Notes on Relationship of P Colonies to Osmotic Computing and Computer Viruses

Abstract

P colonies with transferable programs are one of the newer variants of P colonies, which allow the transfer of programs between agents and the environment when certain conditions are met. Code transfer is also known from other concepts: in the concept of Osmotic computing we encounter the transfer of MELs between IoT devices and the cloud, and the long-standing concept of computer viruses uses infecting common applications with appended code. In this paper, the reader will find an outline comparison of these three concepts concerning the possibilities of transferring code fragments or programs.

Keywords

• eol>P colony
• transferable program
• Osmotic computing
• MEL
• virus
• shellcode

1. Introduction

The paradigm is motivated by procedures from biol

ogy or chemistry, where solvent molecules pass through P colonies are a simple computational model based on a semi-permeable membrane into other regions in the membrane systems. P colonies were introduced in [ 1 ] in environment with higher solute concentration (osmosis). 2004 and since then many variations (types of programs, The issue is further developed in [ 4 ] considering the form of environment, etc.) have been developed. Focus- way in which MELs, in particular, can migrate between ing on the basic variant, the environment containing ob- the cloud and edge resources and focusing more on the jects of a given type is shared by agents that also contain Internet of Things. Datta and Bonnet in [ 5 ] show the use objects in their internal environment and are equipped of MELs in securing connected “smart” cars and other with programs consisting of rules. The programs allow similar devices. the agents to influence not only themselves but also the A virus is malicious program code that spreads by environment. In paper [ 2 ], the concept of P colonies with infecting available programs with a copy of itself. There transferable programs is introduced, where programs can is quite a lot of literature and websites about computer be transferred between an agent and the environment viruses, e.g. [ 6 ]. and vice versa. According to [ 7 ], shellcode can be described as a code

The principle of traveling programs, or code in general, injection attack. An attacker inserts a code into an existcan be found elsewhere: e.g. in the concept of Osmotic ing chosen file to access the command interface (shell) of computing or (if we focus on the nowadays very frequent the compromised system. Shellcode is one of the ways topic of cybersecurity) also in the activity of viruses, a virus can work. shellcode, etc.

Villari et al. in [ 3 ] introduce the concept of “Osmotic In Section 2 we define P colonies, and add a descripcomputing” as a paradigm intended mainly for IoT (In- tion of the possibility of using transferable programs in ternet of Things) network, the main purpose of which is P colonies. This concept is explained with examples. In to increase the accessibility of resources and services in the same section, we follow the definition of the princia computer network, including cloud services. MicroEle- ple of Osmotic computing, where we mainly focus on ments (MELs) are simple entities consisting of programs explaining the possibility of transferring MELs between (MicroServices) and data (MicroData). IoT applications the involved devices. The last topic of Section 2 is the can be decomposited into MELs. The interface between issue of computer viruses and shellcode. Here we also the IoT application and the edge environment (Edge Data- focus on the process of transmitting or adding new code Centers), and also between the edge environment and the to infected programs. cloud (Cloud DataCenters), is called membrane: MELs can In the next two sections, we will try to capture the cormigrate through membranes to where they are needed. relations between P colonies with transferable programs and two other concepts in which computational elements (e.g., program code) are being transmitted: the concept of osmotic computing and the principle of operation of computer viruses and shellcode.

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2. Preliminaries

the given object in the environment. Also, this type of rule can be applied only if the specified objects exist in We assume the reader to be familiar with the basics of the given environments. the formal language theory and membrane computing The checking rules (1/2) are composed of two rules [ 8, 9 ]. We denote the length of a word by ||. The 1 and 2 of any of the previous two types. Only one of empty word is represented by the symbol , so || = 0. these rules will be applied, with the first listed having a higher priority. Only if the first rule cannot be executed, 2.1. P Colonies the second rule in order may be executed. The initial configuration of a P Colony Π is an ( + 1)Membrane computing is a framework of parallel dis- tuple of multisets for 1 ≤ ≤ for the agents , and tributed processing introduced by Gheorghe Paˇun in for the environment. Generally, the configuration of 1998. Information about this paradigm is available in a P Colony Π with capacity is [ 10 ], or the bibliography at http://ppage.psystems.eu/ [2023-07-02]. Membrane systems are based on the hier- (1, . . . , , ) archical structure of membranes in cells and can be used to model distributed computing. Mathematical models where ∈ * , || = , ∈ * , ∈ (−{ })* . of membrane systems have been called P Systems. Several derivation modes have been defined, difering

