NDLI: Confined Guessing: New Signatures From Standard Assumptions

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Confined Guessing: New Signatures From Standard Assumptions

Content Provider	Springer Nature Link
Author	Böhl, Florian Hofheinz, Dennis Jager, Tibor Koch, Jessica Striecks, Christoph
Copyright Year	2014
Abstract	We put forward a new technique to construct very efficient and compact signature schemes. Our technique combines several instances of only a mildly secure signature scheme to obtain a fully secure scheme. Since the mild security notion we require is much easier to achieve than full security, we can combine our strategy with existing techniques to obtain a number of interesting new (stateless and fully secure) signature schemes. Concretely, we get (1) A scheme based on the computational Diffie–Hellman (CDH) assumption in pairing-friendly groups. Signatures contain $$\mathbf {O}(1)$$ and verification keys $$\mathbf {O}(\log k)$$ group elements, where $$k$$ is the security parameter. Our scheme is the first fully secure CDH-based scheme with such compact verification keys. (2) A scheme based on the (nonstrong) RSA assumption in which both signatures and verification keys contain $$\mathbf {O}(1)$$ group elements. Our scheme is significantly more efficient than existing RSA-based schemes. (3) A scheme based on the Short Integer Solutions (SIS) assumption. Signatures contain $$\mathbf {O}(\log (k)\cdot m)$$ and verification keys $$\mathbf {O}(n\cdot m) {\mathbb {Z}}_p$$ -elements, where $$p$$ may be polynomial in $$k$$ , and $$n,m$$ denote the usual SIS matrix dimensions. Compared to state-of-the-art SIS-based schemes, this gives very small verification keys, at the price of slightly larger signatures. In all cases, the involved constants are small, and the arising schemes provide significant improvements upon state-of-the-art schemes. The only price we pay is a rather large (polynomial) loss in the security reduction. However, this loss can be significantly reduced at the cost of an additive term in signature and verification key size.
Starting Page	176
Ending Page	208
Page Count	33
File Format	PDF
ISSN	09332790
Journal	Journal of Cryptology
Volume Number	28
Issue Number	1
e-ISSN	14321378
Language	English
Publisher	Springer US
Publisher Date	2014-04-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Digital signatures CDH assumption Pairing-friendly groups RSA assumption SIS assumption Coding and Information Theory Computational Mathematics and Numerical Analysis Combinatorics Probability Theory and Stochastic Processes Communications Engineering, Networks
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications Software

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