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Computes a sum-of-products `aA + bB + ...` in variable time with w-NAF
multi-exponentiation using the interleaved window method, also known
as Straus' method.
The key insight is that when computing this sum by means of additions
and doublings, the doublings can be shared by performing the additions
within an inner loop.
The API and implementation are inspired in part by `curve25519-dalek`,
namely the `VartimeMultiscalarMul` trait and corresponding
implementation in `straus.rs`.
This results in ~28% speedup on `p256` for a 3 scalar/point input:
ProjectivePoint operations/point-scalar lincomb (variable-time)
time: [149.13 µs 149.80 µs 150.84 µs]
change: [−27.999% −27.645% −27.267%] (p = 0.00 < 0.05)
tarcieri
added a commit
to RustCrypto/elliptic-curves
that referenced
this pull request
May 7, 2026
Companion PR to RustCrypto/group#14, which adds `WnafBase::multiscalar_mul` using Straus' method. When the `alloc` feature is enabled, this is used to compute `LinearCombination::lincomb_vartime`. Also includes updated tests and benchmarks for `p256` to ensure `lincomb_vartime` computes the same results as using the `Add` and `Mul` traits, and show the relative performance improvement, which is a ~28% speedup on `p256` for a 3 scalar/point input: ProjectivePoint operations/point-scalar lincomb (variable-time) time: [149.13 µs 149.80 µs 150.84 µs] change: [−27.999% −27.645% −27.267%] (p = 0.00 < 0.05)
tarcieri
added a commit
to RustCrypto/elliptic-curves
that referenced
this pull request
May 7, 2026
Companion PR to RustCrypto/group#14, which adds `WnafBase::multiscalar_mul` using Straus' method. When the `alloc` feature is enabled, this is used to compute `LinearCombination::lincomb_vartime`. Also includes updated tests and benchmarks for `p256` to ensure `lincomb_vartime` computes the same results as using the `Add` and `Mul` traits, and show the relative performance improvement, which is a ~28% speedup on `p256` for a 3 scalar/point input: ProjectivePoint operations/point-scalar lincomb (variable-time) time: [149.13 µs 149.80 µs 150.84 µs] change: [−27.999% −27.645% −27.267%] (p = 0.00 < 0.05)
tarcieri
added a commit
to RustCrypto/traits
that referenced
this pull request
May 7, 2026
Uses `WnafBase::multiscalar_mul` added in RustCrypto/group#14 to provide a variable-time linear combination operation which can use the precomputed wNAF for a basepoint. This has been tested in `p256` where it provides a 25% speedup for ECDSA verification.
tarcieri
added a commit
to RustCrypto/traits
that referenced
this pull request
May 7, 2026
Uses `WnafBase::multiscalar_mul` added in RustCrypto/group#14 to provide a variable-time linear combination operation which can use the precomputed wNAF for a basepoint. This has been tested in `p256` where it provides a 25% speedup for ECDSA verification.
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Computes a sum-of-products
aA + bB + ...in variable time with w-NAF multi-exponentiation using the interleaved window method, also known as Straus' method.The key insight is that when computing this sum by means of additions and doublings, the doublings can be shared by performing the additions within an inner loop.
The API and implementation are inspired in part by
curve25519-dalek, namely theVartimeMultiscalarMultrait and corresponding implementation instraus.rs.This results in ~28% speedup on
p256for a 3 scalar/point input: