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Bitcoin
Bitcoin Script
Stacked scripting, not specified as OP_CODE is executed as raw data. Turing incomplete prevents loops.
Contstants
When talking about scripts, these value-pushing words are usually omitted.
Word Opcode Hex Input Output |Description
------------------------------------------------------------+-----------
OP_0, OP_FALSE 0 0x00 Nothing. (empty value) |An empty array of bytes is pushed onto the stack. (This is not a no-op: an item is added to the stack.)
N/A 1-75 0x01-0x4b (special) data |The next opcode bytes is data to be pushed onto the stack
OP_PUSHDATA1 76 0x4c (special) data |The next byte contains the number of bytes to be pushed onto the stack.
OP_PUSHDATA2 77 0x4d (special) data |The next two bytes contain the number of bytes to be pushed onto the stack in little endian order.
OP_PUSHDATA4 78 0x4e (special) data |The next four bytes contain the number of bytes to be pushed onto the stack in little endian order.
OP_1NEGATE 79 0x4f Nothing. -1 |The number -1 is pushed onto the stack.
OP_1, OP_TRUE 81 0x51 Nothing. 1 |The number 1 is pushed onto the stack.
OP_2-OP_16 82-96 0x52-0x60 Nothing. 2-16 |The number in the word name (2-16) is pushed onto the stack.
Flow control
Word Opcode Hex Input Output |Description
----------------------------------------------------------------------------------------+-----------
OP_NOP 97 0x61 Nothing Nothing |Does nothing.
OP_IF 99 0x63 <expression> if [statements] [else [statements]]* endif |If the top stack value is not False, the statements are executed. The top stack value is removed.
OP_NOTIF 100 0x64 <expression> notif [statements] [else [statements]]* endif |If the top stack value is False, the statements are executed. The top stack value is removed.
OP_ELSE 103 0x67 <expression> if [statements] [else [statements]]* endif |If the preceding OP_IF or OP_NOTIF or OP_ELSE was not executed then these statements are and if the preceding OP_IF or OP_NOTIF or OP_ELSE was executed then these statements are not.
OP_ENDIF 104 0x68 <expression> if [statements] [else [statements]]* endif |Ends an if/else block. All blocks must end, or the transaction is invalid. An OP_ENDIF without OP_IF earlier is also invalid.
OP_VERIFY 105 0x69 True / false Nothing/fail |Marks transaction as invalid if top stack value is not true. The top stack value is removed.
OP_RETURN 106 0x6a Nothing fail |Marks transaction as invalid. Since bitcoin 0.9, a standard way of attaching extra data to transactions is to add a zero-value output with a scriptPubKey consisting of OP_RETURN followed by data. Such outputs are provably unspendable and specially discarded from storage in the UTXO set, reducing their cost to the network. Since 0.12, standard relay rules allow a single output with OP_RETURN, that contains any sequence of push statements (or OP_RESERVED[1]) after the OP_RETURN provided the total scriptPubKey length is at most 83 bytes.
Stack
Word Opcode Hex Input Output |Description
----------------------------------------------------------------------------+-----------
OP_TOALTSTACK 107 0x6b x1 (alt)x1 |Puts the input onto the top of the alt stack. Removes it from the main stack.
OP_FROMALTSTACK 108 0x6c (alt)x1 x1 |Puts the input onto the top of the main stack. Removes it from the alt stack.
OP_IFDUP 115 0x73 x x / x x |If the top stack value is not 0, duplicate it.
OP_DEPTH 116 0x74 Nothing <Stack size> |Puts the number of stack items onto the stack.
OP_DROP 117 0x75 x Nothing |Removes the top stack item.
OP_DUP 118 0x76 x x x |Duplicates the top stack item.
OP_NIP 119 0x77 x1 x2 x2 |Removes the second-to-top stack item.
OP_OVER 120 0x78 x1 x2 x1 x2 x1 |Copies the second-to-top stack item to the top.
