NDLI: New results and applications for multi-secret sharing schemes

Content Provider	Springer Nature Link
Author	Herranz, Javier Sáez, Germán Ruiz, Alexandre
Copyright Year	2013
Abstract	In a multi-secret sharing scheme (MSSS), $$\ell $$ different secrets are distributed among the players in some set $$\mathcal{P }=\{P_1,\ldots ,P_n\}$$ , each one according to an access structure. The trivial solution to this problem is to run $$\ell $$ independent instances of a standard secret sharing scheme, one for each secret. In this solution, the length of the secret share to be stored by each player grows linearly with $$\ell $$ (when keeping all other parameters fixed). Multi-secret sharing schemes have been studied by the cryptographic community mostly from a theoretical perspective: different models and definitions have been proposed, for both unconditional (information-theoretic) and computational security. In the case of unconditional security, there are two different definitions. It has been proved that, for some particular cases of access structures that include the threshold case, a MSSS with the strongest level of unconditional security must have shares with length linear in $$\ell $$ . Therefore, the optimal solution in this case is equivalent to the trivial one. In this work we prove that, even for a more relaxed notion of unconditional security, and for some kinds of access structures (in particular, threshold ones), we have the same efficiency problem: the length of each secret share must grow linearly with $$\ell $$ . Since we want more efficient solutions, we move to the scenario of MSSSs with computational security. We propose a new MSSS, where each secret share has constant length (just one element), and we formally prove its computational security in the random oracle model. To the best of our knowledge, this is the first formal analysis on the computational security of a MSSS. We show the utility of the new MSSS by using it as a key ingredient in the design of two schemes for two new functionalities: multi-policy signatures and multi-policy decryption. We prove the security of these two new multi-policy cryptosystems in a formal security model. The two new primitives provide similar functionalities as attribute-based cryptosystems, with some advantages and some drawbacks that we discuss at the end of this work.
Ending Page	864
Page Count	24
Starting Page	841
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	3
Volume Number	73
Language	English
Publisher	Springer US
Publisher Date	2013-05-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Information and Communication, Circuits Data Encryption Entropy Multi-policy cryptosystems Measures of information, entropy Data Structures, Cryptology and Information Theory Discrete Mathematics in Computer Science Multi-secret sharing schemes Provable security Coding and Information Theory Authentication and secret sharing Cryptography Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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