Limits This invention relates generally to blockchain technology, and more particularly to implementing complex functionality via the blockchain. Advantageously, the invention allows for the outcome of a computation or executed code to be transferred one to the other, providing a mechanism which uses blockchain transactions as a control mechanism for enabling, influencing and directing the activities of a computer-implemented process. The invention is particularly suited for, but not limited to, the implementation and control of automated processes.

In this document we use the term 'blockchain' to include all forms of electronic, computer- based, distributed ledgers, including, but not limited to blockchain and transaction-chain technologies, permissioned and un-permissioned ledgers, shared ledgers and variations thereof. The most widely known application of blockchain technology is the Bitcoin ledger, although other blockchain implementations have been proposed and developed. While Bitcoin may be referred to herein for the purpose of convenience and illustration, it should be noted that the invention is not limited to use with the Bitcoin blockchain and alternative blockchain implementations and protocols fall within the scope of the present invention.

A blockchain is a consensus-based, electronic ledger which is implemented as a computer- based decentralised, distributed system made up of blocks which in turn are made up of transactions. Each transaction includes at least one input and at least one output. Each block contains a hash of the previous block to that blocks become chained together to create a permanent, unalterable record of all transactions which have been written to the blockchain since its inception. Transactions contain small programs known as scripts embedded into their inputs and outputs, which specify how and by whom the outputs of the transactions can be accessed. On the Bitcoin platform, these scripts are written using a stack-based scripting language. Scripts are made up of instructions (opcodes) which push data items onto the stack, or pop them off the stack. In order for a transaction to be written to the blockchain, it must be "validated". Network nodes (miners) perform work to ensure that each transaction is valid, with invalid transactions rejected from the network. Software clients installed on the nodes perform this validation work on an unspent transaction (UTXO) by executing its locking and unlocking scripts. If execution of the locking and unlocking scripts evaluate to TRUE, the transaction is valid and the transaction is written to the blockchain. Thus, in order for a transaction to be written to the blockchain, it must be i) validated by the first node that receives the transaction - if the transaction is validated, the node relays it to the other nodes in the network; and ii) added to a new block built by a miner; and iii) mined, i.e. added to the public ledger of past transactions.

Although blockchain technology is most widely known for the use of cryptocurrency implementation, digital entrepreneurs have begun exploring the use of both the cryptographic security system Bitcoin is based on and the data that can be stored on the Blockchain to implement new systems. It would be highly advantageous if the blockchain could be used for automated tasks and processes which are not limited to the realm of cryptocurrency. Such solutions would be able to harness the benefits of the blockchain (e.g. a permanent, tamper proof records of events, distributed processing etc) while being more versatile in their applications.

One area of current research is the use of the blockchain for the implementation of "smart contracts" - machine executable programs which act upon the conditions set out in machine-readable documents and comprise rules that can process inputs in order to produce results, which can then cause actions to be performed dependent upon those results.

However, as more and more sophisticated applications are devised for blockchain technology, so the need for ever-increasingly complex script functionality rises as well. A technical problem arises here, though, as blockchain technologies are purposefully designed to restrict and limit what can be legitimately achieved within a script. For example, due to security considerations, the Bitcoin Script language is deliberately non- Turing complete. Furthermore, an upper limit of 200 op-codes is imposed per script so as to prevent Denial of Service attacks. As long as a Bitcoin transaction script contains fewer than 200 op codes, it can be validated and broadcasted. However, with the advent of more sophisticated program elements (e.g. primitives), this limit places a restriction the development of more complex technical solutions for applications such as smart contract execution.

Thus, a technical solution is required which enables complex functionality to be built into blockchain scripts without compromising security and/or requiring any adaptation of the existing protocol. Preferably, this solution would allow the capabilities of existing blockchain protocols such as the Bitcoin protocol, to enable the infrastructure to be used in novel and advantageous ways by using blockchain transactions and the stack to extend the computational abilities of the blockchain beyond its present limits. Such a technique would enable the use of transactions to control, influence and direct the execution of a technical process.

Such a solution has now been devised. The invention provides at least the advantages described herein. The present invention is defined in the appended claims. Therefore, in accordance with the invention there may be provided a method and/or corresponding system.

