/
snr.rs
494 lines (480 loc) · 18.1 KB
/
snr.rs
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// state i64, acc local i32, dyn bit width
//
//! Estimation for signal-to-noise ratio.
//!
//! An estimation of SNR is represented with a SNR struct. Calling update allows
//! to update the SNR state with fresh measurements. get_snr returns the current value
//! of the estimate.
//! The SNR can be computed for np independent random variables and the same measurements.
//! The measurements are expected to be of length ns. The random variable values must be
//! included in [0,nc[.
//!
//! The SNR estimation algorithm works as follows. We consider a single point in the trace (all
//! points are treated in the same way).
//! For every $i=0,\dots,nc-1$ ($nc$ is the number of classes), let $x\_{i,j}$ (for
//! $j=0,\dots,n\_i-1$) be all the leakages of class $i$.
//! Let $\mu\_i = \sum\_{j=0}^{n\_i-1} x_{i,j}/n\_i$ and $n = \sum\{i=0}^{nc-1} n\_i$.
//! Moreover, let
//! $S\_i = \sum\_j x\_{i,j}$, $S = \sum\_i S\_i$, $SS\_i = \sum\_j x\_{i,j}^2$ and $SS = \sum\_i
//! SS\_i$.
//!
//! We compute $SNR = Sig/No$, where
//!
//! $$
//! No
//! = \sum\_{i=0}^{nc-1} \sum\_{j=0}^{n\_i-1} 1/(n-nc) (x\_{i,j}-\mu\_i)^2
//! = \sum\_{i,j} 1/(n-nc) * x_{i,j}^2 - \sum\_i 1/(n-nc)/n\_i (\sum\_j x\_{i,j})^2
//! = 1/(n-nc) (SS - \sum\_i 1/n\_i S\_i^2)
//! = 1/(n(n-nc)) (n SS - \sum\_i n/n\_i S\_i^2)
//! $$
//!
//! so that
//!
//! - the $No$ estimator is non-biased, and
//! - we use a [pooled variance](https://en.wikipedia.org/wiki/Pooled_variance) to ensure an
//! accurate estimation when the samples in the classes are not balanced.
//!
//! For the signal, we proceed similarly:
//!
//! $$
//! Sig = \sum\_i n\_i/(n-nc) (mu\_i-mu)^2
//! = \sum\_i n\_i/(n-nc) (S\_i/n\_i-S/n)^2
//! = \sum\_i n\_i/(n-nc) \left S\_i^2/n\_i^2 -2S\_i/n\_i S/n + S^2/n^2 \right)
//! = 1/(n(n-nc)) \left(\sum\_i n/n\_i S\_i^2 - S^2\right)
//! $$
//!
//! For both $No$ and $Sig$, when some $n\_i$ is zero, it is left out from the sums (avoiding the
//! need to compute $1/n\_i$) and $nc$ is consequently decreased.
//!
//!
//! Regarding the implementation, we have to compute $SS$, $S\_i$, $n\_i$ and $nc$, from which $S$
//! and $n$ can be easily derived.
//! Assuming 16-bit data, and $n<2^32$, we can store $SS$ and $S\_i$ on 64-bit integers (and $S\_i$
//! could even be on 32-bit if $n<2^16$, or for temporary accumulators).
//! For the final computation, for $No$, we can have $S\_i^2$ on 128-bit integer (small loss of
//! performance, should not be too costly), then $S\_i^2/n\_i$ on 64-bit integer.
//! For $Sig$, $(n S\_i^2) / n\_i$ can be computed on 128-bit, as well as $S^2$.
use crate::ScalibError;
use hytra::TrAdder;
use itertools::izip;
use ndarray::{s, Array1, Array2, Array3, ArrayView2, ArrayViewMut2, Axis, Zip};
use num_traits::{Bounded, PrimInt, Signed, WrappingAdd, Zero};
use rayon::prelude::*;
use std::convert::TryInto;
pub trait NativeInt: PrimInt + Signed + WrappingAdd + Send + Sync {}
impl<T: PrimInt + Signed + WrappingAdd + Send + Sync> NativeInt for T {}
pub trait SnrType {
const UPDATE_SNR_CHUNK_SIZE: usize;
type SumAcc;
type Sample;
fn sample2tmp(s: Self::Sample) -> i32;
fn sample2i64(s: Self::Sample) -> i64;
fn tmp2acc(s: i32) -> Self::SumAcc;
fn acc2i64(acc: Self::SumAcc) -> i64;
}
const TRACES_CHUNK_SIZE: usize = 1024;
#[derive(Debug)]
pub struct SnrType64bit;
#[derive(Debug)]
pub struct SnrType32bit;
impl SnrType for SnrType64bit {
const UPDATE_SNR_CHUNK_SIZE: usize = 1 << 13;
type SumAcc = i64;
type Sample = i16;
#[inline(always)]
fn tmp2acc(s: i32) -> Self::SumAcc {
s as i64
}
#[inline(always)]
fn acc2i64(acc: Self::SumAcc) -> i64 {
acc
}
#[inline(always)]
fn sample2tmp(s: Self::Sample) -> i32 {
s as i32
}
#[inline(always)]
fn sample2i64(s: Self::Sample) -> i64 {
s as i64
}
}
impl SnrType for SnrType32bit {
const UPDATE_SNR_CHUNK_SIZE: usize = 1 << 13;
type SumAcc = i32;
type Sample = i16;
#[inline(always)]
fn tmp2acc(s: i32) -> Self::SumAcc {
s as i32
}
#[inline(always)]
fn acc2i64(acc: Self::SumAcc) -> i64 {
acc as i64
}
#[inline(always)]
fn sample2tmp(s: Self::Sample) -> i32 {
s as i32
}
#[inline(always)]
fn sample2i64(s: Self::Sample) -> i64 {
s as i64
}
}
/// SNR state. stores the sum and the sum of squares of the leakage for each of the class.
