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Questions tagged [multiparty-computation]

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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Oblivious transfer with trusted third party Trent

I am trying to solve this exercise. Assume an oblivious transfer protocol that uses a trusted third party Trent. Alice's messages $M_0$ and $M_1$ are binary values of length $k$. Bob's message ...
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MPC using homomorphic encryption

Is there a way to implement secure square root protocol between two parties (using homomorphic encryption)? I couldn't find existing solutions in literature. My desired protocol is as follows: ...
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Algorithm for binary less than in MPC

Given binary shares $[a_{l-1}]_p,...,[a_0]_p, [b_{l-1}]_p,...,[b_0]_p$ such that $a = \sum_{i=0}^{l-1} a_i2^i,b = \sum_{i=0}^{l-1} b_i2^i $ for $a,b \in Z_p$, how to compute $a \overset{?}{\lt} b$ in ...
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Interactive Homomorphic Encryption

Let's say that I have a plain computational process that consists of several divisions and I do not want to do it with non-interactive homomorphic encryption. I would like to ask how can I call this ...
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Blind Computation

Let's say that there are two parties. Party $A$ has ciphertexts $c_1, c_2$ encrypting data $m_1,m_2$ respectively. $A$ does not know the secret key to decrypt $c_1, c_2$. Party $B$ has the secret key. ...
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Algorithm for computing modular inverse in MPC

Is there any known algorithm for calculating $a^{-1} \pmod{q}$, where $ q < p$ and $F_{p}$ is the prime field of the MPC, in a linear secret sharing scheme ? I have tried using the standard ...
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Distributed generation of random integers with prescribed sum

While reading this document I came across the following problem. Assume you have $n$ clients. The clients need to generate random integers in $\mathbb{Z}_p$, say $T_i$ for $i \in \{1, \ldots, n\}$, ...
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Difference between Zero Knowledge Proofs and Multi Party Computation

I am struggling with understanding the difference between the two. From what I am putting together, they have different adversarial models, MPC adds the condition of collusion between parties i.e. ...
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What (Where) is the formal definition of Multiparty Computation? [closed]

I'm just curious where we can see a (original) formal definition of MPC. What (Where) is the formal definition of MPC? We have a bunch of tools to build a MPC protocol. Is oblivious transfer (or OT-...
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55 views

Under what conditions is broadcast possible? (Cryptographically, and in the model of Maurer 2006)

In this paper, Ueli Maurer uses a very cool model to generalize a number of results about broadcast, secret sharing and secure multiparty computation. Rather than talking about an adversary being ...
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How to ensure a trusted computing of a function in untrusted Cloud server?

Could you please let me know the latest practical techniques and cryptographic schemes that allow hiding function execution in an untrusted Cloud?
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Multi-secret sharing (Packed secret sharing) - Some questions

In the publication - "Communication complexity of secure computation", I have encountered a small problem - on page 5 of the literature under the heading "Theorem 1" they have described a $(c,d; k,n)$ ...
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Is the simulation-based proof difficult and needed? [closed]

What is the role for simulation-based proof under the semi-honest model without considering malicious adversaries? I agree with that a view of a some party is important to prove that a protocol is ...
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MPC on boolean circuits

I am reading about Yao's and GMW protocols and was wondering if there is any perfectly secure MPC protocol in the semi-honest setting, where the underlying circuit is a Boolean circuit (eg. n=3 and t=...
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1answer
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Commitment in two party protocols

I have been reading Fast Secure Two-Party ECDSA Signing by Lindell, and I see that in key generating and signing (pages 9-10, especially visible from Figure 1), only the first party performs a ...
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Testing whether a secret value is zero without security bits (in SPDZ)

To test whether a secret value $[x]$ is zero, where $x \in [0,2^{k−1}]$, SPDZ uses the a based on the method of Catrina and de Hoogh [1]. This method requires to working on a field with modulus $p>...
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Using SPDZ over smaller field

While trying to implement SPDZ of a function (using the fresco framework[1]), it enforce me to work on a larger field than the one that I need. This occur because I'm trying to use functions such as "...
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2answers
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How to compute secure sum using secure multparty computation?

