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The problem with a hash function like you ask for is that, if you hash an $n$-bit string and give the hash to someone else, they can recover the string using $n$ hash calculations with a binary search. For a simple example, let's say the $n=8$, your string is $01011001$ in binary, and its hash is $Y = H(01011001)$. To recover the string from the hash, I ...

In Paillier, if it were possible to determine whether an encrypted number is less than 0 (that is, is equivalent modulo N to a value $x$ where $N/2 < x < N$), then it would be possible to decrypt arbitrary encrypted values with only the public key. That is, if someone found such a method, they will have broken Paillier as a public key system. The ...

CryptDB implements order-preserving encryption, and its source code is publicly available. In fact, rather than building your own system that uses order-preserving encryption, you might try just using CryptDB. Alternatively, in a pinch, I suppose you could take one of the papers that describes an order-preserving encryption algorithm and implement it ...

As mentioned above this is not possible in a direct way. However there exists a Zero Knowledge Proof that may do the job. It proofs that a message encrypts one out of a publicly known number of plain text messages. If these known messages only contain values greater or equal 0 this may be what you are looking for but unfortunately message and computation ...

There are a number of ways to do this. The simplest way is to simply add a number to it. Given a key of X, it would show: A>B A+X>B+X Of course, this isn't a very complex method by any means, but more complex formula could be used to give the same result. Generally speaking, they simply need to preserve the sign, which there are a multitude of ...