/// This allows to estimate the mean and the variance for each of the classes which are
/// needed for SNR.
#[derive(Debug)]
pub struct SNR<T = SnrType32bit>
where
T: SnrType,
T::SumAcc: NativeInt,
{
/// Sum of all the traces corresponding to each of the classes. shape (ceil(ns/8),np,nc)
sum: Array3<[T::SumAcc; 8]>,
/// Sum of squares with shape (ceil(ns/8))
/// (never overflows since samples are i16 and tot_n_samples <= u32::MAX)
sum_square: Array1<[i64; 8]>,
/// number of samples per class (np,nc)
n_samples: Array2<u32>,
/// number of independent variables
np: usize,
/// number of samples in a trace
ns: usize,
/// number of classes
nc: u32,
/// max sample bit width
bit_width: u32,
/// total number of accumulated traces
tot_n_samples: u32,
}
impl<T> SNR<T>
where
T: SnrType<Sample = i16> + std::fmt::Debug,
T::SumAcc: NativeInt,
{
/// Create a new SNR state.
/// nc: random variables between [0,nc[
/// ns: traces length
/// np: number of independent random variable for which SNR must be estimated
pub fn new(nc: usize, ns: usize, np: usize) -> Self {
let ns8 = if ns % 8 == 0 { ns / 8 } else { ns / 8 + 1 };
assert!(nc <= 1 << 16);
SNR {
sum: Array3::from_elem((ns8, np, nc), [Zero::zero(); 8]),
sum_square: Array1::from_elem((ns8,), [0; 8]),
n_samples: Array2::zeros((np, nc)),
np,
ns,
nc: nc.try_into().expect("Too many classes"),
bit_width: 1,
tot_n_samples: 0,
}
}
/// Update the SNR state with n fresh traces
/// traces: the leakage traces with shape (n,ns)
/// y: realization of random variables with shape (np,n)
/// If this errors, the SNR object should not be used anymore.
/// traces and y must be in standard C order
pub fn update(
&mut self,
traces: ArrayView2<T::Sample>,
y: ArrayView2<u16>,
config: &crate::Config,
) -> Result<(), ScalibError> {
let n_it = (self.sum.shape()[0] as u64 + 3) / 4;
crate::utils::with_progress(
|it_cnt| self.update_internal(traces, y, it_cnt),
n_it,
"Update SNR",
config,
)
}
#[inline(never)]
/// If this errors, the SNR object should not be used anymore.
