Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   introduce very simple deterministic randomness extractors for Diffie-Hellman distributions. More specifically  show that the k most significant bits or the k least significant bits of a random element in a subgroup of Z* p  are indistinguishable from a random bit-string of the same length. This allows us to show that under the Decisional Diffie-Hellman assumption  can deterministically derive a uniformly random bit-string from a Diffie-Hellman exchange in the standard model. Then,  show that it can be used in key exchange or encryption scheme to avoid the leftover hash lemma and universal hash functions.
['Pierre-Alain Fouque', 'David Pointcheval', 'Jacques Stern', 'Sébastien Zimmer']
I am writing a research paper on a idea Hardness of Distinguishing the MSB or LSB of Secret Keys in Diffie-Hellman Schemes
[{"from": "human", "value": "I am writing a research paper on a idea Hardness of Distinguishing the MSB or LSB of Secret Keys in Diffie-Hellman Schemes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   introduce very simple deterministic randomness extractors for Diffie-Hellman distributions. More specifically  show that the k most significant bits or the k least significant bits of a random element in a subgroup of Z* p  are indistinguishable from a random bit-string of the same length. This allows us to show that under the Decisional Diffie-Hellman assumption  can deterministically derive a uniformly random bit-string from a Diffie-Hellman exchange in the standard model. Then,  show that it can be used in key exchange or encryption scheme to avoid the leftover hash lemma and universal hash functions."}]