Shakti R Shrestha

Caroline H R Orchiston

Kenneth J Elwood

; David

M Johnston

Julia S Becker

Isabella Tomassi

Understanding the wider social and economic context of Post-Earthquake Cordons: A comparative case study between Christchurch, Aotearoa (New Zealand) and L'Aquila, Italy

Keywords: Earthquake, cordons, emergency management, disaster response, recovery, life safety

Post-earthquake cordons have been used after seismic events around the world. However, there is limited understanding of cordons and how contextual information such as geography, sociocultural characteristics, economy, institutional and governance structures affect decisions and operational procedures, including aspects related to spatial and temporal attributes of cordon establishment. This research aims to fill the gap in cordon knowledge through a qualitative comparative case study of two cities: Christchurch, New Zealand (Mw 6.2 earthquake, February 2011) and L'Aquila, Italy (Mw 6.3 earthquake, 2009). Both cities suffered comprehensive damage to their city centres and had cordons established for extended periods of time. Data collection was done through purposive and snowball sampling whereby 23 key informants were interviewed in total. Research participants held expert knowledge in their roles and responsibilities i.e., council members, emergency managers, politicians, business/insurance representatives, academics, and police. Results illustrate that, cordons were primarily established to ensure safety of people and to maintain security. The extent and duration of the cordons were affected by the recovery approaches taken in respective cities i.e., in Christchurch demolition was widely undertaken which supported recovery and allowed for faster removal of cordons. In contrast, authorities in L'Aquila placed high value on heritage buildings which led to recovery strategy based on preserving and restoring most of the buildings which extended the duration of cordon. Extended cordons have many similarities but evolve overtime. This evolution of cordons is affected by site specific needs, thus, cordons should be understood and planned based on contextual realities.

Introduction

Earthquakes, among other natural hazards, pose the highest risk to life safety. Disasters due to seismic events have accounted for 56% of total deaths between 1998-2017 worldwide [START_REF] Wallemacq | Economic Losses, Poverty & DISASTERS[END_REF]. This risk is primarily due to building collapse and falling debris. However, secondary earthquake hazards such as tsunamis, fire hazards and landslides also pose considerable risk to life safety. Even the cascading effects due to secondary hazards can be devastating as evident by the 2011 Fukushima Daiichi nuclear disaster [START_REF] Holt | Fukushima Nuclear Disaster: CRS Report for Congress[END_REF]. The risk due to earthquakes is extended beyond the initial shaking as major seismic events are followed by aftershocks of varying magnitude that last for months or years after the mainshock. The aftershocks are usually smaller than the initial main event (the largest is typically one magnitude less than the mainshock) [START_REF] Godano | How Long is an Aftershock Sequence?[END_REF] and the frequency also number decreases over time [START_REF] Omori | On the after-shocks of earthquakes[END_REF]. However, frequent aftershocks could significantly compromise the structural integrity of undamaged structures and further damage or weaken buildings, potentially leading to falling debris and/or collapse. As a disaster management tool, cordons have been used for extended periods in response to the challenges of managing risk in the aftermath of major seismic events [START_REF] Marquis | Understanding post-earthquake decisions on multi-storey concrete buildings in Christchurch, New Zealand[END_REF], to exclude the public from high-risk areas to protect their safety, as well as to expedite building assessments, demolitions, and restoring services. This is because cordons discourage people from entering dangerous areas thereby protecting them from getting hurt.

Earthquakes and context

Earthquakes cause ground motions that can damage the built and social environments, cause psychosocial trauma for inhabitants and lead to uncertainty for communities and decision-makers. The intrinsic attributes of earthquakes, such as magnitude, frequency, focal depth, epicentre location, time of day and time of year are factors that influence risks [START_REF] Doocy | The Human Impact of Earthquakes: a Historical Review of Events 1980-2009 and Systematic Literature Review[END_REF]. These attributes however are only a piece of the puzzle that determines actual risks to life safety. Understanding the local context of the affected area can inform the level of risk posed by seismic events and guide appropriate response strategies. Similarly, recovery and reconstruction policies need to be contextually sound to be effective [START_REF] Barrios | Expert Knowledge and the Ethnography of Disaster Reconstruction[END_REF][START_REF] Shrestha | Towards Communicative Planning for Rebuilding Communities in Nepal? A comparative study based on Kathmandu's Core City Area and Bungamati[END_REF].

