{"podcast":{"title":"Magic Internet Math","slug":"magic-internet-math-7652323","podcast_index_feed_id":7652323,"rss_url":"https://serve.podhome.fm/rss/7005772a-c12d-4a3f-b3cc-4c05833946e0","website_url":"https://fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ","image_url":"https://assets.podhome.fm/68bd541f-7118-40ad-47f7-08dd33f04393/639136107548391507d7b8be.jpg","author":"Brian Hirschfield","episode_count":16,"summary":"This podcast exists to liberate Bitcoin holders from second-class citizenship by teaching the mathematics that underlies their convictions. We operate on a simple premise: if you don't understand the math of Bitcoin, you cannot truly know what you know—you're dependent on others' authority, forever vulnerable to doubt and manipulation. Mathematics is the primary pathway to conviction in your own reasoning. Through accessible, conversational exploration of Bitcoin's mathematical foundations—treating math as the liberal art it was always meant to be—we equip listeners with genuine understanding rather than borrowed beliefs. We reject the deliberate demoralization campaign that convinced generations they'r…","last_synced_at":"2026-09-28T20:21:51.807293+00:00","page_url":"https://stenobird.com/podcast/magic-internet-math-7652323"},"episode":{"title":"Elliptic Curve Cryptography: Inverses and Group Structure","slug":"elliptic-curve-cryptography-inverses-and-group-structure","published_at":"2026-03-02T12:22:37+00:00","page_url":"https://stenobird.com/podcast/magic-internet-math-7652323/elliptic-curve-cryptography-inverses-and-group-structure","show_page_url":"https://stenobird.com/podcast/magic-internet-math-7652323","url":"https://magicinternetmath.com","audio_url":"https://serve.podhome.fm/episode/68bd541f-7118-40ad-47f7-08dd33f04393/639136107900912589a4ef36cb-7591-4af0-8174-a851e53b148dv1.mp3","summary":"The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of the Magic Internet Math Podcast, the hosts continue their exploration of elliptic curve cryptography, focusing on the inverse problem and the mathematical structures that ensure its existence, as part of their series on Bitcoin security. Key Topics: Inverse Problem Modular Arithmetic Groups and Fields Euclidean Algorithm Fermat's Little Theorem LibSecP Library Summary: The hosts emphasize the importance of understanding the mathematical foundations of Bitcoin, specifically the inverse problem, where a public key can be inverted back into its corresponding private key. They highlight that the existence of an inverse is crucial for the security of Bitcoin, ensuring that transactions can be verified and private keys remain secure. This is supported by the mathematical structures of groups and fields, which guarantee the existence of an inverse for every element under certain operations.","meta_description":"The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of the Magic Internet Math Podcast, the hosts continue their expl…","key_points":[],"chapters":[],"topics":[],"duration_seconds":5536,"processing_state":"not_requested","actions":[{"name":"request_transcript","method":"POST","url":"https://stenobird.com/v1/public/podcasts/magic-internet-math-7652323/episodes/elliptic-curve-cryptography-inverses-and-group-structure/transcription-requests","description":"Idempotently request low-priority transcript generation for this episode."},{"name":"read_markdown","method":"GET","url":"https://stenobird.com/podcast/magic-internet-math-7652323/elliptic-curve-cryptography-inverses-and-group-structure.md","description":"Read the agent-friendly Markdown representation of this episode resource."}]}}