According to one perspective, the invention may be viewed as providing a technique and corresponding implementation which enables complex functions to be performed via the use of a blockchain. Advantageously, this technique may use a combination of a variety of distinct computing components to perform the specified function. These may comprise one or more software-based clients, at least one storage resource (preferably a stack-based data structure), at least one digital wallet executing on at least one processor and arranged to generate a blockchain transaction, and/or a blockchain. Preferably, this may be the Bitcoin blockchain. Embodiments of the invention may involve the decomposition of a technical task over multiple transactions and their respective inputs and outputs. Embodiments of the invention may obtain data from at least one data storage resource and use that data to control the execution of a task or computation which is implemented over multiple blockchain transactions, in particular by passing script outputs between the respective transaction inputs and outputs.

The various system components mentioned above may be arranged so as to obtain and pass data items between the components so as to enable computations and tasks to be performed via the blockchain transactions. These computations/tasks can be lengthy and complex, and could not be performed via blockchain transactions prior to the present invention, possibly due to an enforced limit on the size of the script and/or number of op codes used therein. Once the transactions are on the blockchain, they are recorded in an immutable and permanent manner. Therefore, from one perspective the invention provides an improved blockchain protocol, improved blockchain client, an improved computational technique and corresponding apparatus, and/or an improved process control mechanism. In one sense, the invention enables complex computations to be performed via a blockchain protocol while still preserving the security-based restrictions on script size and opcode limits. Prior to the invention, such lengthy computations would either be impossible using, for example, the current Bitcoin protocol or one would have to use an alternative form of blockchain which does not include script-based restrictions. The latter is not always desirable or feasible. Thus, the invention provides an enhanced security mechanism. As it provides a means for achieving results that were hitherto not possible via the protocol, the invention provides an improved blockchain protocol.

A method in accordance with the invention may be described as a blockchain method (and corresponding system). It may be described as a method of using a plurality of blockchain transactions to execute a computer-implemented task. Additionally or alternatively, it may be described as a method of: • controlling the execution of computer-implemented task by allocating or distributing the execution of portions of the task to locking and unlocking scripts provided in two or more respective blockchain transactions;

• controlling the execution of a computer-implemented task by reading a value from a stack-based data structure and passing it as a value from an unlocking script to a locking script.

The method may comprise the steps:

using an unlocking script (ULS1) in a blockchain transaction (Tx2) to present at least one data item to a locking script (LSI) of another transaction (Txl) so as to provide a result on a stack;

generating a further unlocking script (ULS2) which comprises the result provided on the stack; and/or

presenting the further unlocking script (ULS2) to a further locking script (LS2) such that the result from the stack is provided as input to the further locking script.

The blockchain transactions may be arranged in accordance with a version of the Bitcoin protocol. One or more of the above steps may be repeated, i.e. performed more than once.

The method may further comprise the step(s) of:

using the at least one data item in the execution of a calculation or sequence of instructions provided within the locking script (LS I).

The method may further comprise the step(s) of:

using the result provided on the stack in the execution of a calculation or sequence of instructions provided within the further locking script (LS2). The method may further comprise the step(s) of:

obtaining the result from the stack. The method may further comprise the step(s) of:

validating the blockchain transaction (Tx2) and/or the other transaction (Txl) to generate the result on the stack. The unlocking script (ULS1) and the further unlocking script (ULS2) may be provided in association with different inputs within the same blockchain transaction (Tx2).

The locking script (LSI) and the further locking script (LS2) may be provided in association with different outputs within the same blockchain transaction (Txl).

The unlocking script (ULS1) and the further unlocking script (ULS2) may be provided in association with inputs within different blockchain transactions. The locking script (LSI) and the further locking script (LS2) may be provided in association with outputs within different blockchain transactions.

The step of presenting the further unlocking script (ULS2) to a further locking script (LS2) may provide a further result on the stack, or on a different stack.

The step of generating the further unlocking script (ULS2) may comprise:

amending the blockchain transaction (Tx2) to insert an input (In2), wherein the further unlocking script (ULS2) is associated with the inserted input (In2).

The method may further comprise the step(s) of:

using a blockchain client to obtain the result from the stack. The blockchain client may be a Bitcoin client. The stack may be the main stack or an alt stack.

The method may further comprise the step(s) of:

submitting the blockchain transaction (Tx2) and/or other blockchain transaction (Txl) to the blockchain network.

The at least one data item may be provided as metadata within the unlocking script (ULS1); and/or the result may be provided as metadata within the further unlocking script (ULS2).