Population density, building density, structural integrity of built structures, urban planning choices, risk awareness and preparedness and socio-economic parameters are additional factors that influence vulnerability of a given location and its residents. The influence of these additional elements has been highlighted in recent major seismic events. For example, the magnitude 7.0 Haiti earthquake of 2010 caused an estimated 230,000 deaths and similar numbers of injured people [START_REF] Schuller | The Tremors Felt Round the World: Haiti's Earthquake as Global Imagined Community[END_REF] while more than 50% of the housing in the capital city sustained extensive damages [START_REF] Schwartz | Building Assessments and Rubble Removal in Quake-Affected Neighborhoods in Haiti[END_REF]. In stark contrast, there were no deaths due to the magnitude 7.1 Darfield earthquake (2010) in New Zealand even though it affected 300,000 people. This contrast is partly attributed to New Zealand's strict building code [START_REF] Wallemacq | Economic Losses, Poverty & DISASTERS[END_REF]. It should be noted that the Darfield earthquake occurred at 4:35 AM and the epicentre of the earthquake was in a rural, sparsely populated location [START_REF] Quigley | Surface rupture of the greendale fault during the darfield (CANTERBURY) earthquake, New ZEALAND: Initial findings[END_REF]. This meant that most residents were still in bed at the time of impact limiting their exposure to risk from falling masonry in the denser city centre.

The case of Haiti also points towards the failure of policies and political ideologies that, in parts, created the vulnerabilities long before the actual seismic event occurred [START_REF] Schuller | The Tremors Felt Round the World: Haiti's Earthquake as Global Imagined Community[END_REF][START_REF] Dupuy | Disaster Capitalism to the Rescue: The International Community and Haiti After the Earthquake[END_REF]. Massive population growth in the two decades prior to the earthquake [START_REF] Dupuy | Disaster Capitalism to the Rescue: The International Community and Haiti After the Earthquake[END_REF] and subsequent housing demands of citizens with limited economic capacity resulted in prolific construction of cheap, poorly constructed housing. A tragic consequence followed as 86% of the houses built since 1991 were completely destroyed [START_REF] Etienne | Haiti and Catastrophes: Lessons not learned[END_REF], and significantly contributed to the number of deaths after the quake. A comparison with New Zealand, however, presents a divergent story of earthquake impacts, especially in terms of mortality rates. New Zealand has had a number of strong earthquakes in the last century, the 2011 Christchurch earthquake being the most devastating since 1931. The economic cost of the 2011 earthquake resulted in NZ$40 billion dollars in financial loss [START_REF] Potter | An overview of the impacts of the 2010-2011 Canterbury earthquakes[END_REF] but the mortality rate was relatively low at 185 deaths (albeit one of the highest in the history of New Zealand). This was not a coincidence but a result of sustained effort over a century at the institutional level to improve the resilience of buildings through advancements in research and implementation through the building codes [START_REF] Beattie | The Historic Development of Earthquake Engineering in New Zealand[END_REF][START_REF] Mcsaveney | Earthquakes -Building for earthquake resistance, Te Ara -the Encylopedia of[END_REF].

Japan, which is one of the most earthquake prone countries in the world has developed a range of earthquake risk mitigation and preparedness strategies from national to local level (see [START_REF] Ikeuchi | Earthquake Disaster Mitigation Policy in Japan by Koji Ikeuchi 1 and Nobuharu Isago 2[END_REF]18]). This has led to lower mortality rates for similar magnitude earthquakes compared to developing nations. Additionally, higher economic capacity along with improvement in building codes to address seismic risks after the 1995 Kobe earthquake meant that the magnitude 6.2 Tokyo earthquake in 2009 resulted in just one death even though it affected 2.75 million people [START_REF] Li | Impact of economic development levels on the mortality rates of Asian earthquakes[END_REF]. USA is another developed nation which has not suffered high numbers of fatalities due to earthquakes in the last few decades [START_REF] Jaiswal | Estimating casualties for large earthquakes worldwide using an empirical approach[END_REF]. The differences due to economic capacity are not limited to mortality rates as people from low-income countries, on average, are six times more likely to be displaced/evacuated, injured, lose their homes or require emergency services than citizens of developed countries [START_REF] Wallemacq | Economic Losses, Poverty & DISASTERS[END_REF]. The obvious difference in outcomes due to earthquakes warrants that preparedness, response and recovery planning consider contextual information to be feasible and effective. To this end, use of cordons are no exception.

