define and implement ConstantTime{Partial,}Ord traits

src/lib.rs

@@ -1,7 +1,7 @@
 // -*- mode: rust; -*-
 //
 // This file is part of subtle, part of the dalek cryptography project.
-// Copyright (c) 2016-2018 isis lovecruft, Henry de Valence
+// Copyright (c) 2016-2022 isis lovecruft, Henry de Valence
 // See LICENSE for licensing information.
 //
 // Authors:
@@ -13,14 +13,14 @@
 #![deny(missing_docs)]
 #![doc(html_root_url = "https://docs.rs/subtle-ng/2.5.0")]
 
-
 #[cfg(feature = "std")]
 #[macro_use]
 extern crate std;
 
 #[cfg(test)]
 extern crate rand;
 
+use core::cmp::Ordering;
 use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Neg, Not};
 use core::option::Option;
 
@@ -45,6 +45,11 @@ use core::option::Option;
 pub struct Choice(u8);
 
 impl Choice {
+    /// Create an instance in `const` context.
+    pub const fn of_bool(of: bool) -> Self {
+        Self(of as u8)
+    }
+
     /// Unwrap the `Choice` wrapper to reveal the underlying `u8`.
     ///
     /// # Note
@@ -170,7 +175,7 @@ impl From<u8> for Choice {
     }
 }
 
-/// An `Eq`-like trait that produces a `Choice` instead of a `bool`.
+/// An [`Eq`]-like trait that produces a `Choice` instead of a `bool`.
 ///
 /// # Example
 ///
@@ -728,7 +733,7 @@ macro_rules! generate_unsigned_integer_greater {
                 Choice::from((bit & 1) as u8)
             }
         }
-    }
+    };
 }
 
 generate_unsigned_integer_greater!(u8, 8);
@@ -740,7 +745,7 @@ generate_unsigned_integer_greater!(u128, 128);
 
 /// A type which can be compared in some manner and be determined to be less
 /// than another of the same type.
-pub trait ConstantTimeLess: ConstantTimeEq + ConstantTimeGreater {
+pub trait ConstantTimeLess: ConstantTimeGreater {
     /// Determine whether `self < other`.
     ///
     /// The bitwise-NOT of the return value of this function should be usable to
@@ -778,7 +783,7 @@ pub trait ConstantTimeLess: ConstantTimeEq + ConstantTimeGreater {
     /// ```
     #[inline]
     fn ct_lt(&self, other: &Self) -> Choice {
-        !self.ct_gt(other) & !self.ct_eq(other)
+        other.ct_gt(self)
     }
 }
 
