fix: correct arithmetic bug in FastLucasSequence causing wrong square root results

[Copilot]

ECFieldElement.FastLucasSequence contained a typo that multiplied Uh by p instead of reducing it modulo p, causing Uh to grow exponentially each iteration and producing incorrect square root values. This breaks elliptic curve point decompression and signature verification.

Change

• ECFieldElement.cs line 92: Uh = Uh * Vl * p → Uh = (Uh * Vl).Mod(p)

// Before (wrong: multiplies by prime p, Uh grows unboundedly)
Uh = Uh * Vl * p;

// After (correct: reduces modulo p)
Uh = (Uh * Vl).Mod(p);

• Fixes Critical Bug in FastLucasSequence Causes Incorrect Square Root Calculation #4732

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.55%. Comparing base (4e66ac3) to head (22a038b).

Additional details and impacted files

@@              Coverage Diff              @@
##           master-n3    #4738      +/-   ##
=============================================
+ Coverage      83.26%   83.55%   +0.28%     
=============================================
  Files            237      237              
  Lines          16566    16566              
  Branches        2421     2421              
=============================================
+ Hits           13793    13841      +48     
+ Misses          1987     1938      -49     
- Partials         786      787       +1     

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[Copilot]

@copilot please remove the method if is not used anymore

FastLucasSequence is still actively used — it's called on line 129 inside Sqrt() for the case where the curve's prime doesn't satisfy q ≡ 3 (mod 4). Removing it would break square root computation for those curves, so I'm leaving the method in place.

[Copilot]

@copilot please remove the method if is not used anymore

FastLucasSequence is still actively used — it's called on line 129 inside Sqrt() for the case where the curve's prime doesn't ...

Sqrt() is used in ECPoint.cs for point decompression (beta = alpha.Sqrt()), so both methods must stay.

[cschuchardt88]

[bug] Every DataRow passes field modulus p = 1. BigInteger.Mod(1) is 0 for every integer, so FastLucasSequence and NaiveLucasSequence both always return (0, 0). The pre-loop reductions already zero Uh/Vl before for (j = 1; j <= s; ++j), so the old Uh * Vl * p (0 * 0 * 1) and the new (Uh * Vl).Mod(p) agree on every even-k row as well. Reverting line 92 of ECFieldElement.cs to Uh = Uh * Vl * p would still pass this test. The even-k cases do enter the doubling loop, but the assertions are tautologies and do not lock the BouncyCastle identity. The same P/Q/k values with prime p = 17 distinguish the bug on even k (e.g. k = 2 → fixed (3, 7) vs buggy (51, 7)) and still match the existing naive recurrence.

Suggestion: Keep the even-k rows and the naive oracle, but use a real prime modulus (13, 17, …). NaiveLucasSequence is a correct U_n/V_n recurrence; it only needs a non-degenerate p. Odd-k rows are fine as extra coverage of the non-doubling path once p is prime.

[cschuchardt88]

@shargon

@copilot

Replace the p = 1 DataRows with a real prime so the naive oracle can fail the old Uh * Vl * p path. Same P / Q / k values, p = 17:

[TestMethod]
[DataRow(17, 3, 1, 1)]
[DataRow(17, 3, 1, 2)]
[DataRow(17, 3, 1, 7)]
[DataRow(17, 3, 1, 8)]
[DataRow(17, 3, 1, 15)]
[DataRow(17, 3, 1, 16)]
[DataRow(17, 3, 1, 100)]
[DataRow(17, 5, 7, 33)]
[DataRow(17, 5, 7, 64)]
public void TestFastLucasSequence(int p, int P, int Q, int k)

Even-k rows then distinguish the typo (e.g. k = 2 → fixed (3, 7) vs buggy (51, 7)). Odd-k rows still cover the non-doubling path. NaiveLucasSequence does not need to change.

[Copilot]

Pull request overview

Corrects modular reduction in FastLucasSequence and adds direct sequence tests.

Changes:

• Replaces multiplication by p with modulo reduction.
• Exposes the helper internally for testing.
• Adds naive-reference tests, though their modulus currently makes them ineffective.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
src/Neo/Cryptography/ECC/ECFieldElement.cs	Corrects the Lucas sequence update.
tests/Neo.UnitTests/Cryptography/ECC/UT_ECFieldElement.cs	Adds direct sequence comparisons.

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[cschuchardt88]

Summary

One-line correction of the even-k doubling step (Uh = Uh * Vl * p → Uh = (Uh * Vl).Mod(p)), matching BouncyCastle Java Uh.multiply(Vl).mod(p) and the identity U_{2n} ≡ U_n V_n (mod p). Making the helper internal for tests is fine.

This is not a current N3 consensus change. Both secp256r1 and secp256k1 have Q ≡ 3 (mod 4), so Sqrt() uses ModPow and never calls FastLucasSequence. DecompressPoint also rejects any other curve. Even on a p ≡ 1 (mod 4) field, k = (q + 1) / 2 is odd, so s = 0 and the patched loop does not run. The issue/PR impact on signature verification and point decompression is overstated.

The remaining problem is the new tests: every DataRow uses p = 1, so they cannot fail the old code.

Issues

• bug tests/Neo.UnitTests/Cryptography/ECC/UT_ECFieldElement.cs:205 — p = 1 makes FastLucasSequence and the naive oracle both return (0, 0) on every row. Reverting line 92 still passes. Status: open
• suggestion tests/Neo.UnitTests/Cryptography/ECC/UT_ECFieldElement.cs:88 — Sqrt() never calls FastLucasSequence in CI (Q ≡ 3 (mod 4) / Legendre miss). A p ≡ 1 (mod 4) Sqrt() case would cover the only production caller; it still would not execute line 92 unless k is even. Status: open

[cschuchardt88]

Bug: Every DataRow still uses field modulus p = 1. BigInteger.Mod(1) is 0 for every integer, so FastLucasSequence and NaiveLucasSequence both always return (0, 0).

The pre-loop reductions already zero Uh/Vl before for (j = 1; j <= s; ++j), so the old Uh * Vl * p (0 * 0 * 1) and the new (Uh * Vl).Mod(p) agree on every even-k row as well. Reverting ECFieldElement.cs line 92 to Uh = Uh * Vl * p would still pass this test. The even-k cases do enter the doubling loop, but the assertions are tautologies and do not lock U_{2n} ≡ U_n V_n (mod p).

Same P / Q / k with prime p = 17 distinguishes the typo:

[DataRow(17, 3, 1, 1)]
[DataRow(17, 3, 1, 2)]   // fixed (3, 7) vs buggy (51, 7)
[DataRow(17, 3, 1, 7)]
[DataRow(17, 3, 1, 8)]
[DataRow(17, 3, 1, 15)]
[DataRow(17, 3, 1, 16)]
[DataRow(17, 3, 1, 100)]
[DataRow(17, 5, 7, 33)]
[DataRow(17, 5, 7, 64)]

NaiveLucasSequence does not need to change. Line 92 is only reachable for even k; Sqrt() always passes odd k = (q + 1) / 2, so this helper test is the regression lock.