fn update_internal(
&mut self,
traces: ArrayView2<T::Sample>,
y: ArrayView2<u16>,
acc_ref: &TrAdder<u64>,
) -> Result<(), ScalibError> {
assert_eq!(traces.shape()[0], y.shape()[1]);
assert_eq!(traces.shape()[1], self.ns);
assert_eq!(y.shape()[0], self.np);
assert!(traces.is_standard_layout());
assert!(y.is_standard_layout());
let n_traces: u32 = traces.shape()[0]
.try_into()
.map_err(|_| ScalibError::SnrTooManyTraces)?;
self.tot_n_samples = self
.tot_n_samples
.checked_add(n_traces)
.ok_or(ScalibError::SnrTooManyTraces)?;
let mut max_n_samples: u32 = 0;
let nc = self.nc;
let np = self.np;
izip!(self.n_samples.outer_iter_mut(), y.outer_iter()).try_for_each(
|(mut n_samples, y)| {
y.into_iter().try_for_each(|y| {
if u32::from(*y) >= nc {
Err(ScalibError::SnrClassOutOfBound)
} else {
n_samples[*y as usize] += 1;
max_n_samples = std::cmp::max(max_n_samples, n_samples[*y as usize]);
Ok(())
}
})
},
)?;
let sample_bits_used_msk = (
self.sum.axis_chunks_iter_mut(Axis(0), 32 / 8),
self.sum_square.axis_chunks_iter_mut(Axis(0), 32 / 8),
traces.axis_chunks_iter(Axis(1), 32),
)
.into_par_iter()
.map_init(
|| {
(
Array2::from_elem((4, TRACES_CHUNK_SIZE), [0i16; 8]),
Array3::from_elem((4, np, nc as usize), [0i32; 8]),
)
},
|(traces_tr, tmp_sum), (mut sum, mut sum_square, trace_chunk)| {
let mut sample_bits_used_msk = 0;
izip!(
trace_chunk.axis_chunks_iter(Axis(0), u16::MAX as usize),
y.axis_chunks_iter(Axis(1), u16::MAX as usize)
)
.for_each(|(trace_chunk, y)| {
tmp_sum.fill([0; 8]);
izip!(
trace_chunk.axis_chunks_iter(Axis(0), TRACES_CHUNK_SIZE),
y.axis_chunks_iter(Axis(1), TRACES_CHUNK_SIZE)
)
.for_each(|(trace_chunk, y)| {
let mut traces_tr =
traces_tr.slice_mut(s![.., ..trace_chunk.shape()[0]]);
sample_bits_used_msk |=
transpose_traces(traces_tr.view_mut(), trace_chunk);
izip!(
traces_tr.axis_iter(Axis(0)),
tmp_sum.axis_iter_mut(Axis(0)),
sum_square.axis_iter_mut(Axis(0)),
)
.for_each(
|(traces_chunk, sum, sum_square)| {
let traces_chunk = traces_chunk.to_slice().unwrap();
// SAFETY: y has been checked before, and offset/stride is in bound
unsafe {
inner_snr_update(
traces_chunk,
y,
sum,
sum_square.into_scalar(),
);
}
},
);
});
for (mut sum, tmp_sum) in
izip!(sum.axis_iter_mut(Axis(0)), tmp_sum.axis_iter(Axis(0)))
{
Zip::from(&mut sum).and(tmp_sum).for_each(|sum, tmp_sum| {
for (sum, tmp_sum) in sum.iter_mut().zip(tmp_sum.iter()) {
*sum = sum.wrapping_add(&T::tmp2acc(*tmp_sum));
}
});
}
});
acc_ref.inc(1);
sample_bits_used_msk
},
)
.reduce(|| 0, |a, b| a | b);
self.bit_width = std::cmp::max(self.bit_width, 16 - sample_bits_used_msk.leading_zeros());
// for any sample x, abs(x) < 2^bit_width
// we want max_n_samples*abs(x) < T::SumAcc::max_value(), therefore
// max_n_samples*abs(x) << bit_width \le T::SumAcc::max_value()
// max_val does not overflow since max_n_samples < 2^32 and self.bit_width < 16
let max_val = (max_n_samples as i64) << self.bit_width;
if max_val > T::acc2i64(T::SumAcc::max_value()) {
return Err(ScalibError::SnrClassOverflow {
leak_upper_bound: 1 << self.bit_width,
max_n_traces: max_n_samples as i64,
});
}
return Ok(());
}
/// Generate the actual SNR metric based on the current state.
/// return array axes (variable, samples in trace)
pub fn get_snr(&self) -> Array2<f64> {
let mut snr = Array2::<f64>::zeros((self.np, self.ns));
// on chunks of samples
(
self.sum.axis_iter(Axis(0)),
self.sum_square.axis_iter(Axis(0)),
snr.axis_chunks_iter_mut(Axis(1), 8),
)
.into_par_iter()
.for_each(|(sum, sum_square, mut snr)| {
let sum_square: &[i64; 8] = sum_square.into_scalar();
let general_sum = sum
.slice(s![0usize, ..])