Suppose there are three voters $P$, $Q$ and $R$, and each will vote only on one candidate out of $X$, $Y$ or $Z$, with a 6 bit vote vector corresponding to $X $, $Y$ and $Z$ respectively (with 2 bits ...
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Adding new participants to a multiparty signature scheme

I'm looking for a signature scheme that allows a group of N parties, without the help of a trusted dealer, to: Jointly create a group public key $P$ Produce a valid signatures for an arbitrary ...
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How to determine the layers of a circuit?

In many cryptographic applications like Multiparty Computation (MPC) or Fully Homomorphic Encryption (FHE), you consider a function $f$ described by a circuit over some algebraic structure, typically ...
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1answer
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In Multi-party communication, how can I find that one encrypted value is negative or not?

I'm using Pailier Cryptosystem as an additive homomorphic system in my scenario. I have two parties: Alice and Bob. Alice has one pair of (SK, Pk) keys. She encryptes one value using her public key ...
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computing INV in boolean circuit for MPC

Is it feasible to generate an efficient MPC function that compute $a^{-1}$ for $a \in \mathbb{F_q}$, with Boolean circuit? The naive way seems impossible since the depth of the computation might ...
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What is shared-input for Multi Party Computation?

I heard shared input. For example, original values $x,y \in M$ are divided into pairs of shares $(x_1,x_2)$ and $(y_1, y_2)$ such that $x_1 + x_2 = x \text{ and } y_1 + y_2 = y$. Each share is ...
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Multi-Party Offline Key Exchange Using Public and Private Keys

I hope the title already explains the problem I have in mind; but let me lay out some more details. Given public-private key pairs $P_A, P_B, P_C, ... P_Z$, (first $3$ of which are owned by our usual ...
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complete functionality for fair multiparty computation

I found a statement in a paper "We reduce the fairness problem in MPC to the problem of fair decryption. Fair decryption was shown to be a complete functionality for fair MPC (shown by Dov Gordon in ...
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68 views

Check if $a<b$ in a trustless scenario

Let's say Alice has access only to a value $a$ and Bob has access to both $a$ and $b$. I need ...
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Threshold Bitcoin signature scheme

Any advice would be appreciated: It seems to me that using an uncomplicated combination of a shamir scheme and schnorr it's fairly trivial to have a threshold signature scheme. I think it's also ...
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2answers
158 views

How to use Homomorphic encryption for secure computing Arctan() function?

In the multi-party communication(MPC), if partyA has the coordinate(x1 y1) and partyB has the coordiante(x2,y2), how two parties can securely compute Arctan((y1-y2)/(x1-x2)) without revealing their ...
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2answers
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Atomic multi-party commitments

Alice and Bob publicly choose the messages $M_A$ and $M_B$ and independently sign them (Alice privately signs $M_A$, Bob signs $M_B$). Now Alice and Bob are looking for a protocol that allows them to:...
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3answers
71 views

communication efficient private lookup

I have a scenario where a client has a private set and the server has a large public set, we would like an estimate of the intersection size or more specifically the percent of the private set covered ...
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1answer
152 views

AES encryption using MPC SPDZ protocol

I'm reading the article about SPDZ protocol for secure multiparty computation (and also improvements for offline phase like MASCOT). However I'm thinking about practical application of SPDZ for AES ...
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Can we convert a pseudorandom function (PRF) to an Oblivious PRF (OPRF) through an Oblivious Transfer (OT) protocol?

