Why does the length of a bitcoin key vary? Why aren't they all the same length?
asked Nov 18, 2011 at 6:43
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some interesting bitcoin trivia - the first time a compressed public key is used to spend on the blockchain is in tx 94af4607627535f9b2968bd1fbbf67be101971d682023d6a3b64d8caeb448870, which spends 0.01337 btc. clearly someone was showing off lol– mulllhausenCommented Nov 11, 2014 at 12:45
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the compressed pubkey was 0271f1e54016d623897fa9b973c2f084376ff61651ee5b71eef0d98a8be56a75cc btw– mulllhausenCommented Nov 11, 2014 at 12:55
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2 Answers
The length of a key doesn't vary. Private keys are always 32 bytes, and public keys are always 65 bytes (or 33 bytes for a compressed public key). Public key hashes are always 20 bytes.
The length of addresses vary because in Bitcoin's base58 encoding, leading zero bytes are expressed as a single "1". Other bytes require more than one character in order to be expressed in base58.
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Do you have private keys and public keys reversed in the above answer? It seems to me that private keys are longer. Commented Nov 20, 2011 at 19:34
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2@shoelessjoe I don't think so. Public keys are definitely 64 bytes plus the leading 0x04 byte, and I assume that the 256 in "secp256k1" refers to the size of the private key in bits.– theymosCommented Nov 21, 2011 at 1:33
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You said "Private keys are always 32 bytes, and public keys are always 65 bytes." That makes public keys longer than private keys? Commented Nov 29, 2011 at 18:13
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@shoelessjoe Yes. I think this is the case with all public-key crypto, actually.– theymosCommented Nov 30, 2011 at 22:12
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In fact, we could move to compressed public keys, which are 257 bits long (33 bytes). Slightly longer than the private key indeed, but almost nothing. Commented Dec 4, 2011 at 14:56
Private keys are 256 bit numbers
Public keys are a pair of X,Y coordinates. Each coordinate is a 256 bit number. BUT for every X coordinate there are only two possible Y coordinates (one positive, one negative) so you can store a public key as just the X coordinate (256 bits) and the sign of the Y coordinate (1 bit) and the proper Y coordinate can then be calculated from the X coordinate and the sign.
So private key = 256 bits, public key = 2*256=512 bits OR 256+1=257 bits
Then there is a small amount of formatting overhead of a few bits.
Then these are encoded.
