k256: simplify internal helper functions in the scalar arithmetic (#917)

k256/src/arithmetic/scalar/wide32.rs

@@ -417,28 +417,18 @@ impl WideScalar {
     }
 }
 
-/// Constant-time comparison.
-#[inline(always)]
-fn ct_less(a: u32, b: u32) -> u32 {
-    // Do not convert to Choice since it is only used internally,
-    // and we don't want loss of performance.
-    (a < b) as u32
-}
-
 /// Add a to the number defined by (c0,c1,c2). c2 must never overflow.
 fn sumadd(a: u32, c0: u32, c1: u32, c2: u32) -> (u32, u32, u32) {
-    let new_c0 = c0.wrapping_add(a); // overflow is handled on the next line
-    let over: u32 = if new_c0 < a { 1 } else { 0 };
-    let new_c1 = c1.wrapping_add(over); // overflow is handled on the next line
-    let new_c2 = c2 + ct_less(new_c1, over); // never overflows by contract
+    let (new_c0, carry0) = c0.overflowing_add(a);
+    let (new_c1, carry1) = c1.overflowing_add(carry0 as u32);
+    let new_c2 = c2 + (carry1 as u32);
     (new_c0, new_c1, new_c2)
 }
 
-/// Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero.
+/// Add a to the number defined by (c0,c1). c1 must never overflow.
 fn sumadd_fast(a: u32, c0: u32, c1: u32) -> (u32, u32) {
-    let new_c0 = c0.wrapping_add(a); // overflow is handled on the next line
-    let new_c1 = c1 + ct_less(new_c0, a); // never overflows by contract (verified the next line)
-    debug_assert!((new_c1 != 0) | (new_c0 >= a));
+    let (new_c0, carry0) = c0.overflowing_add(a);
+    let new_c1 = c1 + (carry0 as u32);
     (new_c0, new_c1)
 }
 
@@ -448,11 +438,11 @@ fn muladd(a: u32, b: u32, c0: u32, c1: u32, c2: u32) -> (u32, u32, u32) {
     let th = (t >> 32) as u32; // at most 0xFFFFFFFFFFFFFFFE
     let tl = t as u32;
 
-    let new_c0 = c0.wrapping_add(tl); // overflow is handled on the next line
-    let new_th = th + ct_less(new_c0, tl); // at most 0xFFFFFFFFFFFFFFFF
-    let new_c1 = c1.wrapping_add(new_th); // overflow is handled on the next line
-    let new_c2 = c2 + ct_less(new_c1, new_th); // never overflows by contract (verified in the next line)
-    debug_assert!((new_c1 >= new_th) || (new_c2 != 0));
+    let (new_c0, carry0) = c0.overflowing_add(tl);
+    let new_th = th.wrapping_add(carry0 as u32); // at most 0xFFFFFFFFFFFFFFFF
+    let (new_c1, carry1) = c1.overflowing_add(new_th);
+    let new_c2 = c2 + (carry1 as u32);
+
     (new_c0, new_c1, new_c2)
 }
 
@@ -462,9 +452,9 @@ fn muladd_fast(a: u32, b: u32, c0: u32, c1: u32) -> (u32, u32) {
     let th = (t >> 32) as u32; // at most 0xFFFFFFFFFFFFFFFE
     let tl = t as u32;
 
-    let new_c0 = c0.wrapping_add(tl); // overflow is handled on the next line
-    let new_th = th + ct_less(new_c0, tl); // at most 0xFFFFFFFFFFFFFFFF
-    let new_c1 = c1 + new_th; // never overflows by contract (verified in the next line)
-    debug_assert!(new_c1 >= new_th);
+    let (new_c0, carry0) = c0.overflowing_add(tl);
+    let new_th = th.wrapping_add(carry0 as u32); // at most 0xFFFFFFFFFFFFFFFF
+    let new_c1 = c1 + new_th;
+
     (new_c0, new_c1)
 }

k256/src/arithmetic/scalar/wide64.rs

@@ -221,28 +221,18 @@ impl WideScalar {
     }
 }
 
-/// Constant-time comparison.
-#[inline(always)]
-fn ct_less(a: u64, b: u64) -> u64 {
-    // Do not convert to Choice since it is only used internally,
-    // and we don't want loss of performance.
-    (a < b) as u64
-}
-
 /// Add a to the number defined by (c0,c1,c2). c2 must never overflow.
 fn sumadd(a: u64, c0: u64, c1: u64, c2: u64) -> (u64, u64, u64) {
-    let new_c0 = c0.wrapping_add(a); // overflow is handled on the next line
-    let over = ct_less(new_c0, a);
-    let new_c1 = c1.wrapping_add(over); // overflow is handled on the next line
-    let new_c2 = c2 + ct_less(new_c1, over); // never overflows by contract
+    let (new_c0, carry0) = c0.overflowing_add(a);
+    let (new_c1, carry1) = c1.overflowing_add(carry0 as u64);
+    let new_c2 = c2 + (carry1 as u64);
     (new_c0, new_c1, new_c2)
 }
 
-/// Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero.
+/// Add a to the number defined by (c0,c1). c1 must never overflow.
 fn sumadd_fast(a: u64, c0: u64, c1: u64) -> (u64, u64) {
-    let new_c0 = c0.wrapping_add(a); // overflow is handled on the next line
-    let new_c1 = c1 + ct_less(new_c0, a); // never overflows by contract (verified the next line)
-    debug_assert!((new_c1 != 0) | (new_c0 >= a));
+    let (new_c0, carry0) = c0.overflowing_add(a);
+    let new_c1 = c1 + (carry0 as u64);
     (new_c0, new_c1)
 }
 
@@ -252,11 +242,11 @@ fn muladd(a: u64, b: u64, c0: u64, c1: u64, c2: u64) -> (u64, u64, u64) {
     let th = (t >> 64) as u64; // at most 0xFFFFFFFFFFFFFFFE
     let tl = t as u64;
 
-    let new_c0 = c0.wrapping_add(tl); // overflow is handled on the next line
-    let new_th = th + u64::from(new_c0 < tl); // at most 0xFFFFFFFFFFFFFFFF
-    let new_c1 = c1.wrapping_add(new_th); // overflow is handled on the next line
-    let new_c2 = c2 + ct_less(new_c1, new_th); // never overflows by contract (verified in the next line)
-    debug_assert!((new_c1 >= new_th) || (new_c2 != 0));
+    let (new_c0, carry0) = c0.overflowing_add(tl);
+    let new_th = th.wrapping_add(carry0 as u64); // at most 0xFFFFFFFFFFFFFFFF
+    let (new_c1, carry1) = c1.overflowing_add(new_th);
+    let new_c2 = c2 + (carry1 as u64);
+
     (new_c0, new_c1, new_c2)
 }
 
@@ -266,9 +256,9 @@ fn muladd_fast(a: u64, b: u64, c0: u64, c1: u64) -> (u64, u64) {
     let th = (t >> 64) as u64; // at most 0xFFFFFFFFFFFFFFFE
     let tl = t as u64;
 
-    let new_c0 = c0.wrapping_add(tl); // overflow is handled on the next line
-    let new_th = th + ct_less(new_c0, tl); // at most 0xFFFFFFFFFFFFFFFF
-    let new_c1 = c1 + new_th; // never overflows by contract (verified in the next line)
-    debug_assert!(new_c1 >= new_th);
+    let (new_c0, carry0) = c0.overflowing_add(tl);
+    let new_th = th.wrapping_add(carry0 as u64); // at most 0xFFFFFFFFFFFFFFFF
+    let new_c1 = c1 + new_th;
+
     (new_c0, new_c1)
 }