Explicit-Formulas Database

Ordinary genus-1 curves over binary fields

Short Weierstrass curves
EFD / Ordinary genus-1 binary / Affine coordinates for short Weierstrass curves
# Affine coordinates for short Weierstrass curves

An elliptic curve in short Weierstrass form
[more information]
has parameters
a2
a6
and coordinates
x
y
satisfying the following equations:
y^^{2}+x*y=x^^{3}+a2*x^^{2}+a6

Affine coordinates
[database entry]
represent
x
y
as
X
Y
satisfying the following equations:

x=X
y=Y

## Best operation counts

Smallest multiplication counts assuming I=10M, S=0M, *param=0M, add=0M, *const=0M:
Smallest multiplication counts assuming I=10M, S=0.2M, *param=0M, add=0M, *const=0M:
## Summary of all explicit formulas

## Explicit formulas for addition

The "add" addition formulas
[database entry;
Sage verification script;
Sage output;
three-operand code]:
## Explicit formulas for doubling

The "dbl" doubling formulas
[database entry;
Sage verification script;
Sage output;
three-operand code]:
## Explicit formulas for tripling

## Explicit formulas for differential addition

## Explicit formulas for differential addition and doubling

## Explicit formulas for scaling

The "copy" scaling formulas
[database entry;
Sage verification script;
Sage output;
three-operand code]:
- Cost: 0add.
- Explicit formulas:
X3 = X1
Y3 = Y1