An embodiment of the invention may also provide a method of using a plurality of blockchain transactions to execute a computer-implemented task, comprising the steps: using an unlocking script (ULS1) associated with a first input (Inl) in a blockchain transaction (Tx2) to present at least one data item to a locking script (LSI) of another transaction (Txl) so as to provide a result on a stack;

amending the blockchain transaction (Tx2) to include a second input (In2);

generating a further unlocking script (ULS2) associated with the second input (In2), the further unlocking script (ULS2) comprising the result from the stack; and presenting the further unlocking script (ULS2) to a further locking script (LS2) such that the result from the stack is provided as input to the further locking script (LS2). The method may further comprise the steps of:

performing one or more of the above steps more than once; and/or

using the at least one data item in the execution of a calculation or sequence of instructions provided within the locking script (LSI); and/or

using the result provided on the stack in the execution of a calculation or sequence of instructions provided within the further locking script (LS2); and/or

obtaining the result from the stack; and/or

validating the blockchain transaction (Tx2) and/or the other transaction (Txl) to generate the result on the stack. The unlocking script (ULS1) and the further unlocking script (ULS2) may be provided in association with different inputs (Inl In2) within the same blockchain transaction (Tx2). The locking script (LSI) and the further locking script (LS2) may be provided in association with different outputs within the same blockchain transaction (Txl). The step of presenting the further unlocking script (ULS2) to a further locking script (LS2) may provide a further result on the stack, or on a different stack. The method may comprise the step of using a blockchain client to obtain the result from the stack. The blockchain client may be a Bitcoin client.

The invention may also provide a method of using a plurality of blockchain transactions to execute a computer-implemented task, comprising the steps:

using an unlocking script (ULS1) associated with a first input (Inl) in a blockchain transaction (Tx2) to present at least one data item to a first locking script (LSI) of another transaction (Txl) so as to provide a result on a stack;

generating a further unlocking script (ULS2) associated with a second input (In2) and comprising the result from the stack; wherein the second input (In2) is provided in a further blockchain transaction (Tx3); and

presenting the further unlocking script (ULS2) to a further locking script (LS2) such that the result from the stack is provided as input to the further locking script. The locking script (LSI) and further locking script (LS2) may be associated with outputs in different blockchain transactions. The unlocking script (ULS1) and further unlocking script (ULS2) may be associated with inputs in different blockchain transactions.

The method may further comprise the step of using the at least one data item in the execution of a calculation or sequence of instructions provided within the locking script (LSI).

The method may further comprise the step of using the result provided on the stack in the execution of a calculation or sequence of instructions provided within the further locking script (LS2).

The method may further comprise the step of obtaining the result from the stack.

The method may further comprise the step of using a blockchain client to obtain the result from the stack, preferably wherein the blockchain client is a Bitcoin client.

The method may further comprise the step of validating the blockchain transaction (Tx2) and/or the other transaction (Txl), and/or further transaction (Tx3) to generate the result on the stack. The method may further comprise the step of obtaining the result from the stack and inserting the result into an unlocking script after a return command or instruction. The command or instruction may be the Bitcoin OP RETURN opcode.

Embodiments of the invention also comprise a corresponding system and apparatus. The invention may comprise a computer-implemented system arranged and configured to implement any preceding method step(s) mentioned above or substantially as described hereafter.

These and other aspects of the present invention will be apparent from and elucidated with reference to, the embodiment described herein. An embodiment of the present invention will now be described, by way of example only, and with reference to the accompany drawings, in which:

Figure 1 illustrates the chain of transactions and the sequential steps involved in a multiple inputs/outputs approach according to a first embodiment of the invention.

Figure 2 shows Transaction 1 (Txl) according to an illustrative version of a first embodiment of the invention.

Figure 3 shows Transaction 2 (Tx2) according to an illustrative version of a first embodiment of the invention. Figure 4 shows an illustrative chain of transactions according to an illustrative version of embodiment 2

Figures 5 to 8 show transactions 1, 2, 3, and 4 in accordance with an illustrative version of embodiment 2.

Figures 9a and 9b show illustrations of how an example version of the invention may be provided in accordance with embodiment 1. Figure 10 shows a simple illustration of a blockchain client being used to obtain an item left on top of the stack. Illustrative Embodiments of the Invention

In the following examples, we shall use Bitcoin as our illustrative blockchain implementation and protocol, because it is the most widely known. This is for the purposes of illustration only and it should be noted that the invention is not limited in this regard. Other blockchain implementations will also fall within the scope of the invention.

