Representation of ECC domain parameters
Elliptic curve domains are represented as one of two possibilities.
For curves over prime fields:
Curve = S(type) || S(field.type) || S(field.bitsize) ||
B(p) ||
B(a) || B(b) || B(G.x) || B(G.y) || B(r) || B(h)
For curves over binary polynomial fields:
Curve = S(type) || S(field.type) || S(field.bitsize) ||
S(num_terms) || S(T1) || … || S(Tnum_terms) ||
B(a) || B(b) || B(G.x) || B(G.y) || B(r) || B(h)
In binary fields, field elements are represented as integers.
Bit i
of the integer is the coefficient of xi
.
Component | Field type | Meaning |
---|---|---|
|
both |
Curve parameter |
|
both |
Curve parameter |
|
both |
|
|
both |
|
|
both |
|
|
prime |
The prime modulus |
|
both |
The name |
|
both |
An indicator of the the field size:
|
|
both |
The field type:
|
|
binary |
The number of nonzero terms in the irreducible polynomial, for a binary field.
For example, |
|
binary |
The indices of the nonzero terms Ti in ascending order of the irreducible polynomial, for a binary field.
For example, the polynomial |
|
both |
The curve type:
|