Abstract: With rapid increase in wired/wireless communication traffic and data storage requirements, the performance of error correction codes and data security solutions is become crucial. Random-like codes can be used in symmetric data encryption, cryptographic hash functions, random number/sequence generators, error correction and detection codes, and other data security applications. The present disclosure provides systems and methods that implement a dynamic permutation based coding approach of input based permutation/remapping/repositioning sequence generation. As the encoding process is defined using input bits, the output of the proposed codes depends on the statistic of input bits rather than any fixed predefined encoding structure. This dynamic encoding method can facilitate to implement strong confusion-diffusion logic and randomness in symmetric cryptography, hash functions, error correction codes, and other data security and authentication areas.

Abstract: Parity logic is widely used in forward error correction codes and error detection codes. When used for error correction and error detection applications, the role of parity bits is to increase code distance by introducing memory between encoded bits and input bits at cost of overhead bits. Present disclosure provide systems and methods for implementing invertible parity functions using parity logic wherein ‘k’ input bits are received and encoded using a first invertible parity function. The ‘k’ input bits can be iteratively encoded to obtain nonlinearity and higher dependency between set of encoded parity bits and the ‘k’ input bits or other data bits. Further the decoding is performed on the set of encoded bits to retrieve original ‘k’ input bits using a second invertible parity function.