I'm a software engineer, so I generally think in building blocks. And I'm not so familiar with the Math notation in Crytography, so I'll stick with function calls and function blueprints (which I ...
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How can Alice enable Bob to look-up values in a private map

I think this problem is similar to private set intersection, yet distinct in a way where: Alice has an extensive Mapping of say id to name id1 -> John Doe id2 -> Jane Doe id3 -> Edgar ...
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1answer
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Secure Computation: Reactive Functionalities in the Hybrid Model for Standalone Security

A common approach to make (secure computation) protocol descriptions and proofs simpler is to describe them in a hybrid model, where the protocol in the real world has access to some auxiliary ideal ...
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2answers
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Multiparty secret generation protocol

The goal is to create a secret S on a trusted server by having users A, B and C each send a private seed to the server, in such a way that any 2 of them can later recover S by resubmitting their ...
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Difference in the Powers of Simulator and Environment in Universal Composability

I know that in UC model, environment controls the real world adversaries but there is still a simulator wrapped around these real-world adversaries in the ideal world (which we sometimes collectively ...
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Extractability for Simulator in Malicious Model

It is sometimes required while proving the security of a protocol in the malicious setting that the simulator is able to extract the witness set of the adversary, who tends to be the prover of ...
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1answer
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Private set supporting adding elements and proving elements exist

Is it possible to construct such a set that parties can Add elements to the set without revealing the elements or knowing the elements presently in the set. Proving to other parties that a certain ...
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Enforcing Randomness in Malicious Setting

I was going through some lecture notes where it said that if we have a 2-party protocol that requires both the parties to generate random integers during the course of protocol, then if we migrate the ...
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Anti-collusion cryptography/schemes for multi party authentication

Due to the fact that 95+%, if I remember correctly, of security breaches are done by insiders (due to malicious intent or incompetence), I made a (experimental) server that uses Shamir Secret Sharing ...
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1answer
135 views

In coin flipping protocols, why aborting is allowed, and why the non-aborting party flips a coin at the end?

To convey how an adversary can bias the coin, most often a simple commitment-based two party coin-tossing protocol is given, as in [1]: Alice sends Bob the commitment $c = commit(x)$ Bob sends Alice ...
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How to assert that n distinct users have generate an aggregate signature?

If We have n users, each one generate message m1 and signs it to generate (σ1). then by using aggregate signature scheme, we get the aggregate signature of all messages m from n users. Is there a ...
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1answer
96 views

About DDH over cyclic group Z*p^2

To construct a secure multiparty computation function, we need to use the cyclic group G = Z*p^2 with p is a large prime. However, we are uncertain that DDH holds over this group. Can you show that ...
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Necessity of Randomness when Privately Computing a Sum

I want to show that no 1-private deterministic protocol exists for calculating a sum of $n \geq 3$ parties (within the realms of Perfect rather than Computational Security). I'm having trouble showing ...
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Optimized Random-OT Security in Standard Model

I was going through the paper - " Efficient Oblivious Transfer and Extensions for Faster Secure Computation" by Asharov et al. where the authors propose an optimized OT protocol along with a Random-OT ...
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0answers
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Computationally secure ORAMs with O(lg n)-bit words: shouldn't they fail with $n^{-O(1)}$ probability?

Virtually all "hierarchical" Oblivious RAMs use "cryptographically secure" hash functions to determine the position of an item at a given level; and implicitly assume (as can be evinced from the cost ...
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Can Secure Multi-party Computation be used to reconstruct secret shares?

When using Shamir's Secret Sharing is it possible to use Secure Multi-Party Computation to reconstruct the original secret without revealing one's secret share? When searching I have found results ...
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Is it possible to carry out multiplication of BGW protocol without communication?

I read the following famous two papers related to multiparty computation and I have a question like title. [AL17] Gilad Asharov, and Yehuda Lindell. "A full proof of the BGW protocol for perfectly ...
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Secure multiparty computation connectivity bound

I read some papers which studied the relation between the fault tolerance in secure multiparty computation and the connectivity of the underlying communication graph. Here I consider information-...
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How to perform homomorphic multiplication using Shamirs secret sharing

Shamir's secret sharing (SSS) support additive homomorphism. The problem with it while dealing with multiplication is it will increase the polynomial degree and as a result number of shares required ...