OP_PICK 121 0x79 xn ... x2 x1 x0 <n> xn ... x2 x1 x0 xn |The item n back in the stack is copied to the top.
OP_ROLL 122 0x7a xn ... x2 x1 x0 <n> ... x2 x1 x0 xn |The item n back in the stack is moved to the top.
OP_ROT 123 0x7b x1 x2 x3 x2 x3 x1 |The 3rd item down the stack is moved to the top.
OP_SWAP 124 0x7c x1 x2 x2 x1 |The top two items on the stack are swapped.
OP_TUCK 125 0x7d x1 x2 x2 x1 x2 |The item at the top of the stack is copied and inserted before the second-to-top item.
OP_2DROP 109 0x6d x1 x2 Nothing |Removes the top two stack items.
OP_2DUP 110 0x6e x1 x2 x1 x2 x1 x2 |Duplicates the top two stack items.
OP_3DUP 111 0x6f x1 x2 x3 x1 x2 x3 x1 x2 x3 |Duplicates the top three stack items.
OP_2OVER 112 0x70 x1 x2 x3 x4 x1 x2 x3 x4 x1 x2 |Copies the pair of items two spaces back in the stack to the front.
OP_2ROT 113 0x71 x1 x2 x3 x4 x5 x6 x3 x4 x5 x6 x1 x2 |The fifth and sixth items back are moved to the top of the stack.
OP_2SWAP 114 0x72 x1 x2 x3 x4 x3 x4 x1 x2 |Swaps the top two pairs of items.
Splice
If any opcode marked as disabled is present in a script, it must abort and fail.
Word Opcode Hex Input Output |Description
------------------------------------------------+-----------
OP_CAT 126 0x7e x1 x2 out |Concatenates two strings. disabled.
OP_SUBSTR 127 0x7f in begin size out|Returns a section of a string. disabled.
OP_LEFT 128 0x80 in size out |Keeps only characters left of the specified point in a string. disabled.
OP_RIGHT 129 0x81 in size out |Keeps only characters right of the specified point in a string. disabled.
OP_SIZE 130 0x82 in in size |Pushes the string length of the top element of the stack (without popping it).
Bitwise logic
If any opcode marked as disabled is present in a script, it must abort and fail.
Word Opcode Hex Input Output |Description
--------------------------------------------------------+-----------
OP_INVERT 131 0x83 in out |Flips all of the bits in the input. disabled.
OP_AND 132 0x84 x1 x2 out |Boolean and between each bit in the inputs. disabled.
OP_OR 133 0x85 x1 x2 out |Boolean or between each bit in the inputs. disabled.
OP_XOR 134 0x86 x1 x2 out |Boolean exclusive or between each bit in the inputs. disabled.
OP_EQUAL 135 0x87 x1 x2 True / false |Returns 1 if the inputs are exactly equal, 0 otherwise.
OP_EQUALVERIFY 136 0x88 x1 x2 Nothing / fail | Same as OP_EQUAL, but runs OP_VERIFY afterward.
Arithmetic
Note: Arithmetic inputs are limited to signed 32-bit integers, but may overflow their output.
If any input value for any of these commands is longer than 4 bytes, the script must abort and fail. If any opcode marked as disabled is present in a script - it must also abort and fail.
Word Opcode Hex Input Output |Description
----------------------------------------------------+-----------
OP_1ADD 139 0x8b in out |1 is added to the input.
OP_1SUB 140 0x8c in out |1 is subtracted from the input.
OP_2MUL 141 0x8d in out |The input is multiplied by 2. disabled.
OP_2DIV 142 0x8e in out |The input is divided by 2. disabled.
OP_NEGATE 143 0x8f in out |The sign of the input is flipped.
OP_ABS 144 0x90 in out |The input is made positive.
OP_NOT 145 0x91 in out |If the input is 0 or 1, it is flipped. Otherwise the output will be 0.
OP_0NOTEQUAL 146 0x92 in out |Returns 0 if the input is 0. 1 otherwise.
