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Terminologies & Conventions

Application side

There are some cryptographic algorithms on the application side:

  • Lagrange's Interpolation: An algorithm to reconstruct the Factor's Polynomial.
  • Shamir's Secret Sharing (SSS): An algorithm to create a unique line on the Cartesian coordinate system.

We will encounter some terminologies when talking about mechanisms and algorithms on the application side:

  • Factor: A point on the Cartesian coordinate system where the x-value is the index and the y-value is the Factor's Key. All factors must be on a unique straight line called Factor's Polynomial.
  • Key (Factor's Key): A number which behaves like a private key.
  • Factor's Polynomial: A first degree polynomial which is a unique straight line on the Cartesian coordinate system, the intersection point between it and the y-axis is the user Private Key.

Network side

There are also some cryptographic algorithms on the network side:

  • Lagrange's Interpolation: An algorithm to reconstruct the Share's Polynomial and the Master Share's Polynomial.
  • Distributed Secret Sharing (DSS): An algorithm to generate a Network Key.
  • Proactive Secret Sharing (PSS): An algorithm to protect nodes.
  • Verifiable Secret Sharing (VSS): An algorithm to verify the integrity of the Private Line.

We are proud to introduce our new cryptographic algorithms on the network side used in the mechanisms:

  • Interchangeable Secret Sharing (ISS): An algorithm to handle dead nodes.
  • Recoverable Secret Sharing (RSS): An algorithm to recover dead nodes.

We will encounter some terminologies when talking about those mechanisms and algorithms on the network side:

  • Secret: In the algorithm, whenever user registers, each Validation Node will create a key. Secret is a point on the y-axis of the Cartesian coordinate system whose y-value is that key.
  • Share's Polynomial: A second degree polynomial which is a unique parabolic line on the Cartesian coordinate system, the intersection point between it and the y-axis is the Secret's Key.
  • Generated Shares: A re the points whose each x-value corresponds to the sequence number of a Validation Node (which are x=1,2,3,4,5x = 1, 2, 3, 4, 5), and the y-value is the result of the Share's Polynomial when substituted by the x-value.
  • Received Shares: A re the points which x-values are only one number (the sequence number of a Validation Node) and the y-values are the values when substituted that x-value into all the Share's Polynomials of the Validation Nodes.
  • Share: An element of the Generated Shares or the Received Shares, which is a pair of x-value and y-value.
  • Master Share: Sum of the Received Shares (sum of all Share following an x-value).
  • Master Share's Polynomial: A second degree polynomial which is a unique parabolic line on the Cartesian coordinate system formed by the Master Shares.
  • Network Key: The y-value of the Master Share's Polynomial where x=0x = 0.