arXiv subjects

Kamil Kulesza

Publications and source records attributed to Kamil Kulesza.

8 recordsLinked to original sources

arXiv2007

Can Alice and Bob be random: a study on human playing zero knowledge protocols

The research described in this abstract was initiated by discussions between the author and Giovanni Di Crescenzo in Barcelona in early 2004. It was during Advanced Course on Contemporary Cryptology that Di Crescenzo gave a course on zero knowledge protocols (ZKP), see [1]. After that course we started to play with unorthodox ideas for breaking ZKP, especially one based on graph 3-coloring. It was chosen for investigation because it is being considered as a "benchmark" ZKP, see [2], [3]. At this point we briefly recall such a protocol's description.

cs.CR↗

arXiv2003

The upper bound on number of graphs, with fixed number of vertices, that vertices can be colored with n colors

In the paper we state and prove theorem describing the upper bound on number of the graphs that have fixed number of vertices |V| and can be colored with the fixed number of n colors. The bound relates both numbers using power of 2, while the exponent is the difference between |V| and n. We also state three conjectures on the number of graphs that have fixed number of vertices |V| and chromatic number n.

math.CO↗

arXiv2003

On secret sharing for graphs

In the paper we discuss how to share the secrets, that are graphs. So, far secret sharing schemes were designed to work with numbers. As the first step, we propose conditions for "graph to number" conversion methods. Hence, the existing schemes can be used, without weakening their properties. Next, we show how graph properties can be used to extend capabilities of secret sharing schemes. This leads to proposal of using such properties for number based secret sharing.

cs.CR↗

arXiv2003

Secret Sharing for n-Colorable Graphs with Application to Public Key Cryptography

At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors assigned to vertices form the number with entries from Zn. A secret sharing scheme (SSS) for the graph coloring is proposed. The proposed method is applied to the public-key cryptosystem called "Polly Cracker". In this case the graph structure is a public key, while proper 3-colouring of the graph is a private key. We show how to share the private key. Sharing particular n-coloring (color-to-vertex assignment) for the known-structure graph is presented next.

cs.CR↗

arXiv2002

On ASGS framework: general requirements and an example of implementation

In the paper we propose general framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the dealer from knowing the secret or even to eliminate him at all. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unknown until it is reconstructed. Next, we propose the framework for automatic sharing of a known secret. In this case the dealer does not know the secret and the secret owner does not know the shares. We present opportunities for joining ASGS with other extended capabilities, with special emphasize on PVSS and proactive secret sharing. Finally, we illustrate framework with practical implementation. Keywords: cryptography, secret sharing, data security, extended capabilities, extended key verification protocol

math.CO↗

arXiv2002

On graph coloring check-digit method

We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the result is outlined. Next, graph coloring based check-digit scheme is proposed. We use quantitative result derived, to show, that feasibility of the proposed scheme increases with size of the number which digits are checked, and overall probability of digits errors.

math.CO↗

arXiv2002

On alternative approach for verifiable secret sharing

Secret sharing allows split/distributed control over the secret (e.g. master key). Verifiable secret sharing (VSS) is the secret sharing extended by verification capacity. Usually verification comes at the price. We propose "free lunch", the approach that allows to overcome this inconvenience.

math.CO↗

arXiv2002

On the graph coloring check-digit scheme with applications to verifiable secret sharing

In the paper we apply graph vertex coloring for verification of secret shares. We start from showing how to convert any graph into the number and vice versa. Next, theoretical result concerning properties of n-colorable graphs is stated and proven. From this result we derive graph coloring check-digit scheme. Feasibility of proposed scheme increases with the size of the number, which digits are checked and overall probability of errors. The check-digit scheme is used to build shares verification method that does not require cooperation of the third party. It allows implementing verification structure different from the access structure. It does not depend on particular secret sharing method. It can be used as long as the secret shares can be represented by numbers or graphs.

cs.CR↗