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Secure order preserving hash function

Is there a construction of an order preserving hash function that keeps the preimage property of a crypto hash function? By order preserving hash function (OPHF) i mean for $x<y$ then $OPHF(x) < ...
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In the Paillier cryptosystem, is there a method to judge whether an encrypted number is less than 0 (without the private key)

Or, is there a cryptosystem that is both order-perserving and additive homomorphic?
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How does order-preserving encryption work?

Order-preserving encryption (OPE) is, apparently, a method of encrypting data so that it's possible to make efficient inequality comparisons on the encrypted items without decrypting them. I've been ...
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How to implement order preserving encryption or order preserving hashing

Does anybody know any free implementation of either order preserving encryption or order preserving hashing? I've found some codes like CMPH but I need to dynamically add new DATA and that's why most ...