Can cryptography solve this problem?

Two people are chatting, Mr. X and Ms Y. They give each other a CRC16 hash of someone's name initials and salt a random number at the end (suffix).

Ms Y: "I love someone with the initials {53d4}".

Mr X: "Are that person's initials {da17}?"

{CRC16} -> Original String
{53d4} -> A7777
{da17} -> X123

This means, Ms. Y loves someone with initials name A and Mr. X thought it was someone with initials name X.

How can they both know answer of Mr.X's question WITHOUT knowing the guessed person's initials? So the expectation is to know only the boolean answer, YES or NO without knowing who the person is, no matter who is it. I mean, X shouldn't know who is it and Y shouldn't know who the person of X thought.

Note: You can modify dialogue or totally change dialogue as long as it answers the how question.



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