SPRING: Fast Pseudorandom Functions from Rounded Ring Products
Résumé
Recently, Banerjee, Peikert and Rosen (EUROCRYPT 2012) proposed new theoretical pseudorandom function candidates based on "rounded products" in certain polynomial rings, which have rigorously provable security based on worst-case lattice problems. The functions also enjoy algebraic properties that make them highly parallelizable and attractive for modern applications, such as evaluation under homomorphic encryption schemes. However, the parameters required by BPR's security proofs are too large for practical use, and many other practical aspects of the design were left unexplored in that work. In this work we give two concrete and practically efficient instantiations of the BPR design, which we call SPRING, for "subset-product with rounding over a ring." One instantiation uses a generator matrix of a binary BCH error-correcting code to "determinstically extract" nearly random bits from a (biased) rounded subset-product. The second instan-tiation eliminates bias by working over suitable moduli and decomposing the computation into "Chinese remainder" components. We analyze the concrete security of these instantiations, and provide initial software implementations whose throughputs are within small factors (as small as 4.5) of those of AES.
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