Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: (MATH)  define a new family of collision resistant hash functions whose security is based on the worst case hardness of approximating the covering radius of a lattice within a factor  O (π n  2 log  n ), where π is a value beten  1  and √ \over  n  that depends on the solution of the closest vector problem in certain "almost perfect" lattices. Even for π = √ \over  n , this improves the smallest (worst-case) inapproximability factor for lattice problems known to imply the existence of one-way functions. (Previously known best factor was  O ( n  3+e ) for the shortest independent vector problem, due to Cai and Nerurkar, based on work of Ajtai.) Using standard transference theorems from the geometry of numbers, our result immediately gives a connection beten the worst-case and average-case complexity of the shortest vector problem with connection factor  O (π n  3 }log  n ), improving the best previously known connection factor  O ( n  4+e ), also due to Ajtai, Cai and Nerurkar.
['Daniele Micciancio']
I am writing a research paper on a idea Improved cryptographic hash functions with worst-case/average-case connection
[{"from": "human", "value": "I am writing a research paper on a idea Improved cryptographic hash functions with worst-case/average-case connection"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: (MATH)  define a new family of collision resistant hash functions whose security is based on the worst case hardness of approximating the covering radius of a lattice within a factor  O (\u03c0 n  2 log  n ), where \u03c0 is a value beten  1  and \u221a \\over  n  that depends on the solution of the closest vector problem in certain \"almost perfect\" lattices. Even for \u03c0 = \u221a \\over  n , this improves the smallest (worst-case) inapproximability factor for lattice problems known to imply the existence of one-way functions. (Previously known best factor was  O ( n  3+e ) for the shortest independent vector problem, due to Cai and Nerurkar, based on work of Ajtai.) Using standard transference theorems from the geometry of numbers, our result immediately gives a connection beten the worst-case and average-case complexity of the shortest vector problem with connection factor  O (\u03c0 n  3 }log  n ), improving the best previously known connection factor  O ( n  4+e ), also due to Ajtai, Cai and Nerurkar."}]