Secure Hybrid Encryption from Weakened Key Encapsulation

By Dennis Hofheinz, Eike Kiltz. Annual International Cryptology Conference, 2007

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An Algebraic Framework for Diffie–Hellman Assumptions (2013, methodology): “More recently, the 2-Lin Assumption was generalized to the (k-Lin)k∈ Assumption family [19,29] (1-Lin = DDH), a family of increasingly (strictly) weaker Assumptions which are generically hard in k-linear maps.”
Key Homomorphic PRFs and Their Applications (2013, background): “PRF security is based on the `-decision linear assumption [34, 23] in G.”
Lossy trapdoor functions and their applications (2008, background): “) More recently, Freeman, Goldreich, Kiltz, Rosen and Segev [27] produced more constructions of lossy TDFs, from the quadratic residuosity assumption and the family of k-linear assumptions [39, 62] (which are potentially weaker generalizations of the DDH assumption).”
A New Randomness Extraction Paradigm for Hybrid Encryption (2009, methodology): “The efficient transformation enables the design of new and efficient IND-CCA2 secure hybrid encryption schemes based on various hard subset membership problem, such as the DDH assumption, Paillier’s Decisional Composite Residuosity (DCR) assumption [21], the family of Linear assumptions [14, 23] tha”