Questions tagged [homomorphic-encryption]

Cryptosystems which support computation on encrypted data. They may be partially homomorphic (support for one operation such as + or *), somewhat (or leveled) homomorphic (support for a limited number of two operations) or they may be fully homomorphic (any sequence of + and *).

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Non-interactive proof showing the multiplication of an encrypted matrix with a public vector is as claimed

Consider a "fantasy sports" setting where $m$ contestants each pick $k$ players from a set of $n$ players before a game. The state can be represented by a Boolean matrix $\mathbf{A}$ of size ...
-1 votes
1 answer

How can arbitrary combinational logic be done with just addition and multiplication?

Once when I was reading about SPDZ (a multi-party computation protocol), and once when I was reading about homomorphic encryption, it was taken for granted that since both addition and multiplication ...
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Q: Trusting program output from an untrusted machine

Let's suppose that we create a program P, that given input I, generates output O. We then want to run this program on an untrusted computer C that may either want to tamper with the program (run P' ...
2 votes
1 answer

"Security Against Covert Adversaries" question

I was reading the paper Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries by Aumann and Lindell, and had some questions with the protocol for covert OT given errorless ...
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3 votes
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How and why does Recrypt function work?

The general aproach presented by Craig Gentry in 2009 to create a fully-homomorphic encryption system is roughly the follow: Create a scheme that can evaluate some functions (increasing the noise in ...
2 votes
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Fully Homomorphic Encryption over Integers

On the section 3 of the paper Fully Homomorphic Encryption over the Integers, there is a construction of a somewhat encryption scheme, as follow: key generation Choose an odd η-bit integer $p$ in $(...
3 votes
1 answer

How to homomorphically and "efficiently" evaluate $$(a_1 + b_1) \cdot c_1 + (a_2 + b_2) \cdot c_2 + \ldots + (a_n + b_n) \cdot c_n$$

Can i evaluate a formula $(a_i + b_i) \cdot c_i$ if i have the encryption of $a_i,b_i,c_i$ respectively using a homomorphic encryption scheme that supports multiplications and additions, supposing ...
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-6 votes
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Do irrational numbers contain an infinite number of (or all possible) patterns of sequences? [closed]

I guess the question is "does an 'infinite' number of patterns imply 'every' number of patterns?" For instance, if you could quickly calculate the decimal sequence of π, could you not (in ...
4 votes
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Algorithm Design for only Mutual Information Sharing

Bob and Alice each have a bit string they want to keep private. They each want to know what the bitwise AND of their two strings would be without telling the other or anyone else listening to their ...
2 votes
2 answers

Auditable encrypted ledger

Consider a cloud-based accounting system that needs access to aggregate information such as an account's balance but doesn't need access to individual transaction amounts in a ledger. Does there ...
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9 votes
2 answers

Threshold Fully Homomorphic Cryptosystems

recently, Craig Gentry published the first public key encryption scheme (over plaintext space {0,1}) which is fully homomorphic, meaning that one can efficiently and compactly evaluate AND and XOR on ...
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13 votes
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What languages have been successfully cryptographically trapdoored?

An observation associated with asymmetric cryptography is that some functions are (believed to be) easy to perform in one direction but difficult to invert. Furthermore, if there exists some 'trapdoor'...
22 votes
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Can a fully homomorphic encryption be used for oblivious code execution?

After reading this answer a while ago, I took an interest in fully homomorphic encryption. After reading the introduction of Gentry's thesis, I started wondering if his encryption scheme could be used ...