lhtlp

Linear homomorphic time-lock puzzle implementation in Mathematica

The implementation is based on the construction #5 (Figure 7) of Cicada, A framework for private non-interactive on-chain auctions and voting(2024) .

Script Parameters

The run-script is at the end of the file in "TLP Test" section. You can set the hyperParamters to change the test:

• T : number of iterations to solve the puzzle.
• sMax: max value of the solution. This paramter has been used to construct the lookUp table.
• qRange: range of primes (p and q) to construct N = p * q.
• solution1: solution to puzzle1
• solution2: solution to puzzle2

Functions

pp, lookupTable = setup[T, qRange, sMax]

• outputs
  • publicParamters pp = <|N, g, h, y, T, sMax|> ,
  • lookupTable {y^i mod N, i<sMax}

puzzle = generatePuzzle[pp, solution, r]

• outputs puzzle = <| "c1" = c1, "c2" = c2|> where
  • c1 = (pp.g ^ r) mod N and
  • c2 = (pp.h ^ r * pp.y ^ solution) mod N

ys = solvePuzzle[pp, puzzle]

• outputs ys = (pp.y ^ solution) mod N

puzzle3 = addPuzzles[pp, puzzle1, puzzle2]

• outputs puzzle = <| "c1" = c1, "c2" = c2|> where
  • c1 = (puzzle1.c1 * puzzle2.c1) mod N,
  • c2 = (puzzle1.c2 * puzzle2.c2) mod N

How it works

• first setup would be called to generate public paramters based on hyper-paramteres.
• Then it creates two independant puzzles puzzle1, puzzle2 and solves them.
• Next, it adds two puzzles and generates the third puzzle puzzle3 and solves this one too.
• Then, using the lookupTable, it finds the decoded solutions to the puzzles.
• Finally it asserts the equality of the decoded solution of puzzle3 and summation of solutions 1 and 2.

What's Next?

• Adding rangeProof to assure that solution is in range of sMax