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 (+ and * at the same time).

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59
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8answers
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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 ...
17
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1answer
895 views

Should I trust CipherCloud? [closed]

Should I trust CipherCloud's system for "homomorphic encryption" of data in the cloud? Has the security of their system been subject to peer review or other cryptanalysis? Is there any known analysis ...
12
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2answers
1k views

What is the most practical fully homomorphic cryptosystem?

Craig Gentry recently gave the first fully homomorphic cryptosystem. Quite a bit of work has been done since extending his work. It seems, however, that no system is practical for real world use. ...
8
votes
5answers
340 views

Choose a random number that is different from a bunch of other secret numbers

I'm looking for an algorithm where n participants each have a different secret number between $[0..x]$ (and where $x$ is known) and where the participants then select randomly another, non-secret, ...
7
votes
3answers
2k views

What are some disadvantages of homomorphic encryption schemes?

I'm doing some self-teaching / research for my own benefit in homomorphic cryptography. I've studied both additive and multiplicative schemes (Pallier and RSA respectively), but all I can seem to ...
7
votes
1answer
513 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 ...
6
votes
4answers
1k views

Is Porticor's “homomorphic” key encryption something that can really be done or is it just marketing hype?

Porticor has an interesting file encryption offering for encrypting and decrypting files in an MySQL database quickly. They are an Amazon AWS (Amazon Web Service) Partner Network technology partner ...
6
votes
2answers
398 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 ...
6
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2answers
371 views

A lower bound on the insecurity of CipherCloud?

CipherCloud claims to support , among other things, searchable encryption. A bunch of speculation seems to suggest they did this via some breathtakingly incompetent means( unfortunately such ...
5
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3answers
162 views

Can we give access to controlled functionality in Fully homomorphic encryption schemes?

Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and ...
5
votes
1answer
4k 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 ...
5
votes
1answer
144 views

Can homomorphic encryption filter?

Often in articles homomorphic encryption is praised as the holy grail of encryption for cloud storage. This is done by suggesting that it can do any computation, and as such could be used for ...
5
votes
1answer
203 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, ...
5
votes
1answer
450 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 ...
4
votes
1answer
238 views

What is meant by $\tilde\Omega(\lambda^4)$?

I'm currently reading the paper (Leveled) fully homomorphic encryption without bootstrapping , and the following paragraph was near the start: What is meant by the symbol used? Is it merely to ...
4
votes
2answers
124 views

Is a simple stream cipher “partially homomorphic” if no integrity check is applied?

My understanding is that, simply put, a stream cipher is just a CSPRNG such that $R(i,k)$ will produce a deterministic but statistically random sequence, where $i$ is an IV, and $k$ is the session ...
4
votes
1answer
158 views

Homomorphic Encryption and Semantic Security using Lattices?

I've been reading Brakerski and Vaikuntanathan's "Efficient Fully Homomorphic Encryption from (Standard) LWE" and I'm still digesting pieces at a time. Under section 1.1, "Re-Linearization: Somewhat ...
4
votes
3answers
694 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 $M/D$ ?
4
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2answers
328 views

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?
4
votes
2answers
813 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 ...
4
votes
2answers
649 views

Order Preserving Encryption for Numeric Data Values

How can I ensure order of encrypted data i.e., Enc(m1) < Enc(m2) where m1 < m2, and all messages are integer values. I have gone through Order Preserving ...
4
votes
2answers
218 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 ...
4
votes
2answers
735 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 ...
4
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2answers
206 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.
4
votes
1answer
220 views

FHE - Brakerski's “Scale Invariant” Scheme

I thought the current state of the art for fully homomorphic encryption was Brakerski, Gentry and Vaikuntanathan's scheme (BGV) based on standard/ring LWE employing modulus switching for noise ...
4
votes
1answer
203 views

Can any one explain Circuit Privacy using fully homomorphic encryption from Gentry's thesis?

