srp: store group G constant in ConstMontyForm

Uses `crypto-bigint`'s stack-allocated Montgomery form types to define
group constants, including adding an impl of `ConstMontyParams` to them.

This precomputes all of their Montgomery form constants at compile-time,
meaning initializing a `BoxedMontyForm` (for now, since it's the only
thing that currently has modpow) can use the precomputed constants.

This is also the first step towards supporting a fully stack allocated
implementation (#248).

Author: tarcieri

Cargo.lock

@@ -8,3 +8,6 @@ members = [
 
 [profile.dev]
 opt-level = 2
+
+[patch.crates-io.crypto-bigint]
+git = "https://github.com/RustCrypto/crypto-bigint"

Cargo.toml

@@ -8,8 +8,8 @@
 //! [RFC5054]: https://tools.ietf.org/html/rfc5054
 
 use bigint::{
-    BoxedUint, Odd, Resize,
-    modular::{BoxedMontyForm, BoxedMontyParams},
+    Odd, U1024, U1536, U2048, U3072, U4096,
+    modular::{BoxedMontyForm, ConstMontyForm, ConstMontyParams, MontyParams},
 };
 use core::{
     any,
@@ -18,32 +18,30 @@ use core::{
 
 /// Group used for SRP computations.
 pub trait Group {
-    /// Group generator modulo `N`.
-    const G: u64;
+    /// Group elements.
+    type Element: Into<BoxedMontyForm>;
 
-    /// Big endian bytes representing a large safe prime (`N = 2q + 1`, where `q` is prime) which
-    /// acts as the modulus.
-    const N: &'static [u8];
+    /// Group generator modulo `N` represented as `ConstMontyForm`, where `N` is a large safe prime
+    /// (`N = 2q + 1`, where `q` is prime)
+    const G: Self::Element;
 
     /// Initialize group generator as a [`BoxedMontyForm`].
     fn generator() -> BoxedMontyForm {
-        let n = BoxedUint::from_be_slice_vartime(Self::N);
-        let n = BoxedMontyParams::new(Odd::new(n).expect("n should be odd"));
-        BoxedMontyForm::new(BoxedUint::from(Self::G).resize(n.bits_precision()), &n)
+        Self::G.into()
     }
 }
 
 macro_rules! define_group {
-    ($name:ident, $g:expr, $n:expr, $doc:expr) => {
+    ($name:ident, $uint:ident, $g:expr, $doc:expr, $n:expr) => {
         #[doc = $doc]
-        #[derive(Clone, Copy)]
+        #[derive(Clone, Copy, Default, Eq, PartialEq)]
         pub struct $name;
-        group_trait_impls!($name, $g, $n);
+        group_trait_impls!($name, $uint, $g, $n);
     };
 }
 
 macro_rules! define_deprecated_group {
-    ($name:ident, $g:expr, $n:expr, $doc:expr) => {
+    ($name:ident, $uint:ident, $g:expr, $doc:expr, $n:expr) => {
         /// DEPRECATED:
         #[doc = $doc]
         ///
@@ -52,52 +50,89 @@ macro_rules! define_deprecated_group {
         ///
         /// It is recommended to use a group which is 2048-bits or larger.
         /// </div>
-        #[derive(Clone, Copy)]
+        #[derive(Clone, Copy, Default, Eq, PartialEq)]
         #[deprecated(
             since = "0.7.0",
             note = "this group is too small to be secure. Prefer to use G2048+"
         )]
         pub struct $name;
-        group_trait_impls!($name, $g, $n);
+        group_trait_impls!($name, $uint, $g, $n);
     };
 }
 
 macro_rules! group_trait_impls {
-    ($name:ident, $g:expr, $n:expr) => {
+    ($name:ident, $uint:ident, $g:expr, $n:expr) => {
+        #[allow(deprecated)]
+        impl ConstMontyParams<{ <$uint>::LIMBS }> for $name {
+            const LIMBS: usize = <$uint>::LIMBS;
+            const PARAMS: MontyParams<{ <$uint>::LIMBS }> =
+                MontyParams::new_vartime(Odd::<$uint>::from_be_hex($n));
+        }
+
         #[allow(deprecated)]
         impl Group for $name {
-            const G: u64 = $g;
-            const N: &'static [u8] = include_bytes!($n);
+            type Element = ConstMontyForm<Self, { <$uint>::LIMBS }>;
+            const G: Self::Element = ConstMontyForm::new(&<$uint>::from_u128($g));
         }
 
         #[allow(deprecated)]
         impl Debug for $name {
             fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
                 let name = any::type_name::<$name>();
                 let name = name.split("::").last().unwrap_or(name);
-
-                write!(f, "{} {{ G: {}, N: 0x", name, Self::G)?;
-                for byte in Self::N {
-                    write!(f, "{byte:02X}")?;
-                }
-                write!(f, " }}")
-            }
-        }
-
-        #[allow(deprecated)]
-        impl<Rhs: Group> PartialEq<Rhs> for $name {
-            fn eq(&self, _other: &Rhs) -> bool {
-                Self::G == Rhs::G && Self::N == Rhs::N
+                f.debug_struct(name)
+                    .field("G", &Self::G.retrieve())
+                    .field("N", &**Self::PARAMS.modulus())
+                    .finish()
             }
         }
     };
 }
 
-define_deprecated_group!(G1024, 2, "groups/1024.bin", "1024-bit group.");
-define_deprecated_group!(G1536, 2, "groups/1536.bin", "1536-bit group.");
-define_group!(G2048, 2, "groups/2048.bin", "2048-bit group.");
-define_group!(G3072, 5, "groups/3072.bin", "3072-bit group.");
-define_group!(G4096, 5, "groups/4096.bin", "4096-bit group.");
+// G1024
+define_deprecated_group!(
+    G1024,
+    U1024,
+    2,
+    "1024-bit group",
+    "eeaf0ab9adb38dd69c33f80afa8fc5e86072618775ff3c0b9ea2314c9c256576d674df7496ea81d3383b4813d692c6e0e0d5d8e250b98be48e495c1d6089dad15dc7d7b46154d6b6ce8ef4ad69b15d4982559b297bcf1885c529f566660e57ec68edbc3c05726cc02fd4cbf4976eaa9afd5138fe8376435b9fc61d2fc0eb06e3"
+);
+
+// G1536
+define_deprecated_group!(
+    G1536,
+    U1536,
+    2,
+    "1536-bit group",
+    "9def3cafb939277ab1f12a8617a47bbbdba51df499ac4c80beeea9614b19cc4d5f4f5f556e27cbde51c6a94be4607a291558903ba0d0f84380b655bb9a22e8dcdf028a7cec67f0d08134b1c8b97989149b609e0be3bab63d47548381dbc5b1fc764e3f4b53dd9da1158bfd3e2b9c8cf56edf019539349627db2fd53d24b7c48665772e437d6c7f8ce442734af7ccb7ae837c264ae3a9beb87f8a2fe9b8b5292e5a021fff5e91479e8ce7a28c2442c6f315180f93499a234dcf76e3fed135f9bb"
+);
+
+// G2048
+define_group!(
+    G2048,
+    U2048,
+    2,
+    "2048-bit group",
+    "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"
+);
+
+// G3072
+define_group!(
+    G3072,
+    U3072,
+    5,
+    "3072-bit group",
+    "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"
+);
+
+// G0496
+define_group!(
+    G4096,
+    U4096,
+    5,
+    "4096-bit group",
+    "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"
+);
 
 #[cfg(test)]
 #[allow(deprecated)]