Leakage-resilient identity-based cryptography from minimal assumptions - Zhou, Yanwei; Yang, Bo; Qiao, Zirui; Xia, Zhe; Zhang, Mingwu; Mu, Yi (Designs, codes, and cryptography, 2023)
Identity-based hash proof system (IB-HPS), a variant of hash proof system (HPS) in the identity-based setting, is a useful building block in cryptography. In EUROCRYPT 2010 (Alwen et al in Advances in cryptology-EUROCRYPT 2010, volume 6110 of LNCS, Springer, Berlin, pp. 113–134, 2010), Alwen et al. demonstrated that IB-HPS almost immediately yields an identity-based encryption (IBE) scheme that is secure against partial leakage of the target identity’s decryption key. In FOCS 2010 (Dodis et al in FOCS 2010, IEEE, pp. 511–520, 2010), Dodis et al. further pointed out that a cryptographic system with continuous leakage-resilience can be obtained from a bounded leakage resilient scheme by performing an additional key update algorithm, subject to some conditions. Therefore, to create a generic construction of IBE schemes with continuous leakage resilience, one can use an improved IB-HPS, called updatable IB-HPS (U-IB-HPS), which has a key update algorithm to embed some fresh randomness into the user’s private key. Moreover, identity-based hash proof system with two encapsulation keys (T-IB-HPS) was also proposed. And it can be used to create chosen-ciphertext attacks secure encryption scheme with high computational efficiency. However, most of the existing IB-HPS constructions suffer some restrictions: they either do not have the adaptive security or rely on some non-static security assumptions. After analyzing the existing methods used in creating IBE schemes, we found that it is difficult to design an IB-HPS with adaptive security from classic static assumptions. In this paper, the generic constructions of IB-HPS, U-IB-HPS and T-IB-HPS with adaptive security are created respectively from any standard (updatable) IBE scheme. The security of proposed system is proved based on the semantic security of the underlying (updatable) IBE scheme. These new constructions of leakage-resilient cryptosystems can achieve provable security even if the attacker learns some arbitrary partial information about their internal secret key. While there are many previous works constructing such leakage-resilient cryptosystems under concrete number-theoretic and algebraic assumptions, this work presents the cryptography primitives under general and minimal assumptions. In particular, we construct: Leakage-resilient identity-based cryptosystems from any standard IBE. Leakage-resilient public-key encryption scheme from any standard IBE.