Abstract
The SPRING pseudo-random function (PRF) has been described by Banerjee, Brenner, Leurent, Peikert and Rosen at FSE 2014. It is quite fast, only 4.5 times slower than the AES (without hardware acceleration) when used in counter mode. SPRING is similar to the PRF of Banerjee, Peikert and Rosen from EUROCRYPT 2012, whose security relies on the hardness of the Learning With Rounding (LWR) problem, which can itself be reduced to hard lattice problems. However, there is no such chain of reductions relating SPRING to lattice problems, because it uses small parameters for efficiency reasons.
Consequently, the heuristic security of SPRING is evaluated using known attacks and the complexity of the best known algorithms for breaking the underlying hard problem.
In this paper, we revisit the efficiency and security of SPRING when used as a pseudo-random generator. We propose a new variant which is competitive with the AES in counter mode without hardware AES acceleration, and about four times slower than AES with hardware acceleration. In terms of security, we improve some previous analysis of SPRING and we estimate the security of our variant against classical algorithms and attacks. Finally, we implement our variant using AVX2 instructions, resulting in high performances on high-end desktop computers.
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Notes
- 1.
As discussed in Sect. 3, SPRING seems to have a quite large level of security, even if the \(\mathbf {s}_i\) are known. It has been asked to us why we do not choose to make part of the \(\mathbf {s}_i\) polynomials known to reduce the size of the key. However, as shown by Table 2, it may undermine the security of SPRING, especially when \(p = 16\).
- 2.
Since 3.49 is strictly above the number given in [Gal12], for any \(\epsilon >0\), the complexity of a multiplication is less than \(\epsilon n^{3.49}\) for all sufficiently large n.
- 3.
[BBL+15] used \(i_0=4n/\kappa \log _2(q)\) so that their claimed complexity is \(2^{126}\) but this is not enough to get a constant advantage.
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The authors are supported by the french ANR BRUTUS project.
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Bouillaguet, C., Delaplace, C., Fouque, PA., Kirchner, P. (2017). Fast Lattice-Based Encryption: Stretching Spring . In: Lange, T., Takagi, T. (eds) Post-Quantum Cryptography . PQCrypto 2017. Lecture Notes in Computer Science(), vol 10346. Springer, Cham. https://doi.org/10.1007/978-3-319-59879-6_8
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