Certificateless threshold cryptosystem secure against chosen-ciphertext attack

Efficient chosen-ciphertext secure certificateless threshold key encapsulation mechanism

“…The (decision) 4-BDH problem can be readily extended to (decision) ðk þ 1Þ-BDH problem (k P 2, see appendix for detail, or refer to [27]). Notice that the BDH problem is a special case of the ðk þ 1Þ-BDH problem with k ¼ 2.…”

“…Theorem 5.1 for Type II adversaries follows by Lemma 5.2. Especially, since we make use of decision 4-BDHP/ BDHP instead of 4-BDHP/BDHP directly, the security reduction is tighter than [27].…”

“…As far as we know, until now, no existing work has been considered KEM in the certificateless setting except for our discussion in the extension part of [27], though there are some CCA secure KEM schemes either in the traditional public key infrastructure setting or in the identity-based setting.…”

Certificateless Threshold Ring Signature

“…Its goal is to remove the key escrow property from identity-based cryptography and has attracted a great extent of attention lately [24,18,43,4,19,23,16,27,36,35,33,15]. Certificateless cryptography not only eliminates the key escrow property, but also removes certificates.…”

Secure public-key encryption scheme without random oracles

“…The security of a public-key encryption scheme against adaptive chosen ciphertext attack (CCA2) was introduced by Rackoff and Simon [17] in 1991. Since then, this security notion is generally accepted as a right security for a public-key encryption scheme and many different kinds of public-key encryption schemes have been proposed [1,[4][5][6][7][8][9][10][11][12]14,15,23,25]. The first practical and provably secure public-key encryption scheme against CCA2 under the standard assumption without random oracles was proposed by Cramer and Shoup [10] in 1998.…”