Abstract
In [14], Boneh and Katz introduced a primitive called encapsulation scheme, which is a special kind of commitment scheme. Using the encapsulation scheme, they improved the generic transformation by Canetti, Halevi, and Katz [17] which transforms any semantically secure identity-based encryption (IBE) scheme into a chosen-ciphertext secure public key encryption (PKE) scheme (we call the BK transformation). The ciphertext size of the transformed PKE scheme directly depends on the parameter sizes of the underlying encapsulation scheme. In this paper, by designing a size-efficient encapsulation scheme, we further improve the BK transformation. With our proposed encapsulation scheme, the ciphertext overhead of a transformed PKE scheme via the BK transformation can be that of the underlying IBE scheme plus 384-bit, while the original BK scheme yields that of the underlying IBE scheme plus at least 704-bit, for 128-bit security. Our encapsulation scheme is constructed from a pseudorandom generator (PRG) that has a special property called near collision resistance, which is a fairly weak primitive. As evidence of it, we also address how to generically construct a PRG with such a property from any one-way permutation.
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Matsuda, T., Hanaoka, G., Matsuura, K., Imai, H. (2009). An Efficient Encapsulation Scheme from Near Collision Resistant Pseudorandom Generators and Its Application to IBE-to-PKE Transformations. In: Fischlin, M. (eds) Topics in Cryptology – CT-RSA 2009. CT-RSA 2009. Lecture Notes in Computer Science, vol 5473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00862-7_2
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