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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Can Add and Multiply On Cipher Text achieve all operations?

A Fully homomorphic encryption scheme needs to support an evaluate function that can do add and multiply operations on cipher text. Can we do all kinds of complex operations on cipher text like ...
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Blind quantum computing and fully homomorphic encryption

I am somewhat familiar with current research on fully homomorphic enryption schemes and their possible application to Cloud computing. I've just noticed (somewhat late) that a marketing-savvy group ...
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Security model for privacy-preserving aggregation scheme.

Suppose that $S=(E,D)$ is an additively homomorphic encryption scheme. Now I want to design a protocol $P$ such that given inputs $x_1,x_2,..,x_n$, the adversary $A$ (who can decrypt) can only learn ...
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Can we construct fully homomorphic encryption scheme based on non-circuit approach?

At present, all FHE scheme are be constructed based on circuit approach. Can we construct fully homomorphic encryption scheme based on non-circuit approach? Is Polly cracker non-circuit approach ?
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What is the flaw in this model for homomorphic encryption?

Imagine a Field Isomorphism $g : \mathbb F1 \to \mathbb F2$ given by some $g(x)$ Assume a client is planning to outsource his computations to server, translates every possible $x$ as $g(x)$ and ...
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What is the strength of unpadded RSA?

I would like to use unpadded RSA for homomorphic encryption in a toy P2P game, for things like fair coin flips and shuffling. How many bits of security does unpadded RSA have, in relation to its key ...
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Homomorphic cryptosystems in RSA

Hopefully Crypto can help me understand homomorphic cryptosystems. I'm designing a high score server for a game I made, and because of facets in the language i'm using, the player would be able to ...
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Existing works on pre-computing ElGamal ephermal keys

I was playing around with a problem in e-voting schemes that use additive homomorphic encryption to tally votes, namely that at the end of the day somebody (or somebodies, if the secret material has ...
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Are there any multiparty homomorphic encryption schemes?

Are there any multiparty homomorphic encryption schemes ? Most of the literature is about two party schemes . Is there any generalization made for n party ?
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Cryptographical formalization of computational privacy

Yesteryears problems of communication privacy has been well defined in cryptography through Asymmetric cryptography. Due to rise in Cloud computational model , computational heavy tasks are being ...
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Additive ElGamal cryptosystem using a finite field

I'm trying to implement a modified version of the ElGamal cryptosystem as specified by Cramer et al. in "A secure and optimally efficient multi-authority election scheme", which possesses additive ...
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Is there difference between Algebraic Homomorphic Encryption and Fully Homomorphic Encryption Schemes?

Is there difference between Algebraic Homomorphic Encryption and Fully Homomorphic Encryption Schemes?
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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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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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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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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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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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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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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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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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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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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 ...