Deterministic information loss yields TC0 post-quantum pseudorandomness from lattices
Original title: Information Loss Is All You Need: $TC^0$ Pseudorandomness from Worst-Case Lattices
Learning with algebraic rounding achieves TC0 pseudorandomness from quantum worst-case lattice hardness with fixed polynomial parameters.
The authors show deterministic rounding achieves post-quantum pseudorandomness with TC0 evaluation under quantum worst-case lattice hardness. They introduce learning with algebraic rounding (LAR) which applies an explicit integer rounding map to blocks of secret-dependent linear measurements and encodes the result in a lattice quotient. For one fixed family with polynomially bounded modulus and dimensions, deterministic labels on uniform public matrices are computationally indistinguishable from independent uniform labels for every polynomial number of classical random examples.
- Bases LAR on GapSVP and SIVP over general lattices at approximation factor O~(q)
- First post-quantum weak pseudorandom function with joint key-and-input evaluation in TC0
- Secure against uniform quantum polynomial-time distinguishers given any polynomial number of classical uniform random examples
- Uses source-independent affine transport for proof
- Proves hardness of learning polynomial-size two-hidden-layer ReLU networks from noiseless uniform random examples
From the original article
1 min read at arxiv.orgCan deterministic information loss yield post-quantum pseudorandomness with $TC^0$ evaluation? We show that deterministic rounding achieves this under quantum worst-case lattice hardness, with fixed polynomial parameters and no predetermined sample bound.
By Chen Qian · arxiv.org
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