Abstract
This chapter is devoted to giving a brief introduction to identity-based cryptography (IBC), which presents a nice solution for some problems that limit the wide deployment of public-key cryptography, in particular, the problem of binding public keys with user identities. The basic idea of IBC starts from the realization that there is some minimal information that a user has to learn before communicating with another party, even in unencrypted form, namely, some identity information such as, for example, an email address. In IBC, this basic informacion replaces the need for a public key or, in slightly different terms, the public key of a user is her identity string or some string easily derivable from this identity by a specified method.
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Notes
- 1.
Alternatively, the result given in Proposition 8.5 may be used to mount a ‘common modulus attack’ which allows any user to decrypt messages addressed to another user who shares the same RSA modulus.
- 2.
This can be interpreted as the PKG creating a certificate stating that “the public key of user id is pk”.
- 3.
Recall here that \(\mathcal J _n\) denotes the subset of the elements of \(\mathbb Z _n^*\) with Jacobi symbol modulo \(n\) equal to \(+1\) and \(\mathcal Q \mathcal N _n^1\) is the intersection of \(\mathcal J _n\) with the set of quadratic non-residues modulo \(n\).
- 4.
The definition of IND-ID-CPA is obtained from the definition of IND-ID-CCA above by dropping the decryption queries.
- 5.
Capital letters—often starting with the letter \(P\)—are commonly used to denote the elements of \(G_1\), which comes from the fact that, when \(G_1\) is an elliptic curve group, its elements are points of the curve. Elliptic curve groups are defined in Chap. 11.
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© 2013 Springer-Verlag Berlin Heidelberg
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Gómez Pardo, J.L. (2013). Identity-Based Cryptography. In: Introduction to Cryptography with Maple. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32166-5_10
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DOI: https://doi.org/10.1007/978-3-642-32166-5_10
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