OP_ADD 147 0x93 a b out |a is added to b.
OP_SUB 148 0x94 a b out |b is subtracted from a.
OP_MUL 149 0x95 a b out |a is multiplied by b. disabled.
OP_DIV 150 0x96 a b out |a is divided by b. disabled.
OP_MOD 151 0x97 a b out |Returns the remainder after dividing a by b. disabled.
OP_LSHIFT 152 0x98 a b out |Shifts a left b bits, preserving sign. disabled.
OP_RSHIFT 153 0x99 a b out |Shifts a right b bits, preserving sign. disabled.
OP_BOOLAND 154 0x9a a b out |If both a and b are not 0, the output is 1. Otherwise 0.
OP_BOOLOR 155 0x9b a b out |If a or b is not 0, the output is 1. Otherwise 0.
OP_NUMEQUAL 156 0x9c a b out |Returns 1 if the numbers are equal, 0 otherwise.
OP_NUMEQUALVERIFY 157 0x9d a b Nothing/fail| Same as OP_NUMEQUAL, but runs OP_VERIFY afterward.
OP_NUMNOTEQUAL 158 0x9e a b out |Returns 1 if the numbers are not equal, 0 otherwise.
OP_LESSTHAN 159 0x9f a b out |Returns 1 if a is less than b, 0 otherwise.
OP_GREATERTHAN 160 0xa0 a b out |Returns 1 if a is greater than b, 0 otherwise.
OP_LESSTHANOREQUAL 161 0xa1 a b out |Returns 1 if a is less than or equal to b, 0 otherwise.
OP_GREATERTHANOREQUAL 162 0xa2 a b out |Returns 1 if a is greater than or equal to b, 0 otherwise.
OP_MIN 163 0xa3 a b out |Returns the smaller of a and b.
OP_MAX 164 0xa4 a b out |Returns the larger of a and b.
OP_WITHIN 165 0xa5 x min max out |Returns 1 if x is within the specified range (left-inclusive), 0 otherwise.
Crypto
Word Opcode Hex Input Output |Description
------------------------------------------------------------------------------------------------------------------------+-----------
OP_RIPEMD160 166 0xa6 in hash |The input is hashed using RIPEMD-160.
OP_SHA1 167 0xa7 in hash |The input is hashed using SHA-1.
OP_SHA256 168 0xa8 in hash |The input is hashed using SHA-256.
OP_HASH160 169 0xa9 in hash |The input is hashed twice: first with SHA-256 and then with RIPEMD-160.
OP_HASH256 170 0xaa in hash |The input is hashed two times with SHA-256.
OP_CODESEPARATOR 171 0xab Nothing Nothing |All of the signature checking words will only match signatures to the data after the most recently-executed OP_CODESEPARATOR.
OP_CHECKSIG 172 0xac sig pubkey True/false |The entire transaction's outputs, inputs, and script (from the most recently-executed OP_CODESEPARATOR to the end) are hashed. The signature used by OP_CHECKSIG must be a valid signature for this hash and public key. If it is, 1 is returned, 0 otherwise.
OP_CHECKSIGVERIFY 173 0xad sig pubkey Nothing/fail |Same as OP_CHECKSIG, but OP_VERIFY is executed afterward.
OP_CHECKMULTISIG 174 0xae x sig1 sig2 ... <nr. of signatures> pub1 pub2 <nr. of public keys> True/False |Compares the first signature against each public key until it finds an ECDSA match. Starting with the subsequent public key, it compares the second signature against each remaining public key until it finds an ECDSA match. The process is repeated until all signatures have been checked or not enough public keys remain to produce a successful result. All signatures need to match a public key. Because public keys are not checked again if they fail any signature comparison, signatures must be placed in the scriptSig using the same order as their corresponding public keys were placed in the scriptPubKey or redeemScript. If all signatures are valid, 1 is returned, 0 otherwise. Due to a bug, one extra unused value is removed from the stack.
