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Diffstat (limited to 'docs')
| -rw-r--r-- | docs/IMPLEMENTATIONS.md | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/docs/IMPLEMENTATIONS.md b/docs/IMPLEMENTATIONS.md index 724150f..d333ed5 100644 --- a/docs/IMPLEMENTATIONS.md +++ b/docs/IMPLEMENTATIONS.md @@ -249,7 +249,7 @@ Uses binary addition chain. INPUT: k = (k_{t-1}, ..., k_1, k_0)_2, P ∈ E(F_q). OUTPUT: [k]P. 1. Q ← ∞. - 2. For i from t - 1 downto 0 do + 2. For i from 0 to t-1 do 2.1 If k_i = 1 then Q ← Q + P. 2.2 P ← 2P. 3. Return(Q). @@ -432,7 +432,7 @@ The same name, Montgomery ladder, is used both for the general ladder idea of ex INPUT: k = (k_{t-1}, ..., k_1, k_0)_2, P ∈ E(F_q). OUTPUT: [k]P . 1. P_1 ← P and P_2 ← [2]P - 2. For i = t − 2 downto 0 do + 2. For i = t − 1 downto 0 do 2.1 If k_i = 0 then P_1 ← [2]P_1; P_2 ← P_1 + P_2. Else @@ -443,13 +443,13 @@ The same name, Montgomery ladder, is used both for the general ladder idea of ex INPUT: G ∈ E(F_q), k = (1, k_{t−2}, ..., k_0)2 OUTPUT: Y = kG - R0 ← G; R1 ← [2]G - for j = t − 2 downto 0 do - if (k_j = 0) then - R1 ← R0 + R1; R0 ← [2]R0 - else [if (kj = 1)] - R0 ← R0 + R1; R1 ← [2]R1 - return R0 + 1. R0 ← G; R1 ← [2]G + 2. for j = t − 2 downto 0 do + 2.1 if (k_j = 0) then + R1 ← R0 + R1; R0 ← [2]R0 + else [if (kj = 1)] + R0 ← R0 + R1; R1 ← [2]R1 + 3. return R0 Montgomery addition formulas (Projective coordinates/XZ coordinates):[^2] |