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Polynomial function

As explained in Real-World Cryptography

A polynomial is a mathematical expression formed from coefficients and nonnegative integer powers of a variable.

A polynomial combines coefficients with nonnegative integer powers of a variable. In a zk-SNARK construction, it can gather several program equations into one object. section 15.3.8

A constraint polynomial works in stages:

  • Choose roots such as 1, 2, and 3, assigning one program equation to each point. section 15.3.8
  • Require evaluations such as f(1), f(2), and f(3) to equal zero when the computation is correct. section 15.3.8
  • Use selector polynomials that isolate individual equations, then add their contributions into one polynomial. section 15.3.9
  • Keep secret inputs and intermediate values in coefficients while evaluating the result at a hidden random point. section 15.3.9

How Real-World Cryptography covers it

How deep it goes
Builds polynomials from roots, selector functions, coefficients, and hidden-point evaluations.
Examples
Uses roots 1, 2, and 3 with equations involving a, b, m, v, and w.
What you can do after
Evaluate/understand how polynomial roots represent correct program constraints while hiding selected values.
How it connects
Connects R1CS, zk-SNARKs, Lagrange interpolation, prover behavior, and verifier behavior.
Cover of Real-World Cryptography
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