P colonies develop the concept of P systems by enrich- in the way the rules are selected at each derivation step. ing the system with agents that evolve activities accord- In the maximally parallel derivation mode, all agents ing to specific programs. can work parallely in each derivation step (each agent non-deterministically chooses one of its programs with Definition 1 ([ 2 ]). A P colony of capacity , ≥ 1, is applicable rules). In the sequential derivation mode, only a construct one (non-deterministically chosen) agent can work in Π = ( , , , , 1, . . . , ) where each derivation step. The calculation halts if no agent ifnds an applicable program. • is an alphabet, its elements are called objects, • ∈ is the environmental object of the colony, • ∈ is the final object of the colony, • is a finite multiset over −{ } called the initial

state of the environment, • , 1 ≤ ≤ , are agents where each agent = (, ) is defined as follows: – is the initial state of the agent, a multiset

over consisting of objects, – = {,1, . . . , , } is a finite set of programs where each program consists of rules, the rules can be in one of the following forms: ∗ → , , ∈ called an evolution

rule, ∗ ↔ , , ∈ called a communi

cation rule, ∗ 1/2 called a checking rule, 1, 2 are both evolution or communication rules.

The evolution rules are of the form → . This type

of rule allows the agent to influence itself, i.e. its internal environment: an object inside the agent is rewritten to the specified object . The rule can only be applied if at least one occurrence of the object exists in the internal environment of the agent.

The communication rules ( ↔ ) are intended for communication between the given agent and the environment. An object inside the agent is swapped with 2.2. Transferable Programs in P Colonies In [ 2 ], the concept of transferable programs for P colonies has been introduced. A transferable program is an ordered pair (program, condition) located inside an agent or the environment. The program can be transferred from the agent to the environment or from the environment to the agent (from the source to the destination), and the stated condition determines under what circumstances this transfer will occur.

The condition can be one of the following two types: • Object condition: the destination must contain certain objects for the program to be transfered (or must not contain when there is the negation symbol in the condition). This type of condition is a set of multisets of objects, the size of the given multisets is equal to capacity of the P Colony. • Program condition: the destination must contain a specified program (or must not, if the negation symbol is present).

Thus, the definition of P colony presented in the pre

vious subsection changes in the part specifying the programs of agents, and it is also necessary to add programs located in the environment to the definition, the rest remains the same.

Example 1. Let Π be a P colony of capacity 2. Capacity

is reflected in both the number of objects in the agent environment and the number of rules in each agent pro- programs, for example ⟨ → ⟩. The configuration has been modified to

(, , )

There are three transferable programs in the environ

ment. The first one is suitable for 1, the third for 2.

So the agents are changed as follows:

1 = (︀ , { ⟨ → ⟩ , ⟨ → ⟩ , ⟨ ↔ ⟩ , ⟨ → ⟩ , (⟨ → ; {}⟩)})︀ (⟨ → ; → ⟩)})︀ 2 = (︀ , { ⟨ → ⟩ , ⟨ → ⟩ , ⟨ ↔ ⟩ , ⟨ → ⟩ ,

The set of transferable programs in the environment has changed. The third program was not classified as permanent, so it is no longer part of the environment gram.

For the illustration, we present here an example program of one of agents, using object condition:

(⟨ → ; ↔ ⟩ ; {, ¬})

This means that if this program is in an agent it can

only be transferred to the environment when there are at least two occurrences of the object in the environment and there is no pair. If this program is in an environment, it can be transfered to an agent when the condition holds for the internal environment of that agent.