A cordon is a visible barrier used by an authorized institution to temporarily manage access to and from a given site during critical situations. In relation to earthquakes, the criticality of the situation is indicated by the risks from damaged buildings and potential falling debris due to aftershocks that follow major seismic events [START_REF] Shrestha | To cordon or not to cordon: The inherent complexities of postearthquake cordoning learned from Christchurch and Wellington experiences[END_REF]. Cordons impose a strict spatial demarcation that delineates the degree of safety and security within it. Often, cordons are used for areas encompassing more than one building which was observed in both Christchurch and L'Aquila. The cordons referred to in this paper are from contexts that utilized large cordons as a life safety measure during the response. A cordon established following a seismic event to control the movement of people into affected areas can be termed as post-earthquake cordons (PEC). Although PECs have been used around the world in various ways through time and space, their use (especially for extended periods i.e., more than a month) is an exception and not the rule. Even when established, PECs are poorly documented, and sometimes not documented at all [START_REF] Hulsey | The community impact of Post-earthquake safety decisions based on damage to tall buildings and elevated hazard due to aftershocks[END_REF] which hints at the lack of understanding of cordons and their potential significance as a disaster management tool. However, there is rising interest in PECs and their implications on response and long-term recovery [START_REF] Chang | Urban disaster recovery in Christchurch: The central business district cordon and other critical decisions[END_REF][START_REF] Hulsey | Quantifying the postearthquake downtime induced by cordons around damaged tall buildings[END_REF][START_REF] Toomey | Residential Tenancies[END_REF][START_REF] Collins | The Canterbury earthquakes and the effect on landlords and tenants with commercial leases[END_REF]. This paper aims to add to the growing body of literature of PECs by comparing two case study sites: Christchurch, New Zealand and L'Aquila, Italy where cordons were established and maintained for more than two years after respective seismic events. In Italy, cordons and the space encompassed by the cordon is called zona rossa or red zone, and this term was also used in Christchurch. The case studies are described in detail in the next section.

Methodology

For the purpose of this research, two case study sites were selected: Christchurch in Aotearoa-New Zealand (NZ) following the 2011 earthquake and L'Aquila, Italy, after the 2009 earthquake. Both cities suffered extensive damage after their respective earthquakes and share a common postearthquake response in the use of cordons. They also share similarities in the use of PECs over large spatial and temporal scales which has not been observed in other parts of the world after a major seismic event. Although the damages in both cities were widespread geographically, this study focuses primarily on the city center of each city where the primary cordons were in place.

Christchurch, New Zealand

On February 22 nd , 2011, a major 6.2 Mw earthquake struck the city of Christchurch. This earthquake was an aftershock which followed the 4 September 2010 7.1 Mw Darfield earthquake. Although smaller in magnitude, the Christchurch earthquake was shallow (depth 5km) and much closer to the central business district (CBD). This caused significant destruction resulting in the loss of 185 lives and total or partial collapse of thousands of buildings. More than one third of the buildings within the CBD were completely destroyed [START_REF] Comerio | EERI Special Earthquake Report -Learning from Earthquakes[END_REF]. As a consequence, emergency managers established a cordon around the CBD. Due to the scale of damage, a national state of emergency was declared by the NZ government on the following day, 23 February 2011 and the declaration remained for 66 days [START_REF]Declared States of Emergency[END_REF]. The economic loss was very high as it was the most heavily insured seismic event ever recorded globally [START_REF] Nguyen | Insuring earthquakes : How would the Californian and Japanese insurance programs have fared down under ( after the 2011 New Zealand earthquake )[END_REF]. To support the recovery efforts, a central agency was established, Canterbury Earthquake Recovery Authority (CERA) on 29 March 2011. CERA was responsible for reconstruction and overall recovery of the city [START_REF] Chang | Urban disaster recovery in Christchurch: The central business district cordon and other critical decisions[END_REF] as well as managing the red zones. The use of PECs at such a large scale had been rarely observed prior to the Christchurch event, with exception of L'Aquila city, Italy. Cordons were gradually reduced over time (figure 1) and was finally lifted on 30 June 2013 after more than two years of being in place [START_REF] Potter | An overview of the impacts of the 2010-2011 Canterbury earthquakes[END_REF]. It should be noted that cordons were also placed in other parts of the city besides the CBD predominantly in commercial centers and buildings located in residential areas.

Source: Figures reprinted from [30]

L'Aquila, Italy

L'Aquila city is the capital city of the Abruzzo region in Central Italy. On 6 April 2009 a Mw 6.3 earthquake hit 34 km southwest of the city, at a depth of 10km. The earthquake followed a sequence of shakes ranging from minor to moderate that had begun four months prior with more than 10,000 localized events recorded during that time [START_REF] Tertulliani | An application of EMS98 in a medium-sized city: The case of L'Aquila (Central Italy) after the April 6, 2009 Mw 6.3 earthquake[END_REF]. The main shock resulted in the deaths of 308 people, around 1500 injuries and damage to thousands of buildings [START_REF] Contreras | Spatial connectivity as a recovery process indicator: The L'aquila earthquake[END_REF]. Around €22 billion has already been spent on the rebuild and recovery of the city as of 2017 [START_REF] Finocchiaro | Relazione sullo stato di avanzamento del processo di ricostruzione post-sismica nella regione Abruzzo[END_REF]. This cost was mainly directed to the historic city centre which suffered the most damage. A state of emergency was immediately declared, and red zones were setup with no access for the public. Although cordons were established in villages surrounding L'Aquila as well, the focus of this research is on the centre surrounded by the historic stone walls and multiple access gates. The red zones were reduced in size over the next decade (figure 2) but there still remains areas that continue to be red zoned as of May 2021.

