IBE and function-private IBE under linear assumptions with shorter ciphertexts and private keys, and extensions (Q1626119)

Summary: Many identity-based encryption schemes under the \(k\)-LIN assumption contain \(2k + 1\) group elements in the ciphertext overhead and private keys. In this paper, we push the limit further by constructing an IBE scheme under the \(k\)-LIN assumption with \(2k\) group elements in the ciphertext overhead and private keys. The schemes have variants with shorter public parameters under the \(k\)-SCasc assumption, which is a close assumption to \(k\)-LIN. Furthermore, via additional refinements, we also put efforts in reducing the public parameter size of our schemes, under either \(k\)-LIN or \(k\)-SCasc. While we mainly consider securities in the standard model for our schemes, we also show how to make relatively more efficient schemes secure in the random oracle model. Our technique additionally expands to the scheme of \textit{D. Boneh} et al. [Crypto 2013, Lect. Notes Comput. Sci. 8043, 461--478 (2013; Zbl 1311.94071)] to yield more efficient function-private IBE under the 2-LIN (aka, DLIN) assumption. Overall, the shortened size in ciphertexts and private keys inherently leads to fewer exponentiations and pairings in encryption and decryption, and hence yields schemes with better computational efficiency.