Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial-time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free Abelian group generated by the symbols g 1,…,g n , together with a solution modulo the product of two randomly chosen safe primes when g 1,…,g n are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free Abelian groups under a standard cryptographic assumption and resolves a conjecture of Rivest (Theory of Cryptography Conference—Proceedings of TCC 2004, LNCS, vol. 2951, pp. 505–521, 2004).
['Daniele Micciancio']
I am writing a research paper on a idea The RSA Group is Pseudo-Free
[{"from": "human", "value": "I am writing a research paper on a idea The RSA Group is Pseudo-Free"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial-time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free Abelian group generated by the symbols g 1,\u2026,g n , together with a solution modulo the product of two randomly chosen safe primes when g 1,\u2026,g n are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free Abelian groups under a standard cryptographic assumption and resolves a conjecture of Rivest (Theory of Cryptography Conference\u2014Proceedings of TCC 2004, LNCS, vol.\u00a02951, pp.\u00a0505\u2013521, 2004)."}]