PhD Forum 2017 New Cryptographic Systems Based on Certain Sequences of Arithmetic Progressions

In this paper, we present salient properties of the mathematical object: sequence (collection) of arithmetic progressions, with the inverse property: i^th terms of j^th and (j + 1)^th progressions are multiplicative inverses of each other modulo (i + 1)^th term of j^th progression. The theory developed (in my doctoral thesis) on the defined object paves the way for a novel design of cryptographic primitives for (i) symmetric key cryptography, (ii) entity authentication, (iii) end-end encryption, and (iv) crypto-currencies. In addition to being efficient, the proposed primitives are customizable as they support a wide range of values for their security parameters. The customization feature allows proprietary versions, which can be used in both civilian and military applications. The proposed primitives are amenable to parallelization and well-suited for hardware portability. The security of these primitives is based on an well-defined hard problem. Some special cases of the problem are shown to be equivalent to the problem of factoring large integers, a holy grail of mathematics, whose computational difficulty is central to the security of RSA cryptosystem.