{ "cells": [ { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "meta", "difficulty": 1, "kind": "theme", "title": "Notebook Theme" } }, "source": "## META\n\n\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "meta", "difficulty": 1, "kind": "route_nav", "title": "Route Guardrails" } }, "source": "## META\n\n
\n Level 1\n
\n META\n route nav\n
\n
Route Guardrails
\n
\n\nYou are at **step 13 of 27** in the only supported route.\n\nNever choose the next notebook manually from the file tree. Use only the links in this cell and the final handoff cell.\n\n**Immediate navigation**\n- Next notebook: [Butterfly Mechanics / 03 Fast Forward CT / Studio](studio.ipynb)\n- Previous notebook: [Butterfly Mechanics / 03 Fast Forward CT / Lab](lab.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n\n**Official route chain**\n1. [Start Here](../../START_HERE.ipynb)\n2. [Course Blueprint](../../COURSE_BLUEPRINT.ipynb)\n3. [Foundations / 01 Convolution To Toy NTT / Lecture](../../foundations/01_convolution_to_toy_ntt/lecture.ipynb)\n4. [Foundations / 01 Convolution To Toy NTT / Lab](../../foundations/01_convolution_to_toy_ntt/lab.ipynb)\n5. [Foundations / 01 Convolution To Toy NTT / Problems](../../foundations/01_convolution_to_toy_ntt/problems.ipynb)\n6. [Foundations / 01 Convolution To Toy NTT / Studio](../../foundations/01_convolution_to_toy_ntt/studio.ipynb)\n7. [Foundations / 02 Negative Wrapped NTT / Lecture](../../foundations/02_negative_wrapped_ntt/lecture.ipynb)\n8. [Foundations / 02 Negative Wrapped NTT / Lab](../../foundations/02_negative_wrapped_ntt/lab.ipynb)\n9. [Foundations / 02 Negative Wrapped NTT / Problems](../../foundations/02_negative_wrapped_ntt/problems.ipynb)\n10. [Foundations / 02 Negative Wrapped NTT / Studio](../../foundations/02_negative_wrapped_ntt/studio.ipynb)\n11. [Butterfly Mechanics / 03 Fast Forward CT / Lecture](lecture.ipynb)\n12. [Butterfly Mechanics / 03 Fast Forward CT / Lab](lab.ipynb)\n13. **Butterfly Mechanics / 03 Fast Forward CT / Problems** <- you are here\n14. [Butterfly Mechanics / 03 Fast Forward CT / Studio](studio.ipynb)\n15. [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](../04_fast_inverse_gs/lecture.ipynb)\n16. [Butterfly Mechanics / 04 Fast Inverse GS / Lab](../04_fast_inverse_gs/lab.ipynb)\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](../04_fast_inverse_gs/problems.ipynb)\n18. [Butterfly Mechanics / 04 Fast Inverse GS / Studio](../04_fast_inverse_gs/studio.ipynb)\n19. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n20. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lab](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb)\n21. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Problems](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb)\n22. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Studio](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb)\n23. [Professional / 06 Debugging NTT Failures / Lecture](../../professional/06_debugging_ntt_failures/lecture.ipynb)\n24. [Professional / 06 Debugging NTT Failures / Lab](../../professional/06_debugging_ntt_failures/lab.ipynb)\n25. [Professional / 06 Debugging NTT Failures / Problems](../../professional/06_debugging_ntt_failures/problems.ipynb)\n26. [Professional / 06 Debugging NTT Failures / Studio](../../professional/06_debugging_ntt_failures/studio.ipynb)\n27. [Course Complete](../../COURSE_COMPLETE.ipynb)\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "meta", "difficulty": 1, "kind": "orientation", "title": "Problem Set Goals" } }, "source": "## META\n\n
\n Level 1\n
\n META\n orientation\n
\n
Problem Set Goals
\n
\n\nThis notebook checks whether the CT schedule is now a visible object rather than a name.\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "mandatory", "difficulty": 2, "kind": "quiz", "title": "Multiple-Choice Retrieval" } }, "source": "## MANDATORY\n\n
\n Level 2\n
\n MANDATORY\n quiz\n
\n
Multiple-Choice Retrieval
\n
