10,409 research outputs found
Ideal Tightly Couple (t,m,n) Secret Sharing
As a fundamental cryptographic tool, (t,n)-threshold secret sharing
((t,n)-SS) divides a secret among n shareholders and requires at least t,
(t<=n), of them to reconstruct the secret. Ideal (t,n)-SSs are most desirable
in security and efficiency among basic (t,n)-SSs. However, an adversary, even
without any valid share, may mount Illegal Participant (IP) attack or
t/2-Private Channel Cracking (t/2-PCC) attack to obtain the secret in most
(t,n)-SSs.To secure ideal (t,n)-SSs against the 2 attacks, 1) the paper
introduces the notion of Ideal Tightly cOupled (t,m,n) Secret Sharing (or
(t,m,n)-ITOSS ) to thwart IP attack without Verifiable SS; (t,m,n)-ITOSS binds
all m, (m>=t), participants into a tightly coupled group and requires all
participants to be legal shareholders before recovering the secret. 2) As an
example, the paper presents a polynomial-based (t,m,n)-ITOSS scheme, in which
the proposed k-round Random Number Selection (RNS) guarantees that adversaries
have to crack at least symmetrical private channels among participants before
obtaining the secret. Therefore, k-round RNS enhances the robustness of
(t,m,n)-ITOSS against t/2-PCC attack to the utmost. 3) The paper finally
presents a generalized method of converting an ideal (t,n)-SS into a
(t,m,n)-ITOSS, which helps an ideal (t,n)-SS substantially improve the
robustness against the above 2 attacks
Sharing classical secrets with CSS codes
In this paper we investigate the use of quantum information to share
classical secrets. While every quantum secret sharing scheme is a quantum error
correcting code, the converse is not true. Motivated by this we sought to find
quantum codes which can be converted to secret sharing schemes. If we are
interested in sharing classical secrets using quantum information, then we show
that a class of pure CSS codes can be converted to perfect secret
sharing schemes. These secret sharing schemes are perfect in the sense the
unauthorized parties do not learn anything about the secret. Gottesman had
given conditions to test whether a given subset is an authorized or
unauthorized set; they enable us to determine the access structure of quantum
secret sharing schemes. For the secret sharing schemes proposed in this paper
the access structure can be characterized in terms of minimal codewords of the
classical code underlying the CSS code. This characterization of the access
structure for quantum secret sharing schemes is thought to be new
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
On single server private information retrieval in a coding theory perspective
In this paper, we present a new perspective of single server private
information retrieval (PIR) schemes by using the notion of linear
error-correcting codes. Many of the known single server schemes are based on
taking linear combinations between database elements and the query elements.
Using the theory of linear codes, we develop a generic framework that
formalizes all such PIR schemes. Further, we describe some known PIR schemes
with respect to this code-based framework, and present the weaknesses of the
broken PIR schemes in a generic point of view
- …