OP_CHECKMULTISIGVERIFY 175 0xaf x sig1 sig2 ... <nr. of signatures> pub1 pub2 ... <nr. of public keys> Nothing/fail |Same as OP_CHECKMULTISIG, but OP_VERIFY is executed afterward.
Locktime
Word Opcode Hex Input Output|Description
--------------------------------------------------------------------+-----------
OP_CHECKLOCKTIMEVERIFY (previously OP_NOP2) 177 0xb1 x x/fail|Marks transaction as invalid if the top stack item is greater than the transaction's nLockTime field, otherwise script evaluation continues as though an OP_NOP was executed. Transaction is also invalid if 1. the stack is empty; or 2. the top stack item is negative; or 3. the top stack item is greater than or equal to 500000000 while the transaction's nLockTime field is less than 500000000, or vice versa; or 4. the input's nSequence field is equal to 0xffffffff. The precise semantics are described in BIP 0065.
OP_CHECKSEQUENCEVERIFY (previously OP_NOP3) 178 0xb2 x x/fail|Marks transaction as invalid if the relative lock time of the input (enforced by BIP 0068 with nSequence) is not equal to or longer than the value of the top stack item. The precise semantics are described in BIP 0112.
Pseudo-words
These words are used internally for assisting with transaction matching. They are invalid if used in actual scripts.
Word Opcode Hex |Description
----------------------------+-----------
OP_PUBKEYHASH 253 0xfd|Represents a public key hashed with OP_HASH160.
OP_PUBKEY 254 0xfe|Represents a public key compatible with OP_CHECKSIG.
OP_INVALIDOPCODE 255 0xff|Matches any opcode that is not yet assigned.
Reserved words
Any opcode not assigned is also reserved. Using an unassigned opcode makes the transaction invalid.
Word Opcode Hex |When used: Invalid,...
----------------------------+----------------------
OP_RESERVED 80 0x50 |unless occuring in an unexecuted OP_IF branch
OP_VER 98 0x62 |unless occuring in an unexecuted OP_IF branch
OP_VERIF 101 0x65 |even when occuring in an unexecuted OP_IF branch
OP_VERNOTIF 102 0x66 |even when occuring in an unexecuted OP_IF branch
OP_RESERVED1 137 0x89 |unless occuring in an unexecuted OP_IF branch
OP_RESERVED2 138 0x8a |unless occuring in an unexecuted OP_IF branch
|OP_NOP1, 176, 0xb0,
|OP_NOP4- 179- 0xb3-
|OP_NOP10 185 0xb9 |The word is ignored. Does not mark transaction as invalid.
Script examples
The following is a list of interesting scripts. When notating scripts, data to be pushed to the stack is generally enclosed in angle brackets and data push commands are omitted. Non-bracketed words are opcodes. These examples include the “OP_” prefix, but it is permissible to omit it. Thus “<pubkey1> <pubkey2> OP_2 OP_CHECKMULTISIG” may be abbreviated to “<pubkey1> <pubkey2> 2 CHECKMULTISIG”. Note that there is a small number of standard script forms that are relayed from node to node; non-standard scripts are accepted if they are in a block, but nodes will not relay them.
Standard Transaction to Bitcoin address (pay-to-pubkey-hash)
scriptPubKey: OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG
scriptSig: <sig> <pubKey>
To demonstrate how scripts look on the wire, here is a raw scriptPubKey:
76=OP_DUP A9=OP_HASH160 14=Bytes to push
89 AB CD EF AB BA AB BA AB BA AB BA AB BA AB BA AB BA AB BA=Data to push 88=OP_EQUALVERIFY AC=OP_CHECKSIG
Note: scriptSig is in the input of the spending transaction and scriptPubKey is in the output of the previously unspent i.e. "available" transaction.
Here is how each word is processed:
Stack Script |Description
----------------------------------------------------------------------------------------------------|-----------
Empty <sig> <pubKey> OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |scriptSig and scriptPubKey are combined.
