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- W2945147690 abstract "In this work, we introduce and construct D-restricted Functional Encryption (FE) for any constant $$D ge 3$$ , based only on the SXDH assumption over bilinear groups. This generalizes the notion of 3-restricted FE recently introduced and constructed by Ananth et al. (ePrint 2018) in the generic bilinear group model. A $$D=(d+2)$$ -restricted FE scheme is a secret key FE scheme that allows an encryptor to efficiently encrypt a message of the form $$M=(varvec{x},varvec{y},varvec{z})$$ . Here, $$varvec{x}in mathbb {F}_{mathbf {p}}^{dtimes n}$$ and $$varvec{y},varvec{z}in mathbb {F}_{mathbf {p}}^n$$ . Function keys can be issued for a function $$f=varSigma _{varvec{I}= (i_1,..,i_d,j,k)} c_{varvec{I}}cdot varvec{x}[1,i_1] cdots varvec{x}[d,i_d] cdot varvec{y}[j]cdot varvec{z}[k]$$ where the coefficients $$c_{varvec{I}}in mathbb {F}_{mathbf {p}}$$ . Knowing the function key and the ciphertext, one can learn $$f(varvec{x},varvec{y},varvec{z})$$ , if this value is bounded in absolute value by some polynomial in the security parameter and n. The security requirement is that the ciphertext hides $$varvec{y}$$ and $$varvec{z}$$ , although it is not required to hide $$varvec{x}$$ . Thus $$varvec{x}$$ can be seen as a public attribute. D-restricted FE allows for useful evaluation of constant-degree polynomials, while only requiring the SXDH assumption over bilinear groups. As such, it is a powerful tool for leveraging hardness that exists in constant-degree expanding families of polynomials over $$mathbb {R}$$ . In particular, we build upon the work of Ananth et al. to show how to build indistinguishability obfuscation ( $$imathcal {O}$$ ) assuming only SXDH over bilinear groups, LWE, and assumptions relating to weak pseudorandom properties of constant-degree expanding polynomials over $$mathbb {R}$$ ." @default.
- W2945147690 created "2019-05-29" @default.
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- W2945147690 date "2019-01-01" @default.
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- W2945147690 title "How to Leverage Hardness of Constant-Degree Expanding Polynomials over $$mathbb {R}$$ R to build $$imathcal {O}$$ i O" @default.
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- W2945147690 doi "https://doi.org/10.1007/978-3-030-17653-2_9" @default.
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