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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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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8answers
22k views

How is CipherCloud doing homomorphic encryption?

Much of the literature and latest papers suggest that homomorphic encryption is still not practical yet. How is CipherCloud able to achieve this? Does anyone have an idea? Their website does not ...
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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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4answers
478 views

Verify product without revealing multipliers

Situation: Several participants contribute encrypted random numbers. These numbers will be used to generate community-agreed random (by simple multiplication). Question: Is there any way to detect ...
5
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1answer
1k views

Can Elgamal be made additively homomorphic and how could it be used for E-voting?

Elgamal is a cryptosystem that is homomorphic over multiplication. How can I convert it to an additive homomorphic cryptosystem? How can I use this additive homomorphic Elgamal cryptosystem for ...
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5answers
1k views

Approach towards anonymous e-voting

I want to implement an internet-based e-voting system. Voters shall be able to cast their vote for one out of n possible candidates. Each candidate has his own ballot-box kept by and at a trustworthy ...
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1answer
262 views

Proof of correctness of a homomorphic ElGamal sum

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...
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2answers
1k views

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 ...
5
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0answers
244 views

LT codes with Homomorphic hashing

I have been working on a project implementing LT codes with Homomorphic hashing (inspired from http://blog.notdot.net/2012/08/Damn-Cool-Algorithms-Homomorphic-Hashing and ...
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2answers
256 views

How could Fully Homomorphic Encryption support power operations?

Fully Homomorphic Encryption (FHE) enables arbitrary functions computed on encrypted data, because it supports both addition and multiplication. But I wonder if FHE supports power operations. For ...
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3answers
612 views

additive ElGamal encryption algorithm

I'm performing ElGamal encryption algorithm and using the additive homomorphic property so the product of two ciphertexts is the encryption of the sum of the plaintexts. The problem is that I need to ...
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1answer
85 views

Addition-only PHE in F#

Using homomorphic encryption, I would like to be able to take an encrypted integer and either add 1 or -1 for a new encrypted value. I do not want the encrypted value to be recoverable - just the ...
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1answer
289 views

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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1answer
131 views

Homomorphic Encryption Notation Question

What does the following notation mean in a homomorphic encryption scheme? ENC(x;r) What does x and ...
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2answers
205 views

Real life systems that use concepts of crypto computing [closed]

Are there any working cloud/internet solutions/products that operates on encrypted data such as systems using homomorphic encryption, secure multiparty computation, electronic voting, private ...
6
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2answers
320 views

Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt?

Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt? I've tried digging around on the Internet but haven't found anything conclusive on the topic.
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2answers
384 views

Can we proxy-re-encrypt using homomorphic encryption schemes?

Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. The Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and ...
2
votes
2answers
91 views

Formal security of recycled random blinding in a Paillier scheme

This question is a follow-up/variant on a previous question. Supposing that we are trying to generate a large number of (indistinguishable) ciphertexts of a given plaintext and want to avoid the ...
8
votes
1answer
979 views

Homomorphic (encrypted) comparison to an integer

When working with an additive homomorphic encryption scheme (say Pallier's), is there an efficient way to get the encrypted value of a comparison test to an integer value (I realise that an ...
2
votes
1answer
474 views

Homomorphic Encryption

Homomorphic Encryption (HE) which supports any function on ciphertexts is known as Fully Homomorphic Encryption (FHE), while Partially Homomorphic Encryption (PHE) includes encryption schemes that ...
2
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1answer
381 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
95 views

Cipher text only attacks on deterministic fully homomorphic encryption schemes

If we have encryptions of additive and multiplicative identities in the corpus of cipher text of a deterministic fully homomorphic encryption (FHE) scheme, I guess we can break it. If the FHE scheme ...
3
votes
1answer
423 views

How to compute the dot product on encrypted values?

Is there a practical homomorphic encryption scheme that can give reasonable execution time results in computing a dot product: $$a_1*b_1 + a_2*b_2 +a_3*b_3 +\ldots+ a_n*b_n$$ I imagine the scheme will ...
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0answers
88 views

Obfuscating point-like functions

There are standard schemes for obfuscating a point function; I'm wondering if we know how to obfuscate a slight generalization of a point function. I'll elaborate more precisely. Definition 1. A ...
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1answer
237 views

Homomorphic encryption for vector addition

Building on the question and answer from Addition-only PHE in F# which ponders homomorphic cryptosystems to navigate, relatively, a single dimension without revealing absolute position (an encrypted ...
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1answer
65 views

How bad would it be to reuse the random blinding factor in a scheme like Paillier?

A secure and somewhat fast way to "re-encrypt" (refresh? anonymise?) a Paillier ciphertext, $c$, is to multiply it by an exponentiated random value: $c \gets c \cdot r^n \mod n^2$ (with $r \in ...
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2answers
600 views

Is it possible to subtract/multiply numbers using homomorphic encryption?

Most of the libraries I've seen allow you to add encrypted numbers. Is it possible to subtract and multiply them?
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319 views

Store hashed email and compare hash values

I have a number of different systems sending me email addresses, but I don't actually need the underlying email, just a hash of the email address. I know I can compare hash values to find matches ...
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2answers
216 views

Homomorphic Encryption: how does the equality test on ciphertexts work?

Let's suppose we have a asymmetric crypto-system $H$ which is homomorphic with respect to some function $F$. Alice encrypts a message $m$ with her private key $e$ in the crypto-system $H$ and ...