In order to prevent deployment of DoS (Denial of Service) attacks, the default Bitcoin client sets a limit on the maximum number of bytes and op codes that can be include in a valid script. As it stands at the priority date of the present application, this limit is 10,000 bytes and 201 op codes. Any script comprising more than 201 op-codes or 10,000 bytes will not be valid. While imposed for worthwhile reasons, this restriction hampers the development of more sophisticated script functionality and, therefore, the complexity of the technical solutions that can be designed to operate in conjunction with blockchain technology. The present invention provides two techniques (embodiments) which enable users to split blockchain scripts into multiple inputs/outputs via the use of two or more blockchain transactions. Both embodiments may rely on the capability of automated computing agents (or "bots") which are configured to:

• read the state of the stack,

· propagate i.e. communicate the result(s) of executed script(s) to the input(s) of unspent transaction output(s),

• split up large complex scripts into multiple smaller, simple units.

It should be noted that in some blockchain implementations, such as Bitcoin, a customised reference client may be required to enable the state of the stack to be read after a script has terminated, as the default Bitcoin client does not provide access to this item of information. The stack is represented as a list in a .cpp file, which is included in the bitcoin core program. By inserting a few lines of code into the class which emulates the stack behaviour, it is possible to obtain and return information contained in the list. The information can then be passed on for use by another computing resource and/or in another computation. This is shown in Figure 10. Thus, the invention provides a novel form of blockchain client and apparatus.

The propagation of the result of the executed script does not require any automation and could be performed manually (at least in principle). However, in a typical implementation it is expected that external systems such as compilers would handle the automation of the operations involved in splitting complex scripts.

Advantageously, no modification of the Bitcoin protocol is required by the present invention. In other words, while a custom client may be needed to prepare the transaction(s), once the transactions have been broadcast, all nodes of the Bitcoin network will be able to validate them.

Thus, in accordance with (all versions of) the invention, the underlying concept is to split the script into several chunks or functional parts, and to use the output of a chunk as the input of the next chunk. This is an important deviation from the prior art. It allows the blockchain to be used for ever complex tasks and computations while preserving the security-based limit on script size, and provides a novel technique and architecture for the distributed execution of computational processes. Thus, the invention provides an improved, secure blockchain. However, it must be kept in mind that the ultimate outcome of the execution of a script is binary, i.e. either the transaction is marked invalid or it is marked valid (assuming that it satisfies also the other requirements). Therefore, in order to "connect" the outputs of one chunk of computation with the inputs of the next chunk of computation one must use a non-reference client that can access the values on the stack and reuse them, as explained above.

We start with the following simple example:

x + y > 3 which can be written in terms of OP codes in the following way:

OP <x> OP <y> OP ADD OP 3 OP GREATERTHAN We split this into the following two chunks:

z = x + y

z > 3

In accordance with a first approach, a solution could be adopted as now described.

Alice prepares Txl as follows:

Txl

InO:

amount: A + <dust> + tf

ref: ...

unlocked by: ...

Outl :

amount: <dust>

locked by: OP ADD OP SWAP <Bob's pubKey> OP SWAP OP CHECKSIG

OP DROP

Out2:

amount: A

locked by: OP 3 OP GREATERTHAN OP SWAP <Bob's pubKey> OP DROP

Now Bob begins to prepare Tx2 in the following way: Tx2

InO:

amount: tf

ref: ...

unlocked by: ...

Inl :

amount: <dust>

ref: Txl : Outl

unlocked by: <Bob's signature> OP 2 OP 3

OutO:

amount: <dust>

locked by: ...

Bob will now sign the transaction, validate it, and (use the customised client to) read from the stack the output of the unlocking script of Tx2:Inl chained with the unlocking script of Txl utl .

He will then proceed to alter Tx2 by adding the following input and output: In2:

amount: A

ref: Txl :Out2

unlocked by: <Bob's signature> OP 5

Outl :

amount: A

locked by: ... where obviously OP 5 is the result of the first chunk of the computation. Also in this case, one could use multi-signatures to prevent Bob from broadcasting a transaction within which OP 5 is replaced with something else. This approach has the advantage that a large number of chunks (up to the limit on the number of inputs and outputs in a transaction) can be chained using only two transactions. Therefore, complex functionality and computation can be performed in an efficient manner, requiring only two transactions to be validated and mined by the blockchain network, and using minimal storage requirements on the blockchain.

In accordance with an alternative approach the following steps could be taken.

The first transaction Txl is prepared and jointly signed by all the owners of the inputs. Inputs are sent to Alice's public key using the following locking script:

OP ADD OP SWAP <Alice's pubKey> OP SWAP OP CHECKSIG OP DROP Txl

In:

amount: A + tf

ref: ...

unlocked by: ...

