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6

What you describe is known as Threshold-secret-sharing, for which a good candidate is the threshold version of shamir-secret-sharing. In particular, for your use case I would recommend implementing an "n-1 out of n threshold sharing scheme". Shamir Secret Sharing $(n,k)$-threshold scheme. Shamir's $k$ of $n$ threshold sharing scheme is based on the ...


5

For information theoretic security in Shamir's [m,m] secret sharing scheme, do i need both authentic and confidential channels? Regular shamir secret sharing provides no protection against modified shares. So we typically assume an honest dealer with authentic and confidential channels. That means the adversary cannot change the message in transit. If a ...


4

The main misconception is, that Shamir's secret sharing is not a protocol. It states: If you have enough shares, then you can retrieve the information. And it is information theoretic. Waht does this mean? First off, there is no adversarial model in the sense of malicious or honest-but-curious adversary. It is out of scope of the protocol how and if ...


4

If you perform the distribution digitally (using networks) then you have a problem. Unless you use another one time pad you lose the perfect confidentiality as the distribution itself won't deliver perfect security. But using another one time pad is pointless: you would lose exactly as many key bits as you are distributing, while you are only protecting the ...


4

Actually, you can do Shamir Secret Sharing over any finite field $GF(p^k)$, for any prime $p$ and any integer $k$. If $k=1$, you have the $GF(p)$ field you mentioned; however it works on extension fields as well. We often pick $p=2$ and $k$ a multiple of 8; this makes everything nice even number of bytes (at the cost of doing our calculations in $GF(2^k)$). ...


3

There are no security advantages to evaluating the polynomial at random places instead of sequential. The information theoretic security proof of Shamir secret sharing does not depend on the evaluation points being chosen in any specific manner.


3

To answer your question, the cryptographic complexity will reduce by $2^{k-n}$ where $k$ is the key length and $n$ is the number of bits known. A slightly better scheme that doesn't use a cryptographic key sharing scheme can be as follows: Generate three random numbers $B_1$, $B_2$, $B_3$ with bit length equal to the size of your key $K_p$. Generate each ...


3

Just use Shamir's Secret sharing: wiki link It's designed by Adi Shamir, who is the "S" in RSA. It's fairly simple to use and there are no known weaknesses in it. While it doesn't split the data, splitting the key may work just as well (unless you absolutely must split the data.)


3

Well, first off, unless the updated shares hid a different secret, the problem is impossible (unless $k' = 0$, or you haven't distributed $k$ of the old shares). That's because, since at least $k$ people have the old shares, they can get together and ignore the new shares; instead, they use their old shares to construct the secret. If you need the new ...


2

Yes, that is possible -- that's exactly the problem that secure multiparty computation solves. You should start by reading standard references on secure multiparty computation. You might enjoy the following paper, and follow-on work: Secure Multiparty Computations on Bitcoin, Marcin Andrychowicz and Stefan Dziembowski and Daniel Malinowski and Łukasz ...


2

You can do it with two machines. https://www.iacr.org/archive/crypto2001/21390136.pdf (this paper is for DSA; it's easy to adapt for ECDSA). Here's an open-source JavaScript implementation of two-party ECDSA signing, using Bitcoin parameters: http://www.jpaulgossip.com/demo/split-key.html Unfortunately the protocol requires at least three rounds of ...


1

Is /dev/urandom fine for my use-case or should I use /dev/random? Theoretically, there is no security difference as both are regarded to be cryptographically secure RNGs. Practically, you’ll want to use /dev/urandom as that is “non-blocking” since it re-uses it’s entropy-pool whenever it runs out of random data, while /dev/random may make your ...


1

The best way is to keep things simple. Once the key has been generated, keep it on the server and make sure only authenticated users can request the key from that location. Make all the clients request the key from the server.


1

I'm not sure about your specific system; this only addresses "can a key derived from the password make a good shared secret?" The most common password hashing functions are actually designed for exactly this purpose -- deriving a cryptographic key from a (weak) password. That's actually what PBKDF2 stands for: "password-based key derivation function #2" ...


1

Reform the problem. Instead of each participant picking their givee (which they give to), have them select a giver (which they receive from). Each participant randomly generates a number (appropriately large) and anonymously submits it (e.g., via the tor network) to the site. This number represents them as giver. After all participants have entered, the ...


1

If you have $t-1$ shares of an $(t,n)$ system, you have a chance at learning of the roots of the system... as long as some of your shares have a 0 for the $y$ coordinate. You can't learn any other roots. Demonstration that the possession of a share with a $y$ coordinate of 0 gives you knowledge of a root (and forgive me if this is too obvious): A share ...


1

Just to be specific we are talking about information theoretically secure secret sharing, e.g. Shamir sharing. Lets say a secret $secret$ is shared in $n$ shares $S = \{s_1, \ldots, s_n\}$. Assume further party $P_i$ is given share $s_i$. If I understand your question correctly, you are asking if we give $P_i$ some share $r \ne s_i$ is there anyway for $P_i$ ...


1

Can you use threshold encryption and a mixnet? It might not be the fastest thing in the world but it uses well-understood components. Setup Every player generates an ElGamal keypair and proves knowledge of their secret key. The joint public key is the product of all public keys. (If you're worried about reset attacks, look up "Pedersen threshold key ...



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