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Each share has about an 85% chance of being available when needed and a 2% chance of being independently leaked. Can you calculate the recovery odds, compromise probability, and how many shares I can lose?"},{"title":"Auditing a 2-of-3 seed phrase split","prompt":"I split my crypto seed phrase 3 ways, needing any 2 to recover it. Assuming each share has a 95% survival chance and a 1% independent compromise chance, what's the probability I can recover it, how likely is it to be stolen, and how many qualifying subsets are there?"},{"title":"Designing high-security corporate secret sharing","prompt":"For a corporate signing key split into 10 shares with a threshold of 6, each share surviving with 80% probability and a 0.1% individual compromise chance, tell me the recovery probability, breach odds, number of minimal qualifying sets, and how many shares can be lost without breaking recovery."}],"resultDescription":"Returns a JSON object with: total shares (n), threshold (t), count of all qualifying subsets, minimal qualifying sets, number of shares that can be lost (sharesYouCanLose), shares that reveal nothing (sharesThatRevealNothing), probability the secret is recoverable (probabilityRecoverable), probability it has been breached (probabilityBreached), storage overhead multiple, a human-readable verdict and summary, and optional degraded/disclaimer flags.","failureModes":["t greater than n — returns validation error (t must be ≤ n)","n outside 2–255 range — returns out-of-bounds error","t less than 2 — returns validation error","shareSurvival or shareCompromise outside 0–1 range — returns parameter error","Missing required n or t query parameters — returns 400 bad request","Payment failure or missing x402 header — returns 402 Payment Required"],"whenToPreferThis":"Choose this endpoint when you need to reason about the mathematical properties of a Shamir t-of-n configuration without transmitting any actual secret material. It is the right choice for capacity planning (how many shares to create), risk assessment (loss and compromise probabilities), and compliance documentation of key management schemes. Prefer it over generic combinatorics tools because it is purpose-built for Shamir statistics and returns cryptography-specific vocabulary (qualifying sets, threshold, breach probability) directly.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-21T12:37:54.754Z","isFirstParty":false,"canonicalSlug":"security-math-shamir-secret-sharing-calculator-b2fc9b86"}