Outl :

amount: A

locked by: OP ADD OP SWAP <Alice's pubKey> OP SWAP OP CHECKSIG

OP DROP Alice will now prepare Tx2 in the following way:

Tx2

Inl :

amount: 2*<dust> + tf

ref: ...

unlocked by: ...

In2: amount: A

ref: Txl utl

unlocked by: <Alice's signature> OP 2 OP 3

Outl :

amount: <dust>

locked by: ...

where Tx2:In2 will be now signed with the flag SIGHASH NONE, so that other outputs can be added. As known in the art, SIGHASH NONE is a Bitcoin signature hash type which signs only inputs. Therefore, when SIGHASH NONE is used, anyone is able to modify the outputs in any manner that they choose.

Tx2:Inl presumably references Alice's funds and can be unlocked with

SIGHASH SINGLE so that, again, other outputs can be added. In the current form, the transaction will transfer amount A as transaction fees. However, Alice does not broadcast the transaction in the current form, but simply verifies it locally. In the verification process the unlocking script of Tx2:In2 will be executed together with the locking script of Txl ut:

<Alice' s signature> OP 2 OP 3 OP ADD OP SWAP <Alice' s pubKey> OP SWAP

OP CHECKSIG OP DROP and at the end of the execution of the stack the remaining result will be 5, i.e. the result of the first chunk of computation. Alice's custom Bitcoin client will now save or record the result of the first chunk of computation and modify Tx2 by adding the following two outputs:

Out2:

amount: A

locked by: OP 3 OP GREATERTHAN OP SWAP <Bob ' s pubKey> OP DROP

Out3 :

amount: <dust>

locked by: OP RETURN OP 5 but she will sign Tx2's inputs again, this time with the usual flag SIGHASH ALL, so that now none of the outputs of the transaction can be modified. Bob can now complete the computation by reading the data stored in Out3 after OP RETURN. As known in the art, OP RETURN is a Bitcoin OP CODE which can be used to mark a transaction output (TxO) as invalid. Any data provided after OP RETURN is ignored in respect of Bitcoin payments, and thus OP RETURN has been used in the prior art as a mechanism for conveying non-payment related data via the blockchain.

Bob now prepares the following transaction:

Tx3

In:

amount: A

ref: Tx2:Out2

unlocked by: <Bob's signature> OP 5

Out: ... In principle, after OP RETURN one could store a hash indexed in a DHT, so that arbitrarily long intermediate results can be passed between transactions. Obviously, in this example Alice trusts that Bob will prepare Tx3 as above, so that the computation can be completed successfully. A simple extension could require that Tx2:Out2 is signed by both Alice and Bob, so that Alice can verify that Bob has prepared the correct transaction.

However, Bob could indefinitely delay the execution by refusing either to prepare the transaction or to sign it. Alice could also prepare Tx3, send it to Bob, and avoid to store data after OP RETURN. It is noted that this approach requires one to wait for

confirmation that each chunk of computation is in the blockchain. Detailed examples of these two implementations of the underlying technique are provided below, and in reference to the accompanying figures. The following description is organized as follows:

• "Embodiment 1" describes the first approach that uses only two transactions; multiple inputs and outputs are manipulated

· "Embodiment 2" describes the alternative approach which "links" or chains multiple transactions to achieve the same technical effect. It is worth noting that combinations of the two approaches are also possible.

To illustrate the use of both embodiments, we now consider the following example which evaluates a function f{x,y _} ) defined as follows We (or the compiler) express f(x _r y, ~ ^" ) as a sum of simple functions

In both embodiments, the variables .¾-, , and 2, which represent the arguments of ¾ and ¾ , will be contained in transaction unlocking scripts, while the functions ^ and ¾ themselves will be contained in locking scripts. Therefore, hereafter, we will use the terms "function" and "locking script" interchangeably. In particular, x and will be in the script that unlocks the locking script containing Similarly, f i y) and s will be in the script that unlocks the locking script containing g _s .

