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chore: fix quotation marks #739

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6 changes: 3 additions & 3 deletions curve25519-dalek/docs/ifma-notes.md
Original file line number Diff line number Diff line change
Expand Up @@ -32,14 +32,14 @@ Integer Arithmetic Using Intel IFMA Extensions_][2016_gueron_krasnov].
The basic idea is that multiplication of large integers (such as 1024,
2048, or more bits) can be performed as follows.

First, convert a packed 64-bit representation
First, convert a "packed" 64-bit representation
\\[
\begin{aligned}
x &= x'_0 + x'_1 2^{64} + x'_2 2^{128} + \cdots \\\\
y &= y'_0 + y'_1 2^{64} + y'_2 2^{128} + \cdots
\end{aligned}
\\]
into a redundant 52-bit representation
into a "redundant" 52-bit representation
\\[
\begin{aligned}
x &= x_0 + x_1 2^{52} + x_2 2^{104} + \cdots \\\\
Expand All @@ -49,7 +49,7 @@ y &= y_0 + y_1 2^{52} + y_2 2^{104} + \cdots
with each \\(x_i, y_j\\) in a 64-bit lane.

Writing the product as \\(z = z_0 + z_1 2^{52} + z_2 2^{104} + \cdots\\),
the schoolbook multiplication strategy gives
the "schoolbook" multiplication strategy gives
\\[
\begin{aligned}
&z_0 &&=& x_0 & y_0 & & & & & & & & \\\\
Expand Down
4 changes: 2 additions & 2 deletions curve25519-dalek/docs/parallel-formulas.md
Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,7 @@ using AVX2, and the other using AVX512-IFMA.
# Overview

The 2008 paper [_Twisted Edwards Curves Revisited_][hwcd08] by Hisil,
Wong, Carter, and Dawson (HWCD) introduced the extended coordinates
Wong, Carter, and Dawson (HWCD) introduced the "extended coordinates"
and mixed-model representations which are used by most Edwards curve
implementations.

Expand Down Expand Up @@ -242,7 +242,7 @@ possible to pre-multiply by \\(19\\).

Second, the parallel doubling formulas incur both a theoretical and
practical slowdown. The parallel formulas described above work on the
\\( \mathbb P\^3 \\) extended coordinates. The \\( \mathbb P\^2 \\)
\\( \mathbb P\^3 \\) "extended" coordinates. The \\( \mathbb P\^2 \\)
model introduced earlier by [Bernstein, Birkner, Joye, Lange, and
Peters][bbjlp08] allows slightly faster doublings, so HWCD suggest
mixing coordinate systems while performing scalar multiplication
Expand Down
6 changes: 3 additions & 3 deletions curve25519-dalek/src/edwards.rs
Original file line number Diff line number Diff line change
Expand Up @@ -68,8 +68,8 @@
//!
//! ## Implementation
//!
//! The Edwards arithmetic is implemented using the extended twisted
//! coordinates of Hisil, Wong, Carter, and Dawson, and the
//! The Edwards arithmetic is implemented using the "extended twisted
//! coordinates" of Hisil, Wong, Carter, and Dawson, and the
//! corresponding complete formulas. For more details,
//! see the [`curve_models` submodule][curve_models]
//! of the internal documentation.
Expand Down Expand Up @@ -1236,7 +1236,7 @@ impl EdwardsPoint {
self.mul_by_cofactor().is_identity()
}

/// Determine if this point is torsion-free, i.e., is contained in
/// Determine if this point is "torsion-free", i.e., is contained in
/// the prime-order subgroup.
///
/// # Return
Expand Down
4 changes: 2 additions & 2 deletions curve25519-dalek/src/montgomery.rs
Original file line number Diff line number Diff line change
Expand Up @@ -12,8 +12,8 @@
//! Scalar multiplication on the Montgomery form of Curve25519.
//!
//! To avoid notational confusion with the Edwards code, we use
//! variables \\( u, v \\) for the Montgomery curve, so that Montgomery
//! \\(u\\) here corresponds to Montgomery \\(x\\) elsewhere.
//! variables \\( u, v \\) for the Montgomery curve, so that "Montgomery
//! \\(u\\)" here corresponds to "Montgomery \\(x\\)" elsewhere.
//!
//! Montgomery arithmetic works not on the curve itself, but on the
//! \\(u\\)-line, which discards sign information and unifies the curve
Expand Down
6 changes: 3 additions & 3 deletions curve25519-dalek/src/ristretto.rs
Original file line number Diff line number Diff line change
Expand Up @@ -35,7 +35,7 @@
//! small cofactor \\(h\\) (for instance, Edwards curves, which have
//! cofactor at least \\(4\\)).
//!
//! This abstraction mismatch is commonly handled by pushing the
//! This abstraction mismatch is commonly "handled" by pushing the
//! complexity upwards, adding ad-hoc protocol modifications. But
//! these modifications require careful analysis and are a recurring
//! source of [vulnerabilities][cryptonote] and [design
Expand All @@ -46,8 +46,8 @@
//! the correct abstraction for cryptographic systems, while retaining
//! the speed and safety benefits of an Edwards curve.
//!
//! Decaf is named after the procedure which divides the effect of
//! coffee by \\(4\\). However, Curve25519 has a cofactor of
//! Decaf is named "after the procedure which divides the effect of
//! coffee by \\(4\\)". However, Curve25519 has a cofactor of
//! \\(8\\). To eliminate its cofactor, Ristretto restricts further;
//! this [additional restriction][ristretto_coffee] gives the
//! _Ristretto_ encoding.
Expand Down