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Universally Verifiable Multiparty Computation from Threshold Homomorphic Cryptosystems Read chapter Read first chapter

2015 | OriginalPaper | Chapter

A Signature Scheme with a Fuzzy Private Key

Authors : Kenta Takahashi, Takahiro Matsuda, Takao Murakami, Goichiro Hanaoka, Masakatsu Nishigaki

Published in: Applied Cryptography and Network Security

Publisher: Springer International Publishing

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Abstract

In this paper, we introduce a new concept that we call fuzzy signature, which is a signature scheme that uses a noisy string such as biometric data as a private key, but does not require auxiliary data (which is also called helper string in the context of fuzzy extractors), for generating a signature. Our technical contributions are three-fold: (1) We first give the formal definition of fuzzy signature, together with a formal definition of a “setting” that specifies some necessary information for fuzzy data. (2) We give a generic construction of a fuzzy signature scheme based on a signature scheme with certain homomorphic properties regarding keys and signatures, and a new tool that we call linear sketch. (3) We specify a certain setting for fuzzy data, and then give concrete instantiations of these building blocks for our generic construction, leading to our proposed fuzzy signature scheme.
We also discuss how fuzzy signature schemes can be used to realize a biometric-based PKI that uses biometric data itself as a cryptographic key, which we call the public biometric infrastructure (PBI).

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Appendix
Available only for authorised users
Footnotes
1
Strictly speaking, in this paper we adopt the syntax in which \(\mathsf{Sign}\) also takes a public parameter as input (see Sect. 2.2). In this section, we omit it for simplicity.
 
2
The procedure “Sketch” is actually not the one-time pad encryption, but more like a (one-way) “encoding,” because we do not need to decrypt \(\widetilde{c}\) to recover \(\widetilde{sk}\). This is the main reason why we call \(\widetilde{c}\) “sketch” (something that contains the information of \(\widetilde{sk}\)), not “ciphertext”.
 
3
Recall that the original one-time pad encryption \(c=m \oplus K\) (where c, m, and K are a ciphertext, a message, and a key, respectively) has “linearity” in the sense that given two ciphertexts \(c_1 = m \oplus K_1\) and \(c_2 = m \oplus K_2\) of the same message m under different keys \(K_1\) and \(K_2\), we can calculate the difference \(\varDelta K = K_1 \oplus K_2\) by computing \(c_1 \oplus c_2\).
 
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Metadata
Title
A Signature Scheme with a Fuzzy Private Key
Authors
Kenta Takahashi
Takahiro Matsuda
Takao Murakami
Goichiro Hanaoka
Masakatsu Nishigaki
Copyright Year
2015
Book
Applied Cryptography and Network Security

Print ISBN: 978-3-319-28165-0

Electronic ISBN: 978-3-319-28166-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-28166-7_6

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