What happens to the program at the original location if the conditions for transfer are met? According to [ 2 ], a program can be classified as permament, in this case one copy of the program remains at the original location and the other is transferred. The program remains at the original location (including the “permanent” property), but loses this property at the new location. If a program is not permanent, it is removed at its original location.

In each computation step, an agent can either apply

one of its applicable programs or transfer one of programs in or out.[ 2 ] This implies that the transfer of programs is actually an analogy of programs (but the action would not be transferable). ferable programs. There are two agents:

Example 2. Let Π be a P colony of capacity 1 with trans- is

1 = (︀ , {⟨ → ⟩ , ⟨ → ⟩ , ⟨ ↔ ⟩ , ⟨ → ⟩})︀ 2 = (︀ , {⟨ → ⟩ , ⟨ → ⟩ , ⟨ ↔ ⟩ , ⟨ → ⟩})︀

In their initial state, these agents do not contain any transferable programs (although they could). We have only the symbols in the environment at the beginning of the computation. For the purpose of clarity, if we limit reprezentation of the configuration of the system to just the states of the agents and the environment (the configuration of the environment properly includes programs not imported in any agent), the initial configuration is very simple:

(, , )

There are the following transferable programs in the environment at the beginning of computation: after the transfer.

︀{ (⟨ → ; {}⟩) , (⟨ ↔ ; {}⟩)

︀}

In the next step of the calculation, the agents can use the newly obtained programs, i.e. the state of the agents and the environment has been changed as follows: (, , ) (, , ) 1 can use its third program, 2 can use its fourth program, the new state of the agents and the environment

In the next steps, the agents will use their own programs, import other programs from the environment, or export a transferable program to the environment for use by another agent.

The above example shows how transferable programs

behave. Programs can also be transferred in the other direction, i.e. from agents into the environment. This allows an agent to drop a program it does not need.

Another example of using P colonies with transferable programs, which would be more complex to describe, is as follows: Agents are gardeners. Each of them grows a specific plant whose progressive development (growth phase) and condition (healthy, dry, insect infested, etc.) is captured in their status objects. Agents pick up tools (i.e., programs) from the environment as needed (according to these objects), and return unneeded tools. 2.3. Osmotic Computing ︀{ (⟨ → ; {}⟩) , (⟨ ↔ ; {}⟩) , (⟨ → ; → ⟩) ︀} programs.

The first two programs contain object condition, and

the third program contains program condition. The In biology and chemistry, osmosis is the process of transsymbol in the subscript indicates permanent transferable ferring molecules between two media of diferent den

During the first step of the computation, 1 uses one

of the programs that overwrite the symbol, for exam- here it is about the dynamic migration of microservices ple the first one: ⟨ → ⟩. 2 also has a choice of two between diferent parts of a computer network. sities across a semipermeable membrane. Osmotic computing carries this principle into the field of technology:

According to Osmotic computing[ 4 ], an application ager. The Node Manager continuously analyzes the de(very often running on an IoT device) can be decomposed vice properties and checks whether the MELs in the into parts called MicroElements (MELs) consisting of corresponding set are satisfied. The Osmotic ReMicroServices (code) and MicroData (data). Since IoT source Manager then balances the workload across the devices usually don’t have much computing power, it network in cooperation with the Node Managers from makes sense to move some of the computation (i.e., some each device.[ 12 ] of the MELs) elsewhere, such as to another device on the same network or to the cloud. To do this, we need 2.4. Virus and Shellcode the MEL to be relatively self-contained, independent of other parts of the application, and also to have an inter- The term computer virus is known, at least in a hint, face to enable these transfers and provide the necessary to the general public. It is computer code embedded communication. in a host program that usually performs operations not intended by the author of the program. In addition to Definition 2 (according to [ 11 ]). The infrastructure these operations, the virus also infects other files, i.e. it topology in Osmotic computing can be represented by di- inserts its own code (or its functional equivalent) into rected graph = ( , ) where is the set of nodes other reachable files. The malicious code executed by the (vertices) and is the set of pars of vertices called links. virus is called payload. The payload is usually encrypted Each element in is characterized by various comput- or otherwise encoded to make it more dificult to detect. ing parameters (CPU, memory etc.), each element of In addition to the payload, another code is embedded in is characterized by various network parameters (latency, the infected file to guide the computation to the payload bandwidth, etc.). and, of course, to decrypt or decode it.[ 6, 13 ] Shellcode