Data collection and analysis

The data collection for this study was carried out by interviewing 23 key informants: 13 from Christchurch and 10 from L'Aquila between August 2018 and August 2019. Expert knowledge holders who participated in the research were from varying fields of expertise and included emergency managers, site engineers, council members, communication managers, police, academics and politicians. Their involvement and/or knowledge regarding the establishment and management of cordons and the overall response to the earthquakes was the primary criteria for their selection for this research. The interviewees were selected through purposive and snowball sampling and the interviews were conducted through a semi-structured questionnaire approach. The interviews in Italy were conducted in Italian by a native speaker from L'Aquila. Additional details about the participant's profession, nationality and corresponding interview duration are provided in Table 1. The interview data from L'Aquila was first transcribed into Italian and then translated into English. Then, both data sets were coded in the Nvivo software, grouped based on underlying themes and concepts and then analyzed inductively. This was done through open coding of the data to conceptualize initial categories [START_REF] Khandkar | Open coding, Basics of Qualitative Research[END_REF] followed by axial coding to further refine the codes into distinct themes [START_REF] Williams | The Art of Coding and Thematic Exploration in Qualitative Research[END_REF].

Results and Discussions

The case studies showed that the initial demarcation of cordons is mainly defined by the degree of damage to an area and potential risk to people. However, if the scale of damage is huge, practical considerations are undertaken owing to existing physical demarcations, availability of resources and ease of planning. In Christchurch, initially, the grid pattern of streets in the inner city were cordoned off along four avenues that defined the area of worst damage (Figure 1), even though some blocks within the cordon did not suffer much damage. Similarly, the initial L'Aquila's cordon was demarcated by its pre-existing historic stone walls. In both cities, the spatial extent was gradually reduced once the risk had been mitigated.

From the thematic analysis it was clear that context was key to the set-up and management of cordons in both countries. As context evolved over time, so did the purpose of cordons. We will now discuss cordons in relation to two thematic timeframes; Phase 1 which relates to Safety/Law/Security and Phase 2 which is related to Recovery.

Phase 1: Safety, Law and Security

The primary purpose of establishment of PECs is life safety. This was observed in both Christchurch and L'Aquila where establishment of large cordons helped the respective authorities to significantly minimize citizens' exposure to risk. In the initial phase, owing to observed significant damage to built structures, cordons became necessary as the risk to life safety was apparent.

'It was about removing risk and it was to make safe' -Emergency Manager, Christchurch 'It's an exceptional situation that doesn't allow people to enter (the city centre) because there is a risk to their safety' -Council Representative, L'Aquila

The cordons are also a tool to enable rapid access of first responders during the immediate response phase. In the aftermath of a major seismic event, significant search and rescue efforts become necessary as there are potentially large numbers of injuries and fatalities. A cordon allows emergency responders to act without potential obstructions from the public who may be in a state of panic and loss, or just curious to observe what has happened. Any potential delay caused by the public during the initial response significantly increases the risk to life for people trapped inside buildings awaiting rescue. If the number of deaths is high, then recovering the deceased becomes a priority.

'The initial reason to set it up was to limit obstruction for search and rescue and also to act as a deterrent for general public to enter the defined area' -Emergency Manager, Christchurch

The desire to establish PECs is also be influenced by the legal frameworks that define the duties and responsibilities of the authorities following a disaster. This was evident in L'Aquila as the responsibility of people's safety after a disaster rested on the mayor. There is also a possibility of criminal liability on the mayor in case there are deaths and/or injury that could have been otherwise prevented after an event. There have been multiple cases in Italy where government officials have been prosecuted as one participant remarked:

'The Mayors have this enormous responsibility. The Mayor of Genoa is in jail for the history of the schools' -Politician, L'Aquila

The ex-mayor of Genoa, Italy had been sentenced to five years in prison for not closing the schools and roads despite a Level 2 Alert due to flooding in November 2011 that resulted in the deaths of six people [START_REF]The Italian Insider, Genoa mayor gets five years in jail for flood tragedy[END_REF]. Similarly, two government officials and five scientists were initially sentenced to six years in prison for communicating the risk of a large earthquake to be low, and thus reassuring residents a few days prior to the L'Aquila earthquake [START_REF] Benessia | When the earth shakes … and science with it. The management and communication of uncertainty in the L'Aquila earthquake[END_REF]. While all except one were later exonerated, the convicted government official received a reduced sentence of two years [START_REF] Cartlidge | Seven-year legal saga ends as Italian official is cleared of manslaughter in earthquake trial[END_REF]. Potential liability for criminal offences for decisions taken that may cause harm meant that establishing a cordon becomes a safe and appropriate response tool as reflected by comment below:

'….because everybody knows that there is a time full of action and solidarity and a time when the judiciary appears.

