Part 2: Elliptic curve arithmetic

[dapinkone]

Implementing Ed448-Goldilocks with BigInteger.

Building a library & app for asymmetric encryption and digital signatures at the 256-bit security level.

• [x] DHIES encryption
• [x] Schnorr signatures, with elliptic curves

Note, all arithmetic is modulo p. p is a specific prime defined in the Ed448-Goldilocks spec.

p := 2^448 - 2^224 - 1

• [x] Need a data structure to represent the goldilocks pair (x, y)
  • [x] constructor for neutral element
  • [x] constructor for curve point given it's x and y's least sig bit.
  • [x] .equals method test for equality
  • [x] .opposite method to obtain opposite of a point
  • [x] current.add(other) method to sum two points
  • [x] tests written/passing
  • [x] .mul() to support scalar multiplication
  • [x] tests written/passing

services:

• [x] Generate an elliptic key pair from a given passphrase
• [x] write the public key to a file
• [x] BONUS: Encrypt the private key from that pair under the given password and write it to a different file as well.
• [x] Encrypt a data file under a given elliptic public key file and write the ciphertext to a file.
• [x] BONUS: Encrypt text input by the user directly to the app instead of having to read it from a file (but write the ciphertext to a file).
• [x] Decrypt a given elliptic-encrypted file from a given password and write the decrypted data to a file.
• [x] Sign a given file from a given password and write the signature to a file.
• [x] BONUS: Sign text input by the user directly to the app instead of having to read it from a file (but write the signature to a file).
• [x] Verify a given data file and its signature file under a given public key file.
• [x] BONUS: Verify text input by the user directly to the app instead of having to read it from a file (but read the signature from a file).
• [x] The actual instructions to use the app and obtain the above services must be part of your project report (in PDF).

[Hyunggilwoo]

Question on implementing the y_0 of the GoldilockPair's public generator: How do we compute y_0? Given that:

1. public generator (G) = (x_0, y_0)
2. x = plus_or_minus sqrt( (1 - y^2) / (1 + 39081y^2) mod p)
3. x_0 = -3 (mod p)

Do we have compute y from the equation to compute x?

[Hyunggilwoo]

KMACXOF256. Does Part 1 need to incorporate BigInteger instead of int?

[Hyunggilwoo]

I am debating on if we need to create a separate class to generate a Schnorr signature, or can whether Elliptic Curve class should have the Schnorr signature method, or maybe the KMACXOF256 should have access to it. Right now, I am leaning towards creating a separate class to generate a key pair of Schnorr Signature

[dapinkone]

KMACXOF256. Does Part 1 need to incorporate BigInteger instead of int?

Posting here for reference, verdict was "mostly no"; extending a few select functions for utility moving forward, but the project requirements do not require this functionality in part 1's section.

I am debating on if we need to create a separate class to generate a Schnorr signature, or can whether Elliptic Curve class should have the Schnorr signature method, or maybe the KMACXOF256 should have access to it. Right now, I am leaning towards creating a separate class to generate a key pair of Schnorr Signature

Java / OOP style is pretty heavy on classes. It's probably fine to make a class for this. It's a thing, with associated properties and functionality. sounds like a class to me. We'll see how much it has in common with other classes as the project matures.

Question on implementing the y_0 of the GoldilockPair's public generator: How do we compute y_0? Given that:

1. public generator (G) = (x_0, y_0)

2. x = plus_or_minus sqrt( (1 - y^2) / (1 + 39081y^2) mod p)

3. x_0 = -3 (mod p)

Do we have compute y from the equation to compute x?

See implementation of ElipticCurve.f or the instantiation of G just above. These may answer the question

[dapinkone]

Project completed as far as needed, closing ticket.