Osmotic toolkit consists of pre-configured container can be one of the ways a virus can work, i.e. its payload. images intended for various elements in . Shellcode is, according to [ 14 ], the code that allows

Applications in the Osmotic ecosystem can be repre- a hacker to perform his intent (get access to a file, get sented by graph = ( , ) where is the set of access to certain data, escalate access privileges, start enMELs and is the set of their interconnections. Each cryption, etc.). Originally, this code has been used to run MEL in is characterized by the specific resource re- a shell (a command environment through which a hacker quirements, constraints and scheduling policies. The could e.g. remotely control the system), hence the name, edges in the set determine between which elements but nowadays the term is more generally understood of MELs can be transferred. (shellcodes are also able to run other types of commands or gain higher access privileges).

The implementation is based on the principle of SDN (Software Defined Network), i.e. computer network vir- Definition 3 (according to[ 7 ]). Shellcode can be tualization. Software representation of nodes (MELs) thought of as a sequence of additional commands added is possible using containers ([ 11 ] used the container sys- to a program, which is executed immediately after the tem Docker for this purpose). Each device (node ) can program itself starts and usually lead to the exploitation run various number of containers with MELs (nodes ) of some vulnerability in the system or application. according to its capabilities and MELs requirements. A special type of shellcode, called a bind shell, connects

Containers are actually pre-built images of systems to a network port (HTTP or FTP ports are often used) (operating systems running on computers, IoT devices, when executed and allows an attacker to establish network devices, etc.) so not just the application itself, a remote connection to the device on which it is running. but everything in software it needs. The purpose is to simplify the application deployment as much as possible, Infecting a program is usually done by inserting a speincluding configuration. In the case of Osmotic comput- cial sequence of Bytes into the target program and modiing, there is also an ecosystem for migration and com- fying the rest of the code to force the processor to execute munication of MELs. A MEL can be moved to a diferent the added code at the correct time. And, of course, the node (respectively to a diferent container ) if the purpose is to hide these changes from antivirus programs conditions for it to run, such as memory capacity or CPU as much as possible. performance, are not met in the original location. An- If an antivirus finds an infected program, it either other reasons for moving may be to optimize network moves it to quarantine (it defacto makes the malicious communication, or to ensure cybersecurity, where we code inaccessible) or it can try to repair the infection, pull MELs from cloud to our own network. which means the reverse procedure to the one described

Each element of the set is managed by the Node above.

Manager component, the whole system is managed by As mentioned above, the payload of a virus is usually a special element of called Osmotic Resource Man- encrypted and there is also a decryption sequence in the code. While the payload can be very heterogeneous and therefore harder to detect (and it is encrypted), the decryption instructions are easier to detect. Polymorphic viruses[ 13 ] can modify their decryption sequence as they spread, making detection more dificult. The modification is based on a simple principle: the same computational operation can be performed in many diferent ways. For example, the result 25 can be reached by 5 * 5, 20 + 5, 3 * 6 + 7, 100/4, 9 * 7 − 38. Code instructions can also be put together in various ways: we can add instructions without directly afecting the result, etc.

Antivirus programs use an emulator to detect polymorphic viruses, in which they emulate the process of decrypting a potential locations in a program with an encrypted payload. Attackers have developed a new generation of viruses: metamorphic viruses. Metamorphic code[ 13 ] does not rely on making copies of the payload, but what was to apply to the polymorphic code for the decryption sequence applies to the payload in the metamorphic code: when spread, a functionally equivalent diferent code is produced instead of a copy of the payload. The problem of detecting metamorphic viruses is NP-complete[ 13 ]. However, not only attackers but also defenders can use metamorphic code. It can be very effective in defending against certain types of attacks, as even defensive tools find it useful to be hidden.

