-1
votes
0answers
105 views

Multiparty Computation with ORAM

Hope is not a silly question. I'm really struggling with it and I cannot find an answer anywhere! ORAM works with shared "secure" memory on server that is accessed in an oblivious manner and a client ...
1
vote
0answers
170 views

Secure Secret sharing

I'm trying to come up with a new way to do oblivious transfer that is faster and requires less computation than existing methods. The basis of my method is shamir secret sharing. Below is an example ...
1
vote
0answers
81 views

(n,n) Shamir secret sharing [duplicate]

In (n,n) Shamir secret sharing if n shareholders do not have the public values (X values) can they still obtain the secret with only Y values?
2
votes
2answers
341 views

Shamir's secret sharing scheme - type of channels

For information theoretic security in Shamir's [m,m] secret sharing scheme, do i need both authentic and confidential channels? Another related query is ;is it true that if the channels are only ...
4
votes
1answer
94 views

Back up an information as $n$ pieces and require exactly $n-1$ to recover it

Let $X\in \Bbb F_2^p$ be some information. How do I create $Y_1,\dots,Y_n \in \Bbb F_2^q$ so that having less than $n-1$ of the $Y_i$s gives you no information on $X$ but having $n-1$ of them allows ...
1
vote
1answer
92 views

Numeric combination of passwords

Pls I need explanation on How i can design a Cryptography that use multiple passwords or passphrase to open a safe(Lock). For example, if i need five people to unlock a secured device whereby all the ...
1
vote
2answers
179 views

Diffusion in Shamir's secret sharing scheme

The popular command line utility ssss implements the classic Shamir's secret sharing scheme over the generic field $GF(2^q)$ with $8 \le q \le 1024$. When $q>=64$, the constant coefficient ($c_0$) ...
2
votes
0answers
77 views

Threshold signatures vs. certificate authority+voting verification

Perhaps a silly question, but I am wondering what the advantages are of threshold signatures. Let's consider the following two signature schemes: $(t,n)$-threshold signature with a trusted dealer, ...
1
vote
1answer
54 views

Secret Sharing 1 Required

Devise a scheme so that a message M can be shared among X, Y and Z in such a say that the only way of recovering the message is when X is present with either Y or Z. When X isn't present or each is ...
3
votes
1answer
155 views

Can I use Shamir's secret sharing scheme for multiplicative homomorphism for secure multiparty computation?

I would like to perform a dot product operation among $m$ parties using Shamir's $(m,m)$ secret sharing that is used for Secure Multiparty Computation. I am aware that Shamir's $(m,m)$ scheme is ...
3
votes
1answer
131 views

Does Runge phenomenon affect Shamir's secret sharing scheme?

Lagrange interpolation seems to be affected by the so-called Runge phenomenon when one tries to interpolate polynomials of high degree from a set of equidistant points. Lagrange interpolation is ...
4
votes
1answer
261 views

Coefficients in Shamir's Secret Sharing Scheme

Sorry if this is a stupid question, but: in Shamir's scheme, we construct a polynomial and make our secret $S$ the zero-th coefficient $a_0$. What, if anything, necessitates this - in other words, can ...
2
votes
2answers
113 views

How does secret sharing solve the partial exposure problem?

I have been trying to understand how secret sharing methods like Shamir's secret sharing solve the problem of a share revealing information about the secret. I guess there are some random numbers ...
4
votes
2answers
178 views

How to Distribute the Shares using Secret Sharing for arbitrary Monotone Access Structures

Consider 4 people, $A$,$B$,$C$,$D$, & a secret $s\in\{0,1\}^k$. Construct a scheme which enables the following subsets of people to retrieve the secret $\{A,B\}$, $\{A,C\}$, $\{B,C,D\}$. I know ...
4
votes
1answer
128 views

Shamir's Secret Share Over the Reals

What about using Shamir's secret share over the real numbers leaks information? I know there is a problem with random number generation, and someone suggested it leaks the parity of the polynomial, ...
1
vote
2answers
185 views

Shamir's Secret Share [duplicate]

I'm not quite sure the benefits of working over a prime modulus in Shamir's secret share- but doesn't limiting the numbers you pull from make the secret easier to guess? Instead of being over the real ...
2
votes
1answer
181 views

Shamir's secret sharing with passwords

I'm trying to design an extension to Shamir's Secret Sharing that would allow the participant to specify a password instead of remembering/storing a large integer or binary data. So far, I have two ...
1
vote
3answers
479 views

Lagrange Interpolation for finite field GF(2^8), for Secret Reconstruction

I'm using Lagrange's Interpolation technique to reconstruct the secret from a set of point pairs (x,y). Since I only need the secret, not the whole polynomial, I have simplified the reconstruction ...
3
votes
2answers
590 views

Why does Shamir's Secret Sharing Scheme need a finite field?

I read ampersand's question "Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme", where he asked why Shamir's Secret Sharing Scheme uses arithmetic in a ...
1
vote
3answers
607 views

Implementing secret reconstruction in Shamir's Secret Sharing

I am trying to implement Shamir's secret sharing in C++. I have got the generation of shares working. However, I am very confused with the reconstruction of shares. I get the part on how three users ...
3
votes
1answer
194 views

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 ...
8
votes
4answers
895 views

How do you find a cheater in Shamir Secret Sharing?

If there are 4 people involved, and every two of them should be able to know the secret (the polynomial is just a line) and you are given f(x) and x for each of those people, and you know one of them ...