Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study multi-collision probability. For a hash function H: D→ R with |R| = n, it has been believed that  can find an s-collision by hashing Q = n (s-1)/s  times.  first show that this probability is at most 1/s! which is very small for large s.  next show that by hashing (s!) 1/s  x Q times, an s-collision is found with probability approximately 0.5 for sufficiently large n. Note that if s = 2, it coincides with the usual birthday paradox. Hence it is a generalization of the birthday paradox to multi-collisions.
['Kazuhiro Suzuki', 'Dongvu Tonien', 'Kaoru Kurosawa', 'Koji Toyota']
I am writing a research paper on a idea Birthday paradox for multi-collisions
[{"from": "human", "value": "I am writing a research paper on a idea Birthday paradox for multi-collisions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study multi-collision probability. For a hash function H: D\u2192 R with |R| = n, it has been believed that  can find an s-collision by hashing Q = n (s-1)/s  times.  first show that this probability is at most 1/s! which is very small for large s.  next show that by hashing (s!) 1/s  x Q times, an s-collision is found with probability approximately 0.5 for sufficiently large n. Note that if s = 2, it coincides with the usual birthday paradox. Hence it is a generalization of the birthday paradox to multi-collisions."}]