A Multisecret-Sharing Scheme Based on LCD Codes (original) (raw)
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arXiv (Cornell University), 2021
Hiding a secret is needed in many situations. Secret sharing plays an important role in protecting information from getting lost, stolen, or destroyed and has been applicable in recent years. A secret sharing scheme is a cryptographic protocol in which a dealer divides the secret into several pieces of share and one share is given to each participant. To recover the secret, the dealer requires a subset of participants called access structure. In this paper, we present a multi-secret sharing scheme over a local ring based on linear complementary dual codes using Blakley's method. We take a large secret space over a local ring that is greater than other code-based schemes and obtain a perfect and almost ideal scheme. Multi-secret sharing scheme (MSSS) is an important family of SSSs. It is a case in which many secrets need to be shared. In other words, a multi-secret sharing scheme is a protocol to share m arbitrarily related secrets s 1 , s 2 ,. .. , s m among a
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2008 IEEE Information Theory Workshop, 2008
Secret sharing is an important topic in cryptography and has applications in information security. We use self-dual codes to construct secret-sharing schemes. We use combinatorial properties and invariant theory to understand the access structure of these secret-sharing schemes. We describe two techniques to determine the access structure of the scheme, the first arising from design properties in codes and the second from the Jacobi weight enumerator, and invariant theory.
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In this paper we construct a subclass of the composite access structure introduced in [9] based on schemes realizing the structure given by the set of codewords of minimal support of linear codes. This class enlarges the iterated threshold class studied in the same paper. Furthermore all the schemes on this paper are ideal (in fact they allow a vector space construction) and we arrived to give a partial answer to a conjecture stated in . Finally, as a corollary we proof that all the monotone access structures based on all the minimal supports of a code can be realized by a vector space construction.
Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS Codes
International Conference on Applied and Computational Mathematics, 2012
An ideal conjunctive hierarchical secret sharing scheme, constructed based on the Maximum Distance Separable (MDS) codes, is proposed in this paper. The scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. Also, in our scheme, the size of the ground field is independent of the parameters of the access structure. Further, it is efficient and requires O(n 3), where n is the number of participants.
Application of Secret Sharing Scheme with MDS Codes Defined over
Secret Sharing Scheme is a technique developed for secret information like cryptographic keys and aims to increase the security against attacks by dividing the secret key into pieces and distribute the pieces to different persons in a group so that certain subsets of the group can get together to recover the key. This notion was first proposed by Shamir and Blakley in 1979. Actually they gave threshold secret sharing scheme. Since then, many constructions have been proposed. One of them is based on coding theory. In this paper, we present an application of the (k, n) threshold secret sharing scheme using (n+1, k) MDS (Maximum Distance Separable) codes, which is defined over ) 2 ( n GF . It is also shown that at least k participants of a set of n participants are needed to reconstruct the secret.
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International Journal of Trust Management in Computing and Communications, 2014
Two compartmented secret sharing schemes are proposed in this paper. Constructions of the proposed schemes are based on the maximum distance separable (MDS) codes. One of the proposed schemes is perfect in classical sense and the other scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorised set can always reconstruct the secret in polynomial time whereas for an unauthorised set this is computationally hard. This is in contrast to some of the existing schemes in the literature, in which an authorised set can recover the secret only with certain probability. Also, in our schemes unlike in some of the existing schemes, the size of the ground field need not be extremely large. One of the proposed schemes is shown to be ideal and the information rate for the other scheme is 1/2. Both the schemes are efficient and require O(mn 3), where n is the number of participants and m is the number of compartments.
Lecture Notes in Computer Science, 1994
A multi-secret sharing scheme is a protocol to share m arbitrarily related secrets s1,. . . , sm among a set of participants P. In this paper we put forward a general theory of multi-secret sharing schemes by using an information theoretical framework. We prove lower bounds on the size of information held by each participant for various access structures. Finally, we prove the optimality of the bounds by providing protocols.
Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes
Lecture Notes in Computer Science, 2008
Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of 3-multiplicative LSSS, and establish its relationship with strongly multiplicative LSSS. More precisely, we show that any 3-multiplicative LSSS is a strongly multiplicative LSSS, but the converse is not true; and that any strongly multiplicative LSSS can be efficiently converted into a 3-multiplicative LSSS. Furthermore, we apply 3-multiplicative LSSS to the computation of unbounded fan-in multiplication, which reduces its round complexity to four (from five of the previous protocol based on multiplicative LSSS). We also give two constructions of 3-multiplicative LSSS from Reed-Muller codes and algebraic geometric codes. We believe that the construction and verification of 3-multiplicative LSSS are easier than those of strongly multiplicative LSSS. This presents a step forward in settling the open problem of efficient constructions of strongly multiplicative LSSS from general LSSS.
An extension of Massey scheme for secret sharing
2010 IEEE Information Theory Workshop, 2010
We consider an extension of Massey's construction of secret sharing schemes using linear codes. We describe the access structure of the scheme and show its connection to the dual code. We use the g-fold joint weight enumerator and invariant theory to study the access structure.
On construction of cumulative secret sharing schemes
Lecture Notes in Computer Science, 1998
Secret sharing schemes are one of the most important primitives in distributed systems. Cumulative secret sharing schemes provide a method to share a secret with arbitrary access structures. This paper presents two di erent methods for constructing cumulative secret sharing schemes. First method produces a simple and e cient cumulative scheme. The second method, however, provides a cheater identi able cumulative scheme. The both proposed schemes are perfect.