.iter()
.fold([0i64; 8], |mut acc, s| {
for (acc, s) in izip!(acc.iter_mut(), s.iter()) {
// no overflow: sample on 16 bits, at most 2^32 traces
*acc += T::acc2i64(*s);
}
acc
});
let mut general_sum_sq = [0i128; 8];
for (sq, s) in izip!(general_sum_sq.iter_mut(), general_sum.iter()) {
let s = *s as i128;
*sq = s * s;
}
// on variables
izip!(
sum.axis_iter(Axis(0)),
self.n_samples.axis_iter(Axis(0)),
snr.axis_iter_mut(Axis(0))
)
.for_each(|(sum, n_samples, snr)| {
compute_snr::<T>(
sum.to_slice().unwrap(),
n_samples.to_slice().unwrap(),
sum_square,
&general_sum_sq,
self.tot_n_samples,
snr.into_slice().unwrap(),
);
});
});
snr
}
}
#[inline(never)]
/// # Safety
/// all values in y must be < sum.shape()[1]
unsafe fn inner_snr_update(
// len: n
trace_chunk: &[[i16; 8]],
// (np, n)
y: ArrayView2<u16>,
// (np, nc)
mut sum: ArrayViewMut2<[i32; 8]>,
sum_square: &mut [i64; 8],
) {
assert_eq!(trace_chunk.len(), y.shape()[1]);
assert_eq!(sum.shape()[0], y.shape()[0]);
for trace in trace_chunk {
for (sum_square, trace) in sum_square.iter_mut().zip(trace.iter()) {
let trace = *trace as i64;
// overflow handled with error elsewhere
*sum_square = sum_square.wrapping_add(trace * trace);
}
}
izip!(y.outer_iter(), sum.outer_iter_mut()).for_each(|(y, sum)| {
let sum = sum.into_slice().unwrap();
izip!(y.to_slice().unwrap(), trace_chunk).for_each(|(y, trace_chunk)| {
// sum.get_unchecked_mut is safe due to assumption,
let sum = sum.get_unchecked_mut(*y as usize);
for j in 0..8 {
// overflow handled with error elsewhere
sum[j] = sum[j].wrapping_add(trace_chunk[j] as i32);
}
})
});
}
#[inline(never)]
fn transpose_traces(
// shape: (4, n)
mut traces_tr: ArrayViewMut2<[i16; 8]>,
// shape: (n, ns) with ns <= 32
trace_chunk: ArrayView2<i16>,
) -> u16 {
assert_eq!(traces_tr.shape()[1], trace_chunk.shape()[0]);
assert_eq!(traces_tr.shape()[0], 4);
assert!(trace_chunk.shape()[1] <= 32);
let mut max_width: u16 = 0;
if trace_chunk.shape()[1] == 32 {
let mut max_width_vec = [0u16; 8];
izip!(
traces_tr.axis_iter_mut(Axis(1)),
trace_chunk.axis_iter(Axis(0))
)
.for_each(|(mut traces_tr, trace_chunk)| {
izip!(
traces_tr.iter_mut(),
trace_chunk.axis_chunks_iter(Axis(0), 8)
)
.for_each(|(traces_tr, trace_chunk)| {
let trace_chunk: &[i16; 8] = trace_chunk.to_slice().unwrap().try_into().unwrap();
//traces_tr.clone_from_slice(trace_chunk);
*traces_tr = *trace_chunk;
for (max_width, trace_chunk) in max_width_vec.iter_mut().zip(trace_chunk.iter()) {
// i16::abs_diff returns a u16 without overflow nor panic, while i16::abs
// panics on i16::min_value() input.
*max_width |= trace_chunk.abs_diff(0);
}
});
});
for mw in max_width_vec {
max_width |= mw;
}
} else {
izip!(
traces_tr.axis_iter_mut(Axis(1)),
trace_chunk.axis_iter(Axis(0))
)
.for_each(|(mut traces_tr, trace_chunk)| {
izip!(
traces_tr.iter_mut().flat_map(|x| x.iter_mut()),
trace_chunk.iter()
)
.for_each(|(traces_tr, trace_chunk)| {
*traces_tr = *trace_chunk;
max_width |= trace_chunk.abs_diff(0);
});
});
}
return max_width;
}
#[inline(never)]
fn compute_snr<T>(
sum: &[[T::SumAcc; 8]],
n_samples: &[u32],
sum_square: &[i64; 8],
general_sum_sq: &[i128; 8],
n: u32,
snr: &mut [f64],
) where
T: SnrType,
T::SumAcc: NativeInt,
{
let sum_square_class =
izip!(sum.iter(), n_samples.iter()).fold([0i128; 8], |mut acc, (s, ns)| {
for (acc, s) in izip!(acc.iter_mut(), s.iter()) {
if *ns != 0 {
let s = T::acc2i64(*s) as i128;
// No overflow: s is on <= (16+32) bit (signed), n is on 32-bit therefore, s*s
// in on < 96 bits (signed), and n*s*s is on <128 bits (signed)
// TODO optimize this bottleneck, the division is 75% exec. time (e.g.
// use libdivide)
*acc += s * s * (n as i128) / (*ns as i128);
}
}
acc
});
let l = snr.len();
izip!(
sum_square_class[..l].iter(),
general_sum_sq[..l].iter(),
sum_square[..l].iter(),
snr.iter_mut()
)
.for_each(|(sum_square_class, general_sum_sq, sum_square, snr)| {
let sum_square = *sum_square as i128;
let signal = sum_square_class - general_sum_sq;
let noise = (n as i128) * sum_square - sum_square_class;
*snr = (signal as f64) / (noise as f64);
});
}