We propose a new public-key cryptosystem, the SP Algorithm (Sum-Prime, also Ladhe–RSA), that carries the RSA construction forward into the post-quantum era without aban-doning its algebraic foundations. The scheme is built on an empirical arithmetic regularitywe call Ladhe’s Conjecture, which asserts that every prime P admits at least one additivedecomposition P= a + b + c satisfying a structural constraint (verified in this work for1,620+ primes). Our central observation is that RSA’s vulnerability to Shor’s algorithmstems from the fact that its modulus n = p·q is published. In SP, we replace the publicmodulus by the first prime P1 only; the second prime P2 is derived privately from the Ladhewitness via a secret one-way transform. As a consequence, the adversary has no compositeinteger to factor, and Shor’s period-finding oracle has no input on which to act. Securityreduces to a new problem, the Ladhe's Decomposition Problem (LDP), which is additive innature and exhibits no known multiplicative structure exploitable by quantum algorithms.We describe the scheme, give worked examples, and outline the open problems required fordeployment.
Shubham et al. (Mon,) studied this question.