Cryptosystems which support computation on encrypted data. They might be partially homomorphic (support for one operation such as + or *) or they might be fully homomorphic (any sequence of + and *).

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Algorithm to securely exchange identities

Say four people each have a public/private key pair that they can use to encrypt or sign messages. They have an anonymous way to post messages such that the others can see them. Malicious entities can ...
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298 views

DGK Cryptosystem Key Generation and Decryption Issues

I detailed here the DGK (Ivan Damgård, Martin Geisler and Mikkel Krøigaard) cryptosystem, and I managed to get it to work, most of the time... The BIG problem that I am facing at the moment is that ...
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1answer
386 views

DGK Cryptosystem Encryption Speedup

Following @poncho's nice clarification of the RSA speedup here, let's see if I'm able to do the same in the case of the DGK cryptosystem: We have pk = (n, g, h, u), sk = (p, q, $v_p$, $v_q$) which ...
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1answer
8k views

Chinese Remainder Theorem and RSA

Wikipedia has a nice section regarding the speedup of the RSA decryption using the Chinese Remainder Theorem here. I need to understand the implementation of a similar speedup for the encryption ...
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1answer
215 views

One-way hash on encrypted data, result hidden from hasher

I'm looking for a one-way hash function that can be performed by A on an encrypted piece of data E(D) provided by B, without the performer A able to figure out D or H(D). This similar to HMAC(Message, ...
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983 views

Division in paillier cryptosystem

Is division possible in the Paillier Cryptosystem? i.e. given a the cipher-text $C$ of an integer $M$ the plain-text divisor $D$, and only the public key, can one compute the cipher-text of $M/D$ ?
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494 views

Alternatives to FHE for secure function evaluation

As a followup to a previous question I asked which was more related to Fully Homomorphic Encryption (FHE), what other cryptographic methods are available for computing a private function on public ...
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406 views

secure multiparty computation for multiplication

Suppose there are $N$ parties $p_j$, each with a binary $b_j\in{\{0,1\}}$. The problem needs to compute the multiplication of number of ones times that of zeros, that is, ...
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902 views

How to construct encrypted functions (with either public or private data)?

Homomorphic encryption is often touted for its ability to Compute on encrypted data with public functions Compute an encrypted function on public (or private) data I feel I have a good grasp of #1 ...
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1answer
538 views

How close is homomorphic encryption to handling regular expressions?

Is there any reasonable homomorphic encryption protocol that supports some meaningful fragment of regular languages/expressions and/or edit distance bounds? I'm suspicious that homomorphic encryption ...