Craig Gentry's thesis talks about circuit privacy being straight forward from fully homomorphic encryption in the last chapter. Can somebody explain in simpler terms what that means ? I have read it ...
4
votes
0answers
198 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 ...
3
votes
4answers
441 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 ...
3
votes
1answer
368 views

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 ...
3
votes
2answers
471 views

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 ...
3
votes
1answer
98 views

Logical OR operation in a homomorphic additive cryptosystem

Suppose we have a cryptosystem homomorphic for addition (say Paillier's). Is there a way to perform a logical OR operation between two binary values (with a binary result). We can, of course, obtain ...
3
votes
1answer
194 views

Fully Homomorphic Encryption over the Integers - Runtime Question

I have a question regarding the paper "Fully Homomorphic Encryption over the Integers" (http://eprint.iacr.org/2009/616.pdf): On page 6 after they set their parameters, it says "This setting results ...
3
votes
1answer
260 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 ...
3
votes
2answers
163 views

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 ...
3
votes
3answers
270 views

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 ...
3
votes
1answer
109 views

FHE over the Integers - reduction to approximate gcd problem

I have three quick questions concerning the reduction of the scheme to the approximate gcd problem: What exactly do the authors mean by $q_p(z_1')$ being the odd part of the gcd? (last line of step ...
3
votes
1answer
97 views

Homomorphic Encryption - Smart Vercauteren Batching

I'm going through Smart and Vercauteren's paper "Fully Homomorphic SIMD operations" and had a question about some notation used in the paper. In section 2 of the above it is stated that for each ...
3
votes
1answer
403 views

What kind of multiparty computation is this?

The classic multiparty computation protocols are defined around " Untrusted parties trying to compute something together". But is there a cryptographic abstraction for, "Trusted parties trying to ...
3
votes
3answers
233 views

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 ...
3
votes
1answer
89 views

Can a homomorphic encryption scheme be made CCA2 Secure?

Is it possible to modify a homomorphic encryption scheme so that it can be CCA2 secure? From the definition of a homomorphic scheme, it seems that it is malleable, which would result in lack of CCA2 ...
3
votes
1answer
72 views

Multiplication-homomorphic schemes

I'm looking into multiplication-homomorphic schemes now and basically I see that there are 3 options: RSA, Boneh-Goh-Nissim and ElGamal. RSA was proved to be insecure unless message is randomly ...
3
votes
2answers
118 views

secure integer comparison

I have been going through a huge amount of papers to find a simple and a practical method to compare integer numbers without revealing their original values. I know that this falls within the area of ...
3
votes
2answers
332 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, ...
3
votes
1answer
95 views

Public key in fully homomorphic encryption over the integers

I'm reading “Fully Homomorphic Encryption over the Integers” by van Dijk et al. I wonder why $x_0$, which is a component of the public key, should be an odd number?
3
votes
2answers
132 views

Why do fully homo-morphic constructions use 'ring' or 'lattice' structures?

Is there a significantly advantage to these data structures, or is it simply the status-quo and the easiest to use for describing constructions?
3
votes
1answer
44 views

Distributing blocks with validation and non-dependant list generation

Problem Suppose I have a system of nodes that can communicate with a parent node, but not among each other. Suppose then a file on the parent node is split up into blocks and divided among the ...
3
votes
3answers
435 views

Searching over encrypted data

Is there any library/tool available which can allow me to search over encrypted data? I would like to encrypt data on client side, send it to cloud and perform search in cloud. I've been reading ...
3
votes
1answer
223 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 ...
3
votes
0answers
107 views

Lowest number challenge scheme

Suppose Alice knows a secret number $a$, and Bob knows a secret number $b$. Is there a simple way for Alice and Bob to know who has the lowest number, without Alice & Bob exchanging their numbers ...
3
votes
0answers
82 views

FHE over the integers - Is that paper's scheme known to be insecure against quantum adversaries?

I was reading the paper Fully Homomorphic Encryption over the Integers, and started wondering if there is a known quantum attack on their main scheme, because There is an efficient quantum attack ...