The two phases have different times and the second one comes always after, to blame you for something' -Council Representative, L'Aquila

Generally, in New Zealand, government employees have statutory protections from liability unless criminal negligence is found [START_REF]Quake Outcasts v The Minister Of Christchurch Earthquake Recovery & Anor[END_REF]. This allows government employees to work and take actions based on their judgement without the fear of prosecution later. However, it should be noted that legal actions indeed take place. A Royal Commission was setup after the earthquake, but its scope was limited to adequacy of building codes and standards of built environment around the Christchurch CBD [START_REF] Brownlee | Canterbury Earthquakes Royal Commission Reports[END_REF]. Additionally, criminal investigation w carried out against engineers of the CTV building for gross negligence of its structural design resulting in collapse of the building and 115 deaths but ultimately the engineers were not prosecuted [see 43 for more details].

'We don't have any issues; we were under Civil Defence, and we were protected on this regard (regarding decisions)'-Council Representative, Christchurch

While human safety is of the utmost importance, PECs are also established and/or maintained to secure the place against theft and vandalism. While crimes may increase [START_REF] Prelog | Modeling the Relationship between Natural Disasters and Crime in the United States[END_REF][START_REF] Roy | The impact of natural disasters on violent crime, Working Paper Retrieved from the New Zealand Association of Economics[END_REF][START_REF] Leitner | THE IMPACT OF HURRICANES ON CRIME IN THE CITY OF HOUSTON, TX: A SPATIO-TEMPORAL ANALYSIS[END_REF] or decrease/remain stagnant [START_REF] Hombrados | The lasting effects of natural disasters on property crime: evidence from the 2010 Chilean earthquake Working Paper Series[END_REF][START_REF] Barsky | Disaster realities in the aftermath of Hurricane Katrina: Revisiting the looting myth[END_REF] after a disaster, it is understandable that authorities would seek to reduce further disorder that may be caused by theft and looting in an already precarious situation created by the earthquake. The perceived risk of such crimes also informed the initial decision to establish the cordons.

'There is obviously quite a potential for looting which did actually occur even with the cordon in place. People In both L'Aquila and Christchurch, interviewees discussed multiple cases of theft and looting. In L'Aquila, the true extent of looting is thought to have been overstated [START_REF] Imperiale | Command-and-control, emergency powers, and the failure to observe United Nations disaster management principles following the 2009 L'Aquila earthquake[END_REF], which contradicts the accounts of the interviewees who remarked:

'…but it was needed since the Jackals2 were taking away the little that had remained' -Council Representative, L'Aquila 'The Jackals! It was a dramatic problem that lasted for about two years' -Politician, L'Aquila

The differences in official counts of crimes and claimed number of crimes is likely due to the limited use of official data for reporting thefts, as well as potential under reporting, reduced or poorly managed record keeping, lack of resources (as police are busy with other urgent matters such as helping emergency managers and fire fighters for search and rescue operations, cordon management) in the aftermath of a disaster [START_REF] Prelog | Modeling the Relationship between Natural Disasters and Crime in the United States[END_REF]. It is however clear that cordons can reduce the incidence of thefts and vandalism. This is highlighted in the study by [START_REF] Breetzke | The impact of the Canterbury Earthquakes on the temporal and spatial patterning of crime in Christchurch, New Zealand[END_REF] where researchers demonstrate the significant reduction of crime in Christchurch city centre from official data obtained July 2008 to June 2013. The researchers also note that almost 70% less crime observed in Cathedral square (CBD area) post-earthquake was spatially displaced to other parts of Christchurch.

To support establishing and maintaining cordons, in both cities, local police and army personnel were utilized. These officials helped with operational activities as well as kept the area secure. In Christchurch, the army together with the local council and emergency managers controlled the entry for public to retrieve their belongings. This was done through a comprehensive access program with photo ID as verification to enter the cordons. The residents could request permission to get into the cordons and depending on the risks involved, authorities allowed people to enter, provided they were accompanied by fire fighters or emergency managers. The time allowed varied as one interviewee explained:

'There was a cordon access program that was setup, and we would do that city block by city block. We would have the engineers to do the assessments and we would have the security and safety staff around so that it could be done and figure out what they were trying to do and work with them on some sort of agreeable time frames to get their stuff. In some cases, it was minutes and other cases it was hours'-Emergency Manager, Christchurch

A similar system was also deployed in L'Aquila where authorized badges were used to verify one's ability to access the cordons. Here too, residents were allowed to access their homes to retrieve their belongings, always accompanied by fire fighters.

