Abstract
AbstractWe propose a new FHE scheme F-NTRU that adopts the flattening technique proposed in GSW to derive an NTRU based scheme that (similar to GSW) does not require evaluation keys or key switching. Our scheme eliminates the decision small polynomial ratio assumption but relies only on the standard R-LWE assumption. It uses wide key distributions, and hence is immune to Subfield Lattice Attack. In practice, our scheme achieves competitive timings compared to the existing schemes. We are able to compute a homomorphic multiplication in 24.4 msec and 76.0 msec for 5 and 30 levels, respectively, without amortization. Furthermore, our scheme features small ciphertexts, e.g. 2376 KB for 30 levels. The assurance gained by using wide key distributions along with the message space flexibility of the scheme, i.e. bits, binary polynomials, and integers with a large message space, allows the use of the proposed scheme in a wide array of applications.
Highlights
The notion of fully homomorphic encryption (FHE) scheme stayed as an open question for a few decades since its introduction by Rivest et al [23]
We propose a new FHE scheme F-NTRU that adopts the flattening technique proposed in GSW to derive an NTRU based scheme that does not require evaluation keys or key switching
We present a new leveled FHE scheme F-NTRU that is based on the Stehlé and Steinfeld variant of NTRU [25] and adopts Flattening – the noise management technique introduced in (GSW) [15]
Summary
The notion of fully homomorphic encryption (FHE) scheme stayed as an open question for a few decades since its introduction by Rivest et al [23]. The scheme uses a method called modulus switching to mitigate noise growth in ciphertexts Another leveled FHE scheme was presented by López-Alt, Tromer, Vaikuntanathan (LTV) in [20]. In [2] the authors introduce a modification (YASHE’) to their scheme to eliminate the problems of expensive tensor product calculations and large evaluation keys This modification re-introduces the DSPR assumption due to increase in noise. We present a new leveled FHE scheme F-NTRU that is based on the Stehlé and Steinfeld variant of NTRU [25] and adopts Flattening – the noise management technique introduced in (GSW) [15]. Our scheme does not use any expensive noise reduction techniques such as relinearization and does not require prohibitively large evaluation keys. Featuring a very large message space, the integer version of F-NTRU is capable to support a wide range of applications where such arithmetic is required
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