In the subsequent section of this paper, the example we use include the op codes OP ADD and PrO MULT. These identifiers represent the arithmetic operations addition ( ) and multiplication ( ) respectively. The op codes OP X, OP Y, and OP Z represent the variables x, y, and s. The symbols Gi and G ₂ represent the values at the top of the stack after the locking scripts corresponding to g _s and _$s will have been unlocked. OP ADD is an op code which forms part of the Bitcoin script language. We use the term "PrO MULT", short for "primitive operator" to refer to an operation which can be executed to perform a multiplication operation. In the current version of Bitcoin, the op codes for multiplication (such as OP MUL, OP 2MUL) are disabled and so PrO MULT could be a custom-defined operation to provide that currently disabled functionality. Of course, if the OP MUL etc opcodes are re-enabled then these could be used instead. Thus, the present invention can be used solely with functions that use standard (enabled) opcodes, and the implementation details of custom-built operators are not part of, or relevant to, the present invention. Therefore, details relating to how PrO MULT could be implemented are not necessary to the understanding of the present invention, and have not been included herein for the sake of clarity.

The example presented herein corresponds to the execution of a very simple smart contract in which funds are transferred from Alice to Bob, conditional on the successful execution of a long script. The script inputs are provided by Bob, and one can envisage two possible malicious behaviours. Firstly, Bob might provide incorrect inputs such that the script executes successfully and the funds are transferred to him. However, when the transaction(s) is/are stored in the blockchain, the inputs become publicly available allowing Alice to dispute the contract. Secondly, if Bob has any reason to refuse the transfer from Alice, he might decide to stall the transaction indefinitely, therefore preventing the execution of the contract. In the most straightforward scenario, Alice must simply trust that Bob will not stall the execution of the contract and that he will provide the correct inputs. Additional security mechanisms may be utilised in conjunction with the inventive concept to enhance security.

Embodiment 1 : Splitting scripts into multiple inputs and outputs

Figures 1, 9a and 9b illustrate the chain of transactions and the sequential steps involved in a multiple inputs/outputs approach of embodiment 1. Txl contains a set of Unspent Transaction Outputs (UTXOs) that will be consumed by Tx2. The construction of Tx2 proceeds incrementally, step by step. At each phase, an (automated software) agent presents an unlocking script to one UTXO of Txl . The agent validates Tx2, reads the value(s) on top of the stack, and prepares a new unlocking script. The automated generation of blockchain transactions and scripts is known in the art and therefore not explained herein.

The agent may use the information obtained from the stack in the previous step (or from earlier steps), and presents this new unlocking script to another UTXO contained within Txl . Tx2 is broadcasted when all the necessary steps are accomplished for the present task. Advantageously, this technique decouples the functions contained in the locking scripts of Txl from the arguments contained in the unlocking scripts provided by Tx2. Functions become immutable once Txl has been added to the blockchain and verified. In addition, at this stage, the function arguments (inputs) may even be unknown. They are revealed only later, when Tx2 is prepared. This may be advantageous and provide enhanced security.

The sequence of steps for embodiment 1 is shown in Figure 1, Figures 9a and 9b and can be described as follows:

Step 0: Alice submits transaction 1 (as shown in figure 1) to the Bitcoin network.

Step 1 : Bob prepares an initial version of transaction 2

Step 3 : Bob presents <Bob's signature> <OP_X> <OP_Y> <Redeem script 1> to outputO.

Bob validates transaction 2, reads the value Gi on top of the stack, but does not broadcast transaction 2.

Step 4: Bob presents <Bob's signature> <Gi> <OP_Z> <Redeem script 2> to outputl . Bob validates transaction 2, reads the value G ₂ on top of the stack, but does not broadcast transaction 2.

Step 5: Bob presents <Bob's signature> <G ₂ > <OP_X> <Redeem script 3> to output2.

Bob validates transaction 2 and broadcasts it. For the sake of simplicity, we do not provide extensive details regarding Txl 's inputs and Tx2's output(s). Figure 2 shows Transaction 1 (Txl). Figure 3 shows transaction 2 (Tx2).

Embodiment 2: Splitting Scripts in Multiple Transactions

The second embodiment uses blockchain transactions to compose functions (see figure 4). This approach is similar in principle to the previous embodiment. However, during the validation phase, the agent reads the value(s) on top of the stack, and adds it/them after an OP RETURN as explained above.

Figures 5 to 8 show transactions 1, 2, 3, and 4 in accordance with an illustrative version of embodiment 2. It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be capable of designing many alternative embodiments without departing from the scope of the invention as defined by the appended claims. In the claims, any reference signs placed in parentheses shall not be construed as limiting the claims. The word "comprising" and "comprises", and the like, does not exclude the presence of elements or steps other than those listed in any claim or the specification as a whole. In the present specification, "comprises" means "includes or consists of and "comprising" means "including or consisting of. The singular reference of an element does not exclude the plural reference of such elements and vice-versa. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In a device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.