3. P Colonies with Transferable

Programs vs. Osmotic

Computing Concept

In this section, we focus on the correlations between

P colonies with transferable programs and the concept of Osmotic computing. directly equipped with a transfer condition, this condition concerns either the (non) presence of certain objects or programs in the target. MELs in the Osmotic computing concept have a condition built into the properties of the elements of the set , the transport of a given MEL is possible if these conditions match the equipment of the target node in the set .

3) P colonies are a mathematical model and have been

designed to be easy to analyze their computation. Capacity of P colony is determined, which is reflected in the number of objects in each agent’s internal environment, and also in the number of rules in the agents’ programs.

As for transferable programs, the number of rules in such a program must also be equal to the capacity of the P colony.

The concept of Osmotic computing is more free in this respect, it is heterogeneous in principle. The analogue of the agents from P colonies are the devices in the network hosting MELs, which can be very diferent from each other in their parameters, and the analogue of the transmitted programs are just the MELs. MELs can be of varying complexity (longer or shorter programs). On the other hand, there is also a similarity: an agent of a P colony may contain diferent amounts of programs, a device in the Osmotic computing concept may contain various amounts of MELs. In both cases, the number of MELs can be changed dynamically. 4) Programs in P colonies use three types of rules, as follows from Definition 1. Their task is to work with objects (transformation or transfer). MELs, on the other hand, are composed of instructions prescribed by implementations for a given host type (operating system and processor on a given device). Thus, the set of usable instructions varies but is certainly very large (tens, hundreds). These instructions may also work with data (analogous to objects), but they may also be other types of tasks. 1) The concept of Osmotic computing can be described using graphs – Definition 2 uses graph for the infrastructure and graph for the communication structure 5) Although the rules in the P colony do not directly creof applications. Since not all nodes of the graph can ate new symbols, the object is available in any quantity. host MELs and there can be multiple MELs (from ) in Therefore, the quantity of other objects within the envia single node in , the graphs do not overlap in their ronment can be freely increased simply by transforming nodes. the environment object into some other object. MELs typ

We can also represent the structure of a P colony with ically run in an IoT device (or, for example, in cloud). IoT transferable programs using graphs. The graph for devices are very often composed of sensors, and sensors the infrastructure is very simple, the agents are not con- are typically the source of data. Thus, MELs can generate nected to each other but only to the environment. With data without the need for any auxiliary object. However, the next graph we can describe the nodes and paths the impacts are similar. The reverse operation (removal for transferring programs. Since programs can be both or consumption of objects or data) is also implemented at the agents and in the environment, the two graphs in P colony by transforming an object into an object; practically overlap. for MELs, this procedure is straightforward.

2) In both systems there is some transfer conditionality

(programs in the case of P colonies and MELs in the case of Osmotic computing). A P colony program is

6) The concept of Osmotic computing is rather intended

to be centralized: each node in has its own Node Manager, and there is an Osmotic Resource Manager in

4. P Colonies with Transferable

Programs vs. Computer Viruses

the network managing the whole system. In contrast, rules of type → for various symbols ∈ with P colonies are decentralized in principle. a suitable condition (here the condition would prescribe the existence of the symbol in the agent’s internal environment). If an agent were infected by such a rule, it would lose its internal state.

Next, we focus on the similarities between P colonies with transferable programs and the operation of viruses and shellcode. 1) In the case of P Colony, the transfer of programs can be considered as an alternative activity. An agent can either execute one of its programs, or receive a new program from the environment, or divest itself of one of its programs. In the Osmotic computing concept, the migration of MELs can also occur repeatedly and can be seen as an alternative activity on the devices involved.

