Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures
Summary :
It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.1 pp.101-112
- Publication Date
- 2007/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.1.101
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
- Protocols
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Keyword
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Mitsugu IWAMOTO, Hirosuke YAMAMOTO, Hirohisa OGAWA, "Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 1, pp. 101-112, January 2007, doi: 10.1093/ietfec/e90-a.1.101.
Abstract: It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.1.101/_p
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@ARTICLE{e90-a_1_101,
author={Mitsugu IWAMOTO, Hirosuke YAMAMOTO, Hirohisa OGAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures},
year={2007},
volume={E90-A},
number={1},
pages={101-112},
abstract={It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.},
keywords={},
doi={10.1093/ietfec/e90-a.1.101},
ISSN={1745-1337},
month={January},}
Copy
TY - JOUR
TI - Optimal Multiple Assignments Based on Integer Programming in Secret Sharing Schemes with General Access Structures
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 101
EP - 112
AU - Mitsugu IWAMOTO
AU - Hirosuke YAMAMOTO
AU - Hirohisa OGAWA
PY - 2007
DO - 10.1093/ietfec/e90-a.1.101
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2007
AB - It is known that for any general access structure, a secret sharing scheme (SSS) can be constructed from an (m,m)-threshold scheme by using the so-called cumulative map or from a (t,m)-threshold SSS by a modified cumulative map. However, such constructed SSSs are not efficient generally. In this paper, a new method is proposed to construct a SSS from a (t,m)-threshold scheme for any given general access structure. In the proposed method, integer programming is used to derive the optimal (t,m)-threshold scheme and the optimal distribution of the shares to minimize the average or maximum size of the distributed shares to participants. From the optimality, it can always attain lower coding rate than the cumulative maps because the cumulative maps cannot attain the optimal distribution in many cases. The same method is also applied to construct SSSs for incomplete access structures and/or ramp access structures.
ER -
English