@@ -788,3 +793,123 @@ impl ConstantTimeLess for u32 {}
 impl ConstantTimeLess for u64 {}
 #[cfg(feature = "i128")]
 impl ConstantTimeLess for u128 {}
+
+/// A [`PartialOrd`][core::cmp::PartialOrd]-like trait for constant-time comparisons.
+///
+/// This trait is automatically implemented for types supporting the "equals", "less", and
+/// "greater" comparisons.
+///
+/// # Example
+///
+/// ```
+/// use std::cmp::Ordering;
+/// use subtle_ng::{ConstantTimePartialOrd, CtOption};
+/// let x: u8 = 5;
+/// let y: u8 = 13;
+///
+/// assert_eq!(x.ct_partial_cmp(&x).unwrap(), Ordering::Equal);
+/// assert_eq!(x.ct_partial_cmp(&y).unwrap(), Ordering::Less);
+/// assert_eq!(y.ct_partial_cmp(&x).unwrap(), Ordering::Greater);
+/// ```
+pub trait ConstantTimePartialOrd {
+    /// This method returns an ordering between `self` and `other`, if it exists.
+    ///
+    /// This method should execute in constant time.
+    fn ct_partial_cmp(&self, other: &Self) -> CtOption<Ordering>;
+}
+
+/// Select among `N + 1` results given `N` logical values, of which at most one should be true.
+///
+/// This method requires a whole set of logical checks to be performed before evaluating their
+/// result, and uses a lookup table to avoid branching in a `match` expression.
+///
+///```
+/// use subtle_ng::index_mutually_exclusive_logical_results;
+///
+/// let r = [0xA, 0xB, 0xC];
+///
+/// let a = index_mutually_exclusive_logical_results(&r, [0.into(), 0.into()]);
+/// assert_eq!(*a, 0xA);
+/// let b = index_mutually_exclusive_logical_results(&r, [1.into(), 0.into()]);
+/// assert_eq!(*b, 0xB);
+/// let c = index_mutually_exclusive_logical_results(&r, [0.into(), 1.into()]);
+/// assert_eq!(*c, 0xC);
+///```
+pub fn index_mutually_exclusive_logical_results<T, const N: usize>(
+    results: &[T],
+    logicals: [Choice; N],
+) -> &T {
+    assert_eq!(results.len(), N + 1);
+    let combined_result: u8 = logicals.iter().enumerate().fold(0u8, |x, (i, choice)| {
+        x + ((i as u8) + 1) * choice.unwrap_u8()
+    });
+    results
+        .get(combined_result as usize)
+        .expect("multiple inconsistent mutually exclusive logical operations returned true")
+}
+
+impl<T: ConstantTimeGreater + ConstantTimeLess + ConstantTimeEq> ConstantTimePartialOrd for T {
+    /// We do not assume a total ordering for `T`, so we have to individually check "less than",
+    /// "equal", and "greater". This also respects non-default implementations of `ct_lt()`.
+    fn ct_partial_cmp(&self, other: &Self) -> CtOption<Ordering> {
+        let is_eq = self.ct_eq(other);
+        let is_lt = self.ct_lt(other);
+        let is_gt = self.ct_gt(other);
+
+        const PARTIAL_ORDERS: [CtOption<Ordering>; 4] = [
+            CtOption {
+                value: Ordering::Equal,
+                is_some: Choice::of_bool(false),
+            },
+            CtOption {
+                value: Ordering::Equal,
+                is_some: Choice::of_bool(true),
+            },
+            CtOption {
+                value: Ordering::Less,
+                is_some: Choice::of_bool(true),
+            },
+            CtOption {
+                value: Ordering::Greater,
+                is_some: Choice::of_bool(true),
+            },
+        ];
+        *index_mutually_exclusive_logical_results(&PARTIAL_ORDERS, [is_eq, is_lt, is_gt])
+    }
+}
+
+/// An [`Ord`][core::cmp::Ord]-like trait for constant-time comparisons.
+///
+/// This trait is automatically implemented for types supporting the "equals" and
+/// "greater" comparisons.
+///
+/// # Example
+///
+/// ```
+/// use std::cmp::Ordering;
+/// use subtle_ng::ConstantTimeOrd;
+/// let x: u8 = 5;
+/// let y: u8 = 13;
+///
+/// assert_eq!(x.ct_cmp(&x), Ordering::Equal);
+/// assert_eq!(x.ct_cmp(&y), Ordering::Less);
+/// assert_eq!(y.ct_cmp(&x), Ordering::Greater);
+/// ```
+pub trait ConstantTimeOrd {
+    /// This method returns an ordering between `self` and other`.
+    ///
+    /// This method should execute in constant time.
+    fn ct_cmp(&self, other: &Self) -> Ordering;
+}
+
+impl<T: ConstantTimeEq + ConstantTimeGreater> ConstantTimeOrd for T {
+    /// We assume a total ordering for `T`, so we need to check only "equal" and "greater", and can
+    /// assume "less" if both `ct_eq()` and `ct_gt()` are false.
+    fn ct_cmp(&self, other: &Self) -> Ordering {
+        let is_gt = self.ct_gt(other);
+        let is_eq = self.ct_eq(other);
+
+        const ORDERS: [Ordering; 3] = [Ordering::Less, Ordering::Greater, Ordering::Equal];
+        *index_mutually_exclusive_logical_results(&ORDERS, [is_gt, is_eq])
+    }
+}