### Abstract

In this paper, we consider the robustness of a special type of secret sharing scheme known as visual cryptographic scheme in which the secret reconstruction is done visually without any mathematical computation unlike other secret sharing schemes. Initially, secret sharing schemes were considered with the presumption that the corrupted participants involved in a protocol behave in a passive manner and submit correct shares during the reconstruction of secret. However, that may not be the case in practical situations. A minimal robust requirement, when a fraction of participants behave maliciously and submit incorrect shares, is that, the set of all shares, some possibly corrupted, can recover the correct secret. Though the concept of robustness is well studied for secret sharing schemes, it is not at all common in the field of visual cryptography. We, for the first time in the literature of visual cryptography, formally define the concept of robustness and put forward (2, n)-threshold visual cryptographic schemes that are robust against deterministic cheating. In the robust secret sharing schemes it is assumed that the number of cheaters is always less than the threshold value so that the original secret is not recovered by the coalition of cheaters only. In the current paper, We consider three different scenarios with respect to the number of cheaters controlled by a centralized adversary. We first consider the existence of only one cheater in a (2, n)-threshold VCS so that the secret image is not recovered by the cheater. Next we consider two different cases, with number of cheaters being greater than 2, with honest majority and without honest majority.

Original language | English |
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Title of host publication | Digital Forensics and Watermarking - 15th International Workshop, IWDW 2016, Revised Selected Papers |

Editors | Hyoung Joong Kim, Feng Liu, Fernando Perez-Gonzalez, Yun Qing Shi |

Publisher | Springer Verlag |

Pages | 251-262 |

Number of pages | 12 |

ISBN (Print) | 9783319534640 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | 15th International Workshop on Digital-Forensics and Watermarking, IWDW 2016 - Beijing, China Duration: Sep 17 2016 → Sep 19 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10082 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 15th International Workshop on Digital-Forensics and Watermarking, IWDW 2016 |
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Country | China |

City | Beijing |

Period | 9/17/16 → 9/19/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Digital Forensics and Watermarking - 15th International Workshop, IWDW 2016, Revised Selected Papers*(pp. 251-262). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10082 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-53465_719

**On the robustness of visual cryptographic schemes.** / Dutta, Sabyasachi; Roy, Partha Sarathi; Adhikari, Avishek; Sakurai, Kouichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Digital Forensics and Watermarking - 15th International Workshop, IWDW 2016, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10082 LNCS, Springer Verlag, pp. 251-262, 15th International Workshop on Digital-Forensics and Watermarking, IWDW 2016, Beijing, China, 9/17/16. https://doi.org/10.1007/978-3-319-53465_719

}

TY - GEN

T1 - On the robustness of visual cryptographic schemes

AU - Dutta, Sabyasachi

AU - Roy, Partha Sarathi

AU - Adhikari, Avishek

AU - Sakurai, Kouichi

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, we consider the robustness of a special type of secret sharing scheme known as visual cryptographic scheme in which the secret reconstruction is done visually without any mathematical computation unlike other secret sharing schemes. Initially, secret sharing schemes were considered with the presumption that the corrupted participants involved in a protocol behave in a passive manner and submit correct shares during the reconstruction of secret. However, that may not be the case in practical situations. A minimal robust requirement, when a fraction of participants behave maliciously and submit incorrect shares, is that, the set of all shares, some possibly corrupted, can recover the correct secret. Though the concept of robustness is well studied for secret sharing schemes, it is not at all common in the field of visual cryptography. We, for the first time in the literature of visual cryptography, formally define the concept of robustness and put forward (2, n)-threshold visual cryptographic schemes that are robust against deterministic cheating. In the robust secret sharing schemes it is assumed that the number of cheaters is always less than the threshold value so that the original secret is not recovered by the coalition of cheaters only. In the current paper, We consider three different scenarios with respect to the number of cheaters controlled by a centralized adversary. We first consider the existence of only one cheater in a (2, n)-threshold VCS so that the secret image is not recovered by the cheater. Next we consider two different cases, with number of cheaters being greater than 2, with honest majority and without honest majority.

AB - In this paper, we consider the robustness of a special type of secret sharing scheme known as visual cryptographic scheme in which the secret reconstruction is done visually without any mathematical computation unlike other secret sharing schemes. Initially, secret sharing schemes were considered with the presumption that the corrupted participants involved in a protocol behave in a passive manner and submit correct shares during the reconstruction of secret. However, that may not be the case in practical situations. A minimal robust requirement, when a fraction of participants behave maliciously and submit incorrect shares, is that, the set of all shares, some possibly corrupted, can recover the correct secret. Though the concept of robustness is well studied for secret sharing schemes, it is not at all common in the field of visual cryptography. We, for the first time in the literature of visual cryptography, formally define the concept of robustness and put forward (2, n)-threshold visual cryptographic schemes that are robust against deterministic cheating. In the robust secret sharing schemes it is assumed that the number of cheaters is always less than the threshold value so that the original secret is not recovered by the coalition of cheaters only. In the current paper, We consider three different scenarios with respect to the number of cheaters controlled by a centralized adversary. We first consider the existence of only one cheater in a (2, n)-threshold VCS so that the secret image is not recovered by the cheater. Next we consider two different cases, with number of cheaters being greater than 2, with honest majority and without honest majority.

UR - http://www.scopus.com/inward/record.url?scp=85013436530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013436530&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-53465_719

DO - 10.1007/978-3-319-53465_719

M3 - Conference contribution

AN - SCOPUS:85013436530

SN - 9783319534640

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 251

EP - 262

BT - Digital Forensics and Watermarking - 15th International Workshop, IWDW 2016, Revised Selected Papers

A2 - Kim, Hyoung Joong

A2 - Liu, Feng

A2 - Perez-Gonzalez, Fernando

A2 - Shi, Yun Qing

PB - Springer Verlag

ER -