"source": "## META | difficulty 1 | Objectives\n\nThis final bundle turns common failure modes into visible patterns instead of vague warnings.\n\nFocus:\n\n- wrong sign in wraparound\n- wrong root or wrong zeta\n- wrong BO / NO comparison\n- missing final scaling\n- wrong mental model for the Kyber modulus\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 3,
"kind": "explanation",
"title": "Bad Outputs Have Fingerprints"
}
},
"source": "## MANDATORY | difficulty 3 | Bad Outputs Have Fingerprints\n\nDebugging NTTs is easier when you stop staring at the final vector as one blob.\nEach common mistake leaves a characteristic fingerprint:\n\n- wrong sign flips specific wrapped slots\n- wrong order makes a correct value set appear shuffled\n- missing `n^-1` keeps the shape but scales everything wrong\n- wrong zeta corrupts local pair structure early\n"
"source": "## MANDATORY | difficulty 2 | Retrieval Check\n\n1. Which mistake keeps the general shape of the inverse output but leaves every entry too large by a shared factor?\n2. Which mistake often disappears once you apply the correct BO -> NO reorder?\n3. Which mistake shows up earliest in local pair traces rather than only at the very end?\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "facultative",
"difficulty": 4,
"kind": "exploration",
"title": "Optional: Trace Rows For Debugging"
}
},
"outputs": [],
"source": "# FACULTATIVE | difficulty 4 | Optional: Trace Rows For Debugging\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace, stage_rows\n\ntrace = fast_ntt_psi_ct_trace([1, 2, 3, 4], 7681, 1925)\nfor stage in trace.stages:\n print(\"stage\", stage.stage_index)\n for row in stage_rows(stage):\n print(row)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "handoff",
"title": "Next Notebook"
}
},
"source": "## META | difficulty 1 | Next Notebook\n\nNext notebook: `lab.ipynb`\n"
