{"uid":"cap_IAPpBTtRsNstJyNkH5QP9","slug":"crypto-math-entropy-calculator-041f6f8e","name":"Crypto Math Entropy Calculator","description":"Shannon entropy in bits per symbol from a frequency table, plus min-entropy, collision entropy and efficiency.","url":"https://crypto-math.x402tookit.com/entropy?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["table"],"properties":{"table":{"type":"string","description":"Comma-separated counts or probabilities, optionally label:count, e.g. a:5,b:3,c:2 or 0.5,0.25,0.25 (1 to 1000 symbols)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"symbols":{"type":["null","number"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"disclaimer":{"type":["null","string"]},"efficiency":{"type":["null","number"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"sampleSize":{"type":["null","number"]},"maxEntropyBits":{"type":["null","number"]},"minEntropyBits":{"type":["null","number"]},"redundancyBits":{"type":["null","number"]},"collisionEntropyBits":{"type":["null","number"]},"entropyBitsPerSymbol":{"type":["null","number"]},"symbolsWithZeroCount":{"type":["null","number"]},"totalInformationBits":{"type":["null","number"]},"perfectBitsToEncodeOneSymbol":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Od8dT_fgWVshwep3zHcP_","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Shannon entropy, min-entropy, collision entropy, and efficiency in bits per symbol from a frequency table of counts or probabilities.","exampleAgentPrompt":"Can you calculate the Shannon entropy, min-entropy, and efficiency for a symbol distribution with counts: a:50, b:30, c:15, d:5?","exampleUseCases":[{"title":"Password character distribution analysis","prompt":"I have a password generator that produces characters with these frequencies — lowercase:120, uppercase:45, digits:30, symbols:5. Can you compute the Shannon entropy per symbol and tell me how efficient that distribution is?"},{"title":"Cryptographic key source quality check","prompt":"I sampled a hardware RNG and got these byte value counts: 0:512, 1:498, 2:505, 3:489, 4:510, 5:486. What's the min-entropy per symbol and how does it compare to the maximum possible entropy?"},{"title":"Language symbol entropy measurement","prompt":"I'm analyzing English letter frequencies — e:1202,t:910,a:812,o:768,i:731,n:695,s:628,h:609,r:602,d:432 — can you compute the Shannon entropy in bits per symbol and show me the redundancy?"}],"resultDescription":"Returns a JSON object containing: entropyBitsPerSymbol (Shannon H), minEntropyBits, collisionEntropyBits, maxEntropyBits, redundancyBits, totalInformationBits, perfectBitsToEncodeOneSymbol, efficiency (ratio of actual to max entropy), symbols count, symbolsWithZeroCount, sampleSize, plus metadata fields (summary, verdict, source, asOf, disclaimer).","failureModes":["Missing 'table' query parameter returns an error","Malformed table string (invalid characters, non-numeric counts) causes parse failure","All symbols having zero count yields undefined entropy","Single-symbol distribution returns 0 bits entropy (valid but edge case)","Exceeding 1000 symbols limit returns a validation error","Probabilities that don't sum to 1 may produce unexpected results","Payment not completed results in 402 response blocking the computation"],"whenToPreferThis":"Choose this endpoint when you need a fast, precise multi-measure entropy analysis (Shannon, min-entropy, collision entropy, and efficiency) for a discrete frequency or probability distribution, especially in cryptographic or information-theoretic contexts. It's particularly useful when you want all entropy measures in one call rather than computing each separately.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:35:23.482Z","isFirstParty":false,"canonicalSlug":"crypto-math-entropy-calculator-041f6f8e"}