Adaptively Secure Broadcast Encryption with Short Ciphertexts
We propose an adaptively secure broadcast encryption scheme with short ciphertexts. That is the size of the broadcast encryption message is fixed, regardless of the size of the broadcast group. In our proposed scheme, members can join and leave the group without requiring any change to public parameters of the system or private keys of existing members. Our construction has a twofold improvement over best previously known broadcast encryption schemes. First, we propose a scheme that immediately yields adaptive security in the CCA model without any (sub-linear) increase in the size of ciphertexts or use of a random oracle. Secondly, the security model in our system includes decryption queries for any member, even including the members in the challenge set. This a more secure model, as it is closer to the adversary in real world.
New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields (full version)
We present a new methodology to derive faster composite operations of the form dP+Q, where d is a small integer >= 2, for generic ECC scalar multiplications over prime fields. In particular, we present an efficient Doubling-Addition (DA) operation that can be exploited to accelerate most scalar multiplication methods, including multiscalar variants. We also present a new precomputation scheme useful for window-based scalar multiplications that is shown to achieve the lowest cost among all known methods using only one inversion. In comparison to the remaining approaches that use none or several inversions, our scheme offers higher performance for most common I/M ratios. By combining the benefits of our precomputation scheme and the new DA operation, we can save up to 6.2% in the scalar multiplication using fractional wNAF.
New Multibase Non-Adjacent Form Scalar Multiplication and its Application to Elliptic Curve Cryptosystems (extended version)
In this paper we present a new method for scalar multiplication that uses a generic multibase representation to reduce the number of required operations. Further, a multibase NAF-like algorithm that efficiently converts numbers to such representation without impacting memory or speed performance is developed and showed to be sublinear in terms of the number of nonzero terms. Additional representation reductions are discussed with the introduction of window-based variants that use an extended set of precomputations. To realize the proposed multibase scalar multiplication with or without precomputations in the setting of Elliptic Curve Cryptosystems (ECC) over prime fields, we also present a methodology to derive fast composite operations such as tripling or quintupling of a point that require less memory than previous point formulae. Point operations are then protected against simple side-channel attacks using a highly efficient atomic structure. Extensive testing is carried out to show that our multibase scalar multiplication is the fastest method to date in the setting of ECC and exhibits a small footprint, which makes it ideal for implementation on constrained devices.