'These people were accompanied, they were authorized by badges and accompanied inside by the firefighters. So the firefighters accompanied these people to their houses so they could take what was possible to take' -ANCE representative One major difference observed between the two case sites is that, in Christchurch, the army did not carry any weapons whereas in L'Aquila, armed forces were deployed. It is possible that this influenced how the public perceived the role of army and the use of cordons over time. In Christchurch, the army as cordon managers were the face of emergency management and were respected for their efforts by the public [START_REF] Parfitt | Disaster response: Lessons from Christchurch[END_REF]. However, the presence of armed personnel was not always welcomed in L'Aquila and for many locals were a cause of further distress [START_REF] Imperiale | Command-and-control, emergency powers, and the failure to observe United Nations disaster management principles following the 2009 L'Aquila earthquake[END_REF].

'It was especially the presence of the soldiers..... I mean, the red zone was making me feel very uncomfortable, but more than that it was the presence of the soldiers….. the constant presence of the soldiers was making me feel very uncomfortable because they were armed people that I was seeing regularly' -Community Leader, L'Aquila

Phase 2: Recovery

As time goes by, the nature of the emergency changes as the urgency is reduced due to a reduced risk profile. This results in corresponding changes in response strategies adapting to new priorities and increased involvement of various organizations. However, in the case of earthquakes, due to the nature of on-going aftershocks, the risks may persist for an extended period (months to years) beyond the initial event. Tremors can further deteriorate an already damaged building into collapse. This directly affects the spatial and temporal extent of cordon placement [START_REF] Marquis | Understanding post-earthquake decisions on multi-storey concrete buildings in Christchurch, New Zealand[END_REF] as illustrated by the following remarks from one participant:

'I would say, prior to the June (2011) aftershock, I would have said we would be cordon free by October that year.

That was probably what we had in mind, what we couldn't knock down in time we would just isolate it. Later we realised that there was so much more work to do because buildings were even more damaged. Some buildings which had suffered only moderate damage in the earlier earthquakes but after the June aftershocks, they were completely damaged. The cathedral, more of the cathedral fell down' -Demolitions Manager, Christchurch

In both cities, the damage to buildings was high and thus the risk of further damage to buildings and collapse remained for a long period of time. However, the recovery approach taken was governed by the contextual realities of each city. In Christchurch, the main damage was primarily observed around the central city which mostly hosted commercial and institutional buildings and fewer residential properties. The authorities focused on demolition of unsafe buildings as it was the quickest and most efficient way to reduce the risks posed by them. To this end, CERA had overreaching legal powers to demolish buildings that it deemed unsafe even without the consent of the owners of the building. Almost 1000 buildings were demolished within the Christchurch CBD by April 2012 [START_REF] Cera | Earthquake Recovery Update Issue 9[END_REF] 'Demolitions within the four avenues was in the order of sort of 1600-1800 hundred buildings' -Demolition Manager, Christchurch

'So, at the start when it's about just saving lives or protecting, you know protecting people by getting a building down quick there's no questions asked' -Council Representative, Christchurch

This urgency for demolition in Christchurch was partly driven by businesses and homeowners actively opting for this option. This is because once a building was declared a total loss by insurers, the insurance settlement would be processed faster, which allowed owners more financial flexibility [START_REF] Marquis | Understanding post-earthquake decisions on multi-storey concrete buildings in Christchurch, New Zealand[END_REF]. This was furthered by the fact there was growing uncertainty over the recovery of the city. People also wanted to get back to the city and a growing dissatisfaction among businesses resulted in demonstrations and breaching of cordons at one point [START_REF]The press, Angry cordon jumpers seek talks[END_REF]. The authorities did consider these pleas and worked together with businesses to facilitate the opening of the Re:Start3 shopping mall by prioritising demolitions on the access route to the mall.

'The government was really good in that respect. We needed to clear this street, so Re:Start sat where this building is right now, sat here and across the road. The government had to clear all the roads and all the dangerous buildings, and they had to get it done quickly so we could Re:Start' -Business Representative, Christchurch

The cordons assisted in demolition works in multiple ways. Since the public could not get in, the demolition contractors could work faster without worrying about risk to bystanders. In essence, the space within the cordon worked as a giant construction site. Additionally, there was no unauthorized vehicular movement leading to minimum traffic which also allowed for larger roads and vacant lots to be used for storing demolition debris, construction materials and large vehicles.

