# Tagged Questions

Multi-party computation (MPC) allows a set of parties, each with a private input, to securely and jointly perform any computation over their inputs.

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### What are the roles of the simulator in simulation based proofs

I'm trying to better understand simulation based proofs in the UC model - but the guidelines to construct a simulator confuse me. To my understanding, the simulator is activated in two ways: ...
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### Why use a 1-2 Oblivious Transfer instead of a 1 out of n Oblivious Transfer?

When initiating an oblivious transfer, why would someone use a 1-2 oblivious transfer rather than going for an 1 out of n oblivious transfer? Perhaps a slight time overhead for the extra message ...
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### Shared secret: Generating Random Permutation

-- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ...
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### What is an example of a secure sigma proof?

I want to implement Threshold Elgamal as described in section 6.3.1 and in the decryption phase each party must broadcast a sigma proof to show that it actually has a valid secret share of the secret ...
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### What does “circuits” mean in Cryptography?

I am not a hardcore cryptographer so this might be a really stupid question. I am looking through some papers in homomorphic encryption and discovered they describe computation as "circuits", why do ...
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### Secure degree reduction for Shamir's secret sharing

I understand the basic Shamir Secret Sharing protocol, and when two shares are multiplied, the degree of the polynomial increases. I've seen in a number of papers a reference to a degree reduction ...
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### Single Party Encryption, Multi Party Decryption

I am looking for an adequate protocol for public key decryption, which would allow $n$ parties to jointly decrypt a cipher text. The usage scenario for such a protocol would be a mixnet that wouldn't ...
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### Hamiltonicity proof of knowledge

I'm learning the POK notion and definitions and as a self exercise I wante to prove the statement that the Hamiltonicity protocol is a POK system with knowledge error $1/2$. So the question will be ...
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### Is a composition of clocked entities a clocked entity in the UC model?

In the book titled "Secure Multiparty Computation and Secret Sharing" the authors define an interactive agent and an interactive system. Further, the author defines a clocked entity for considering ...
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### ORAM over Third Party DB

Oblivious Ram (ORAM) is a cryptographic technique that is used for secure DB querying without leakage on the access patterns. There are several schemes for ORAM, amongst the most popular ones, there ...
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### 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 ...
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### Exact mathematical definition of simulation based security?

I've been trying to understand cryptographic protocols and how to define their security. The problem is that while I can understand what the intuitive definition says, I have trouble understanding how ...
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### Is it possible for a simulator to always abort?

In this paper of J. Baron, et al. (PDF), simulator always aborts the ideal functionality before client outputs its pattern-matching result obtained from the ideal functionality. (See bottom of page 30,...
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### Designing Secure Multi-Party Computation Sub-Protocols Based on Homomorphic Encryption

When designing SMPC protocols using secret-sharing, it is a common approach to compose a protocol from several sub-protocols (each proven secure under the formal definition of security w.r.t. semi-...
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### Secure multiparty computation of conjunction

Suppose Alice and Bob each have bits a and b, respectively. How can Alice and Bob compute the function ...
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### How many polynomials are used in Secure Multiparty Computation?

Secure Multiparty Computation based on Samir Secret sharing methods rely on Polynomials. Imagine corpus of data should be outsourced to bunch of untrusted servers for any computations. Now the data ...
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### An MPC protocol from Elgamal is a good solution a homomorphic multiplication?

I want to compute a multiplication between many secret values and then distribute the result to everyone involved. For this, I thought about an MPC protocol built from Threshold Homomorphic Elgamal. ...
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### Motivation for the definition of statistical distance

Statistical distance is a widely used measure in cryptography for comparing two distributions. One can define various other measures for capturing the differences between two distributions, but why do ...
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### Beavers Triple Vs BGW Multiplication on MPC

Typically MPC protocols that are secure against semi-honest adversaries recommend the use of the revised GMW multiplication protocol by Gennaro et al. This is not the case against Active adversaries ...
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### Real world use cases of Multi-Party Computation

Most of the research papers give imaginary applications of multi-party computation. Either they talk about Yao's millionares' problem or two or more corporates willing to compute some intrustion ...
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### Generate a random number $r \in \{1,2, \dots , k\}$, where $k$ is not public and is distributedly held

A set of parties can securely generate a random number $r \in \{1,2,3,\dots, k\}$ when $k$ is publicly known. However, can we generate the random number $r$ if $k$ is not publicly known and is held by ...
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### Yao's Garbled Circuit- Why does Alice need to rearrange the circuit?

