Cryptographic Primitives

JubJub Curve 

Iron Fish makes use of the JubJub curve, which is a 255-bit twisted Edwards curve with the following affine equation:

$a x^2 + y^2 \equiv 1 + d x^2 y^2 \pmod{p}$

where:

• $p$: 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 (255 bits)
• $a$: 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000 ($a \equiv -1 \pmod{p}$)
• $d$: 0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1 ($d \equiv -10240/10241 \pmod{p}$)

JubJub Group 

The points on the JubJub curve give origin to a finite cyclic group of order:

$n$: 0x73eda753299d7d483339d80809a1d8053341049e6640841684b872f6b7b965b8 (255 bits)

With the 2-torsion point (0, 1) serving as the identity element.

This group contains a subgroup with a large prime order:

• order ($r$): 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7 (252 bits)
• cofactor ($h$): 0x08

Iron Fish operates in this large prime subgroup.

Generators 

Iron Fish makes use of different generators for the JubJub group. The generators are:

Note that these generators all generate the large prime subgroup mentioned above, so multiplication by the cofactor is not needed when performing algebra using these generators.

Summary of cryptographic schemes 

This is an overview of all the cryptographic keys and cryptographic schemes used by Iron Fish in different places. The exact details of how these are employed are laid out in Accounts, Transactions, and Blocks.

Keys:

Schemes:

Signature Scheme 

The signature scheme used by Iron Fish is RedDSA, which is a variant of the Elliptic Curve Schnorr Signature scheme defined in the Sapling protocol (see https://zips.z.cash/protocol/protocol.pdf#concretereddsa).

The hashing algorithm used in conjunction with RedDSA is Blake2b.