Because access points into the cordons were controlled and records kept with regular monitoring, it also became easier to keep track of demolition and construction works which was useful for avoiding other potential hazards such as asbestos poisoning, as one interviewee explained.

'And the other purpose of the cordon that we used it for was waste in and out of the waste stations and check it, washing bays, to see where it is going so that it does not go into the water because people were worried about the asbestos that is being trucked down from the centre of the city' -Demolition Manager, Christchurch

A Christchurch simulation study conducted by [START_REF]'s Chief Science Advisor, Asbestos exposure in New Zealand: Review of the scientific evidence of non-occupational risks[END_REF] showed that the asbestos exposure due to demolition and home remediation was well below the standard exposure permissible in workplace.

However, the concerns regarding potential asbestos poisoning were evident throughout the demolition process. Cordons also presented an opportunity for businesses/homeowners to undertake repair, retrofit or redesign work on their buildings even if there was limited or no damage to them as the cost of doing operations within the cordon was significantly less compared to normal times. This was assisted by reduced administrative processes and costs related to getting permits and approval from the council.

'Because inside the cordons they could work in a far accelerated rate. So, if you have a broken building and you got to repair it and deal with public traffic and pedestrians and access and resource consents and all that, normally it can take years to get started….. So, some of the business owners pretty quickly figured that out that they can use the cordon to their advantage and speed up the recovery and maybe it did. It accelerated some of the rebuild by years' -Emergency Manager, Christchurch

While the presence of cordons assisted in demolition and rebuilding works thereby supporting recovery of Christchurch city, it also presented challenges. One major issue was around insurance. New Zealand is one of the few countries in the world with high uptake of private earthquake insurance. Around 98% of buildings (residential/commercial/offices) in Christchurch had insurance coverage [START_REF]RNC, Type and timing of insurance pay-outs after the Canterbury earthquakes were significant in the recovery of residential areas and businesses[END_REF] when the earthquake hit, thus making it the highest insured seismic event in history [START_REF] Nguyen | Insuring earthquakes : How would the Californian and Japanese insurance programs have fared down under ( after the 2011 New Zealand earthquake )[END_REF]. While there were many issues surrounding insurance (see [START_REF] Merkin | The Christchurch earthquakes: insurance and reinsurance issues[END_REF][START_REF] Brown | The role of insurance in organisational recovery following the 2010 and 2011 Canterbury earthquakes[END_REF]), cordons created or exacerbated the situation for insurers, claimants, and the authorities. Firstly, during the initial phase there were instances where neither the insurers nor homeowners were duly consulted before demolitions were carried, citing safety concerns, despite opposition from the owners and insurers. This complicated the situation as insurance coverage was only activated from damage caused due to the earthquake i.e., it did not cover the damage caused due to the action of the authorities. Since the demolitions were enforced by the authorities, it was debated by the insurers that the subsequent damage did not fall under the earthquake insurance coverage. The complexity of the situation is described by the insurance representative as follows:

'From an insurance perspective, is there material damage or not to properties within the cordon? And then there is the interruption to business within that cordon and what triggers the business interruption relief which may well be dependent upon the material damage or not to the building. And the decisions that are made around which buildings are demolished, when they're demolished, what level of consultation or no consultation is provided to the business, to the owner of the property, or to the tenants of the property who have businesses that are demolished without any consultation whatsoever. And then they have difficulties making claims because the damage was done by the authority and not by the earthquake and they took an insurance policy for earthquake cover' -Insurance Representative, Christchurch

'Virtually all insurance policies covering property, there are exclusions and one of the common exclusions around the world is acts of civil authorities' -Insurance Representative, Christchurch

Furthermore, cordons also created situations where the building in question was not damaged but was placed within the cordon due to the risk posed by neighbouring structures. Again, 'damage' which usually triggers the insurance claim (unless there was a specific clause stating 'loss of access') was not observed. This inability for owners to access insurance because their building was not technically damaged, resulted in disputes. People with coverage for business interruption also faced similar challenges to claim for loss of earnings and business disruption. Additionally, tenants of the buildings also faced multiple sets of challenges as most leases are different from one to another which complicated the situation. Also, claims made by the tenants would generally be processed once the landlord and landlord's insurer came to a mutual understanding about the fate of the building [START_REF] Brown | The role of insurance in organisational recovery following the 2010 and 2011 Canterbury earthquakes[END_REF] which meant that there was a lot of uncertainty for the tenants for a long time. It should be noted that, in part, large scale demolitions in the CBD eased the situation for business interruption claims [START_REF] Marquis | Understanding post-earthquake decisions on multi-storey concrete buildings in Christchurch, New Zealand[END_REF] as the claims shifted towards damage of buildings.

