the scheme employs a key-dependent transformation based on multiplicative inverses, removing the need for static lookup tables. Although inversion is generally costly, our optimized method uses a single binary right-shift inversion per block, with subsequent inverses computed via complement and cyclic shifts. This enhances security while maintaining flexibility and scalability. The cipher is spatially efficient, supporting encryption and decryption on the same platform without additional overhead. We assess the performance of the proposed scheme by analyzing its security, processing speed, avalanche effect, memory consumption, throughput, and expansion ratio, all of which yield competitive results. Its scalability is further validated through simulations using a 127-bit block size. Additionally, an in-depth theoretical analysis of security and computational complexity confirms the scheme’s strength and efficiency, making it well-suited for big data encryption.