<sig> <pubKey> OP_DUP OP_HASH160<pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Contstants are added to the stack.
<sig> <pubKey> <pubKey> OP_HASH160<pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Top stack item is duplicated.
<sig> <pubKey> <pubHashA> <pubKeyHash>OP_EQUALVERIFY OP_CHECKSIG |Top stack item is hashed.
<sig> <pubKey> <pubHashA> <pubKeyHash>OP_EQUALVERIFY OP_CHECKSIG |Constant added.
<sig> <pubKey> OP_CHECKSIG |Equality is checked between the top two stack items.
true Empty. |Signature is checked for top two stack items.
Obsolete pay-to-pubkey transaction
OP_CHECKSIG is used directly without first hashing the public key. This was used by early versions of Bitcoin where people paid directly to IP addresses, before Bitcoin addresses were introduced. scriptPubKeys of this transaction form are still recognized as payments to user by Bitcoin Core. The disadvantage of this transaction form is that the whole public key needs to be known in advance, implying longer payment addresses, and that it provides less protection in the event of a break in the ECDSA signature algorithm.
scriptPubKey: <pubKey> OP_CHECKSIG
scriptSig: <sig>
Checking process:
Stack Script |Description
------------------------------------+-----------
Empty <sig> <pubKey>OP_CHECKSIG |scriptSig and scriptPubKey are combined.
<sig> <pubKey> OP_CHECKSIG |Constants are added to the stack.
true Empty. |Signature is checked for top two stack items.
Provably Unspendable/Prunable Outputs
The standard way to mark a transaction as provably unspendable is with a scriptPubKey of the following form:
scriptPubKey: OP_RETURN {zero or more ops}
OP_RETURN immediately marks the script as invalid, guaranteeing that no scriptSig exists that could possibly spend that output. Thus the output can be immediately pruned from the UTXO set even if it has not been spent. eb31ca1a4cbd97c2770983164d7560d2d03276ae1aee26f12d7c2c6424252f29 is an example: it has a single output of zero value, thus giving the full 0.125BTC fee to the miner who mined the transaction without adding an entry to the UTXO set. You can also use OP_RETURN to add data to a transaction without the data ever appearing in the UTXO set, as seen in 1a2e22a717d626fc5db363582007c46924ae6b28319f07cb1b907776bd8293fc; P2Pool does this with the share chain hash txout in the coinbase of blocks it creates.
Freezing funds until a time in the future
Using OP_CHECKLOCKTIMEVERIFY it is possible to make funds provably unspendable until a certain point in the future.
scriptPubKey: <expiry time> OP_CHECKLOCKTIMEVERIFY OP_DROP OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG
scriptSig: <sig> <pubKey>
Stack Script |Description
--------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------
Empty. <sig> <pubKey> <expiry time> OP_CHECKLOCKTIMEVERIFY OP_DROP OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |scriptSig and scriptPubKey are combined.
<sig> <pubKey><expiry time>OP_CHECKLOCKTIMEVERIFY OP_DROP OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Constants are added to the stack.
<sig> <pubKey><expiry time>OP_DROP OP_DUP OP_HASH160 <pubKeyHash>OP_EQUALVERIFY OP_CHECKSIG |Top stack item is checked against the current time or block height.
<sig> <pubKey> OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Top stack item is removed.
<sig> <pubKey><pubKey> OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Top stack item is duplicated.
<sig> <pubKey><pubHashA> <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Top stack item is hashed.
<sig> <pubKey><pubHashA> <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG |Constant added.
<sig> <pubKey> OP_CHECKSIG |Equality is checked between the top two stack items.
true Empty. |Signature is checked for top two stack items.
Transaction puzzle
Transaction a4bfa8ab6435ae5f25dae9d89e4eb67dfa94283ca751f393c1ddc5a837bbc31b is an interesting puzzle.
scriptPubKey: OP_HASH256 6fe28c0ab6f1b372c1a6a246ae63f74f931e8365e15a089c68d6190000000000 OP_EQUAL
scriptSig:
To spend the transaction you need to come up with some data such that hashing the data twice results in the given hash.