\n\nChoose one answer for each:\n\n1. CT makes the transform faster by:\n A. changing the ring\n B. reusing bracket structure through staged butterflies\n C. deleting the inverse\n\n2. The natural output order of the direct CT schedule discussed here is:\n A. normal order\n B. bit-reversed order\n C. random order\n\n3. A stage explorer is useful mainly because it:\n A. hides the pairings\n B. makes data movement and zeta usage inspectable\n C. removes the need for examples\n" }, { "cell_type": "code", "execution_count": null, "metadata": { "pedagogy": { "role": "mandatory", "difficulty": 2, "kind": "quiz", "title": "Answer Key" } }, "outputs": [], "source": "# MANDATORY\n# title: Answer Key\n# kind: quiz | level: 2\n\nanswers = {1: \"B\", 2: \"B\", 3: \"B\"}\nprint(answers)\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "mandatory", "difficulty": 2, "kind": "exercise", "title": "Paper Example Check" } }, "source": "## MANDATORY\n\n
\n Level 2\n
\n MANDATORY\n exercise\n
\n
Paper Example Check
\n
\n\nVerify that the CT trace on `[1,2,3,4]` in `Z_7681` with `\u03c8 = 1925` lands on the paper\u2019s BO output.\n" }, { "cell_type": "code", "execution_count": null, "metadata": { "pedagogy": { "role": "mandatory", "difficulty": 2, "kind": "exercise", "title": "Check The BO Output" } }, "outputs": [], "source": "# MANDATORY\n# title: Check The BO Output\n# kind: exercise | level: 2\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace\n\ntrace = fast_ntt_psi_ct_trace([1, 2, 3, 4], 7681, 1925)\nprint(trace.raw_output)\nassert list(trace.raw_output) == [1467, 3471, 2807, 7621]\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "mandatory", "difficulty": 2, "kind": "reflection", "title": "Written Reflection" } }, "source": "## MANDATORY\n\n
\n Level 2\n
\n MANDATORY\n reflection\n
\n
Written Reflection
\n
\n\nExplain why the phrase \u201csame transform, better schedule\u201d is the right headline for CT.\n" }, { "cell_type": "code", "execution_count": null, "metadata": { "pedagogy": { "role": "facultative", "difficulty": 4, "kind": "exploration", "title": "Optional Challenge" } }, "outputs": [], "source": "# FACULTATIVE\n# title: Optional Challenge\n# kind: exploration | level: 4\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace, find_psi\n\ntrace = fast_ntt_psi_ct_trace([3, 1, 4, 1, 5, 9, 2, 6], 97, find_psi(8, 97))\nfor stage in trace.stages:\n print(stage.stage_index, stage.output_values)\n" }, { "cell_type": "markdown", "metadata": { "pedagogy": { "role": "meta", "difficulty": 1, "kind": "handoff", "title": "Next Notebook" } }, "source": "## META\n\n
\n Level 1\n
\n META\n handoff\n
\n
Next Notebook
\n
\n\nYou finished **Butterfly Mechanics / 03 Fast Forward CT / Problems**.\n\n**Primary next action**\n- Next notebook: [Step 14 of 27 - Butterfly Mechanics / 03 Fast Forward CT / Studio](studio.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Butterfly Mechanics / 03 Fast Forward CT / Lab](lab.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n" } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "name": "python" }, "ntt_learning": { "title": "Problems: Fast Forward CT", "contract_version": "0.2", "sequence": [ "notebooks/START_HERE.ipynb", "notebooks/COURSE_BLUEPRINT.ipynb", "notebooks/foundations/01_convolution_to_toy_ntt/lecture.ipynb", "notebooks/foundations/01_convolution_to_toy_ntt/lab.ipynb", "notebooks/foundations/01_convolution_to_toy_ntt/problems.ipynb", "notebooks/foundations/01_convolution_to_toy_ntt/studio.ipynb", "notebooks/foundations/02_negative_wrapped_ntt/lecture.ipynb", "notebooks/foundations/02_negative_wrapped_ntt/lab.ipynb", "notebooks/foundations/02_negative_wrapped_ntt/problems.ipynb", "notebooks/foundations/02_negative_wrapped_ntt/studio.ipynb", "notebooks/butterfly_mechanics/03_fast_forward_ct/lecture.ipynb", "notebooks/butterfly_mechanics/03_fast_forward_ct/lab.ipynb", "notebooks/butterfly_mechanics/03_fast_forward_ct/problems.ipynb", "notebooks/butterfly_mechanics/03_fast_forward_ct/studio.ipynb", "notebooks/butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb", "notebooks/butterfly_mechanics/04_fast_inverse_gs/lab.ipynb", "notebooks/butterfly_mechanics/04_fast_inverse_gs/problems.ipynb", "notebooks/butterfly_mechanics/04_fast_inverse_gs/studio.ipynb", "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb", "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb", "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb", "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb", "notebooks/professional/06_debugging_ntt_failures/lecture.ipynb", "notebooks/professional/06_debugging_ntt_failures/lab.ipynb", "notebooks/professional/06_debugging_ntt_failures/problems.ipynb", "notebooks/professional/06_debugging_ntt_failures/studio.ipynb", "notebooks/COURSE_COMPLETE.ipynb" ] } }, "nbformat": 4, "nbformat_minor": 5 }