My understanding of Yao's Garbled Circuit (based mostly on this summary) is as follows: Alice creates a garbled circuit based on the function f to be computed. She then hard-codes her input into the ...
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### Private set intersection, using a semi-trusted server

Alice has a set $S$ of words. Bob has a set $T$ of words. They want to compute the intersection $S \cap T$ of their words, with the help of a semi-trusted third party Trent. Trent runs a central ...
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### Oblivious Transfer where neither party learns the index of the message

In a traditional Oblivious Transfer setting, the sender has a list $(x_1, x_2, ... , x_n) \in G$ where $G$ is the chosen group. The receiver has $b \in \mathbb{N}$, such that engaging in the protocol ...
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### Is there an example of a “robust, yet not private” SMC protocol?

I have been trying to understand the interplay between robustness and privacy of an SMC protocol. It is easy to come up with a protocol that is private but not robust. Can someone provide an example ...
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### Are any of the practical implementations of ORAM being used in a real world system?

The concept of Oblivious RAM (ORAM) was first introduced by Oded Goldreich and Rafail Ostrovsky in 1996. However, in the past 5-10 years there has been a surge in the amount of research that looks ...
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### Is it possible to perform an MPC protocol to compute a product in a polynomial ring?

I hope not to be asking much, but I have N parties, each one holding a polynomial in with 0-1 coefficients and fixed degree $n-1$. I was wandering if it is possible (I mean feasible) to compute the ...
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### How can I implement decryption for NTRU homomorphic encryption scheme?

I have come across this paper On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., where authors describe a NTRU-based homomorphic ...
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### 2 party AND computation under passive perfect security

In the book written by Ivan Damagard titled "Secure Multiparty Computation and Secret Sharing", at the end of the third chapter he provides a proof for why it is impossible to securely compute 2 party ...
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### Importance of round complexity in determining the efficiency of an MPC protocol

Literature has different ways of specifying complexity of an MPC protocol: computation complexity that measures the number of (assumed primitive) operations performed by all the parties; ...
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### Why can't garbled circuits be reused?

There are a bunch of papers do research on resizable garbled circuits. But I wonder why garbled circuits cannot be reused? For example, the constructor constructs a garbled circuit of "AND" like this:...
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In the ideal/real proof paradigm we sometimes find simulators with the capacity of set adversary random tape. My question: when do we have to consider the necessity of simulators set adversary random-...
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### Why do the outputs of parties in an MPC protocol have to be indistinguishable from the ideal / real world (as opposed to inputs)?

In this paper at the bottom of pg. 1235 and beginning of pg. 1236 it says: An MPC protocol is said to be secure, if for every real world leakage adversary A there exists an ideal world ...
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### Equivalents to a physical hat+shaking?

I would like a multiparty protocol, secure in the honest-but-curious model at least, but hopefully other situations as well, that can do the following: every party among $\{P_1, P_2, \ldots P_n\}$ ...
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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 ...
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### Where can I find source code for ideal world simulation?

In many crypto papers I see they use a Real World / Ideal World Paradigm. However, I have never see the source code of such Simulators that try to simulate the adversary. Could somebody point me to ...
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### What's efficient MPC protocol for determining if sum's bigger than y?

My secure multi-party computation (MPC) in need is simply to determine if a sum of two private variable is bigger than a given value $y$, as $f(x_0, x_1) = [(x_0 + x_1) > y]$ in which the value ...
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### Yao's Garbled circuit: Does Bob ever see the circuit?

I asked a question about whether the circuit structure for Yao's garbled circuit needs to be rearranged. I understand from Yehuda Lindell's response that the circuit structure itself does not need to ...
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### Multi-Party Encryption for a Shared Document

Is there an encryption algorithm/protocol where any of a pre-defined set of keys/passwords will succeed in decrypting a document? The number of keys can be fixed, say, 10 or 20 possible passwords. ...
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### 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 ...
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### 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 ...
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### Addition with Shamir secret sharing

When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$. I believe this would be the correct solution (correct me if I'm wrong): Each party ...