In the case of a virus, the program is infected once (unless it is a massive infection with a wide range of diferent viruses), and the opposite operation (removal of malicious code by the antivirus) is not expected to be repeated often. These operations are not considered an alternative to other activities. 2) Another significant diference is the contextuality of operation. P colonies with transferable programs have a certain type of context built into the program transfer conditions, consisting of the presence or absence of objects or programs in the target. The context for viruses and the shellcode embedding mechanism is much more strict: each shellcode must be customized for the target system (it must be made up of instructions that the target system understands), and in addition, the application that is to host the added code must be modified in multiple places (it is not enough just to add a new section of code e.g. to the end of the given file). There is no space for details in this paper (see [ 13 ], e.g. hackers use the bufer overflow mechanism, which requires modifications at several places in addition to inserting new code).

P colonies are motivated by biological processes (simple 3) The next criterion being compared is similar to cri- cell, passing of nutrients across membranes, etc.) but are terion #3 and #4 from the previous section. Also, the intended from the beginning as a mathematical model. structure of virus code is much less strict than the struc- The concept of Osmotic computing is motivated by proture of agents in the P colony. It depends on what exactly cesses in biology and chemistry (membrane as a comthe shellcode (or other type of virus payload) is supposed munication interface) but from the beginning they are to do, and its length and complexity depends on that. intended to be used in practice, in technology. While in There are also diferent approaches to writing shellcode. the computational model of P colonies, is defined as the The best known type probably is Aleph1[ 14 ], but there ifnal object and the end of the computation is assumed are many others. The situation is further complicated by (the number of objects is considered as the result of the polymorphic and metamorphic viruses, where there is computation), the concept of Osmotic computing does a large variability even within the same virus family. not assume any end of the activity, the important thing

If we wanted to simulate infecting agents with ma- is the process itself. This is not only a significant diferlicious code in a P colony with transferable programs, ence between the two systems, but it also complicates it would not be so complicated. It would be enough to somewhat the comparison of other parameters of these insert one or more programs containing, for example, systems. 4) Similar to the concept of Osmotic computing, for viruses, it is not so important what (numerical) result is reached at the end of the computation, but the process itself is significant, unlike P colonies. 5) Infecting an application with malicious code does not usually mean that part of the original application code is lost (although this is not impossible) but rather that something new is added. Overwriting occurs elsewhere rather than inside the application itself, for example, data on disk is encrypted or deleted. If we are looking for an equivalent in the transferable programs in P colonies, it would be a transferable program containing rules that afect the environment (in P colony, an agent cannot affect another agent directly, except by planting a program through the environment). 6) If we focus on the activity of antivirus, simulating its operations in a P colony with transferable programs would consist in enriching the environment with “disinfecting” programs. If an agent is disabled by a malicious program (e.g. such that its environment consists only of objects for which it has no programs), then in the next derivation step it imports a suitable disinfecting program whose purpose is to repair its internal environment.

7) P colonies are decentralized in principle. The system

of computer viruses is decentralized too. But, on the other hand, the operation of antivirus, which is based on a similar principle (finding a target and working with its code), is centralized.

5. Conclusions

The design of a virus and shellcode in general is also

motivated by an ending (infecting other programs and selected malicious actions in the form of encrypting content, taking control, stealing data, etc.), but this ending cannot be simply represented by numbers.

In conclusion, some similarities can be found between the three systems (the possibility of code transfer), other similarities always exist in the particular pair being compared. Therefore, to a limited extent, there are possibilities to simulate certain operations of one system in another, as we showed in the previous section on the comparison of P colonies with transferable programs and viruses.

Colonies with transferable programs have not yet been studied in detail; in fact, there is no precise definition. For example, it is not clear from [ 2 ] whether the action of importing/exporting a program is an alternative for agents to using some other program, or whether this import/export can be performed in the single step at the same time as the use of another program. In this paper, we assume the first option.

Therefore, future research can be targeted in the following direction: to establish a precise and detailed definition of P colonies with transferable programs, to investigate the behavior of the system in specific situations and with specific parameters, taking into account the impact of the use of transferable programs, the impact of marking programs as permanent, etc.

Another interesting direction of research is the possibility of using P colonies with transferable programs to simulate various systems and processes, e.g. in the area of security (distributing program updates, managing encryption algorithms,. . . ).

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