Variants of Waters’ Dual System Primitives Using Asymmetric Pairings

Abstract

Abstract. Waters, in 2009, introduced an important technique, called dual-system encryption, to construct identity-based encryption (IBE) and related schemes. The resulting IBE scheme was described in the setting of symmetric pairing. A key feature of the construction is the presence of random tags in the ciphertext and decryption key. Later work by Lewko and Waters has removed the tags and proceeding through composite-order pairings has led to a more efficient dual-system IBE scheme using asymmetric pairings whose security is based on non-standard but static assumptions. In this work, we have systematically simplified Waters 2009 IBE scheme in the setting of asymmetric pairing. The simplifications retain tags used in the original description. This leads to several variants, the first one of which is based on standard assumptions and in comparison to Waters original scheme reduces ciphertexts and keys by two elements each. Going through several stages of simplifications, we finally obtain a simple scheme whose security can be based on two standard assumptions and a natural and minimal extension of the decision Diffie-Hellman problem for asymmetric pairing groups. The scheme itself is also minimal in the sense that apart from the tags, both encryption and key generation use exactly one randomiser each. This final scheme is more efficient than both the previous dual-system IBE scheme in the asymmetric setting due to Lewko and Waters and the more recent dual-system IBE scheme due to Lewko. We extend the IBE scheme to hierarchical IBE (HIBE) and broadcast encryption (BE) schemes. Both primitives are secure in their respective full models and have better efficiencies compared to previously known schemes offering the same level and type of security.

Constant-Size Structure-Preserving Signatures: Generic Constructions and Simple Assumptions

“…Our construction bases on a variant of Waters' dual system encryption proposed by Ramanna, Chatterjee, and Sarkar [34].…”

Extended dual system group and shorter unbounded hierarchical identity based encryption

“…Since being introduced, the dual system technique has been successfully used to obtain adaptive security for not only (H)IBE [5,13,14,[21][22][23]30] but also more expressive FE [4,[24][25][26]29,37]. Recently, the dual system technique helped us to go further.…”

Improving the Message-Ciphertext Rate of Lewko’s Fully Secure IBE Scheme

“…In the security proof of our IBE scheme, we use semi-functional ciphertexts and semi-functional keys, which are widely used in previous literatures [12,17,10,15].…”

“…However, the scheme was bothered by too long parameters and complicated structure. In [15] Ramannal, et al gave a simplification of Waters' scheme in asymmetric bilinear groups, but based on assumptions which are not so standard.…”