Stack Script |Description
--------------------------------------------------------+-----------
Empty. <data> OP_HASH256 <given_hash>OP_EQUAL|
<data> OP_HASH256 <given_hash> OP_EQUAL |scriptSig added to the stack.
<data_hash> <given_hash> OP_EQUAL |The data is hashed.
<data_hash> <given_hash> OP_EQUAL |The given hash is pushed to the stack.
true Empty. |The hashes are compared, leaving true on the stack.
This transaction was successfully spent by 09f691b2263260e71f363d1db51ff3100d285956a40cc0e4f8c8c2c4a80559b1. The required data happened to be the Genesis block, and the given hash in the script was the genesis block header hashed twice with SHA-256. Note that while transactions like this are fun, they are not secure, because they do not contain any signatures and thus any transaction attempting to spend them can be replaced with a different transaction sending the funds somewhere else.
Incentivized finding of hash collisions
In 2013 Peter Todd created scripts that result in true if a hash collision is found. Bitcoin addresses resulting from these scripts can have money sent to them. If someone finds a hash collision they can spend the bitcoins on that address, so this setup acts as an incentive for somebody to do so.
For example the SHA1 script:
scriptPubKey: OP_2DUP OP_EQUAL OP_NOT OP_VERIFY OP_SHA1 OP_SWAP OP_SHA1 OP_EQUAL
scriptSig: <preimage1> <preimage2>
See the bitcointalk thread [2] and reddit thread[3] for more details. In February 2017 the SHA1 bounty worth 2.48 bitcoins was claimed.
Personal drafts, Library documentation challenge at the midnightpub.
====================================================================
Legenda:
? = No idea
& = and
algebra = +-*/()^√...
logic = (Grouping)[entity]}--Transaction--}('=/=' = ≠ = (inequal))
specifiers = :algebra:"Rawdata"
=========================================================================================================
UTXO (Unspent Transaction Output) Is the index of Bitcoin values that can be spend
(n[Addres]) (n(}-- (? BTC) --}))
[A(has now (n BTC) over (? UTXO's))]
}== (X BTC) == (n BTC) --} [B] & }-- ((n BTC)-(X BTC)) --} [A(gets change back)]
Simple view:
[n*a] [aA]{-- > 0,5 BTC output--, [aB]
_________________________________________________________|__________________________
}== (2,5 BTC) ==} |
[Addres]}------(1 BTC) output--}[A] }-- (1 BTC) input----+-- (2,5 BTC) output--}[B]
[[Addres]*?]}--(2 BTC) output--}[A] }-- (2 BTC) input----'
Timechain validation cost grows: Scaling problem:
(t= -- =Tijd=--) S=Scale P=Problem n=amount N=Nodes C=Capacity ?='something'
t=-- S -- < -- S -- P= (n N -- < -- n N -- C(verify) '≠' -- < -- C(needed))
₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿₿
Timechain section = Header 863623:
[0*20]+
5179197aad3f3ddbf542b53b79f7b11cd719eed4cc54
₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿ ₿₿
Input of sha256 hash 1 "c1866366374d5d1f22704d5d7999168f440ff8b5ef18c8c1a1d21f33286e7bef" = nyet revealed
9 input of sha256 hash "abb2311beb5a2c01dae0d4b9918a997bb307530782b468288edfa8127a5932fa" = >-----------X
Need method to repeat this indefinitly when asked a given moment, with the above being a provable input.
Problem? Alice posts the above secret to a forum. Therefore she proves to witnesses that she knew already what the secret was. Bob, sees this secret and starts posting it to other forums. Therefore, those users don't know if Bob is fake or not. So Bob has to proof himself on request. Which is really easy when using Public key cryptography.
But how to do this using the setup above? I added another secret so that she has to prove that again. But this only delays the problem.