'Well, its owners signing agreements with the Crown to put the Crown to take control and take those (demolition) works. We did that most of the time by mutual agreement. There's a few that was not a mutual agreement. We still took control of that because it impacted on cordon reductions and the neighbours' -Emergency Manager, Christchurch

Secondly, even when there was clear damage to buildings in question, it was difficult for claimants as well as insurers to conduct an assessment of damage because access within the cordons was tightly controlled. Additionally, there were limited resources initially as hundreds of thousands of claims were registered which neither the private insurers nor the EQC 4 had the capacity to process [START_REF] Merkin | The Christchurch earthquakes: insurance and reinsurance issues[END_REF]. As such, the process of claiming damages and being compensated was long and arduous. The complexity of the whole situation is highlighted by the fact that there are still hundreds of cases which are yet to be resolved more than a decade later [START_REF] Olano | Elderly homeowner still fighting for quake claim 10 years on[END_REF].

'So, the insurer can't inspect the damage. (Yeah) Well that will slow the process. So, the insured has no access, so the insured has difficulty making a claim as to what the losses are' -Insurance Representative, Christchurch 'Well, the demolition sort of hinged on people getting their insurances sorted out too. So, you know, if there is a dispute about a building, it could or could not be repaired, umm, that could take time. That is why there was that hold up. If you'd had, let's say, a whole sort of, we are pulling everything down and blow the insurance, it would have been a lot faster. But of course, they have to all work with their insurance processes individually with their insurers. Some of them argued' -Business Representative, Christchurch

In contrast to New Zealand, Italy is significantly underinsured against earthquakes. With penetration rate of less than 10% [START_REF] Maccaferri | Natural Catastrophes : Risk relevance and Insurance Coverage in the EU[END_REF], insurance did not play a significant role in relation to PECs. However, L'Aquila has faced multiple challenges of its own due to contextual realities that have persisted till this date. The fact that cordons still remain in some parts of the historic centre at the time of writing is a reflection of the complexity associated with use of cordons and overall recovery of the city. The first challenge emerged with the decision to establish the cordon itself. As the city centre was a residential area, around 70,000 people needed to be evacuated immediately from the dangerous red zone and required temporary housing. Approximately one third of evacuees found accommodation by themselves, another third were sheltered in state-sponsored hotels and the remaining third in temporary camps (tents) [START_REF] Alexander | An evaluation of medium-term recovery processes after the 6 April 2009 earthquake in L'Aquila, Central Italy[END_REF]. After a decade, there were still over 10,000 people in temporary accommodation [START_REF] Imperiale | Command-and-control, emergency powers, and the failure to observe United Nations disaster management principles following the 2009 L'Aquila earthquake[END_REF]. The complications of managing immediate (and temporary) housing needs after a disaster have been discussed thoroughly in the literature [START_REF] Johnson | Impacts of prefabricated temporary housing after disasters: 1999 earthquakes in Turkey[END_REF][START_REF] Johnson | Strategic planning for post-disaster temporary housing[END_REF][START_REF] Comerio | Housing Issues After Disasters[END_REF][START_REF] Félix | Temporary housing after disasters: A state of the art survey[END_REF]. The recurring issues of cultural insensitivity, delays, inappropriate location, environmental unsuitability, economic sustainability and construction quality were compounded by the command-and-control approach of the military which exacerbated the discomfort and discontent of L'Aquila residents [START_REF] Imperiale | Command-and-control, emergency powers, and the failure to observe United Nations disaster management principles following the 2009 L'Aquila earthquake[END_REF]. There was lower demand for temporary housing in Christchurch [START_REF] Giovinazzi | reconstruction between temporary and definitive[END_REF] as the city centre primarily accommodated businesses and few residents. This meant that the significant housing challenges experienced in L'Aquila were avoided in Christchurch. Nevertheless, temporary housing after a disaster is a complex issue and a potentially unavoidable reality if PECs are to be established for a long time where residents live as illustrated by comments from one of the participants:

'After I signed that document, about 75,000 / 80,000 people, considering also university students, became evacuees' -Politician, L'Aquila Many buildings in L'Aquila were significantly damaged but did not fully collapse. Although demolitions of such buildings were carried out for a short period of time in the beginning, the focus was always on protecting the historic buildings and cultural heritage. Then, one of the first steps was to ensure the stability of the buildings by shoring 5 to protect against further damage and to minimize risk for emergency managers, fire fighters and the police to carry out their operations.

'In this case, however, the Cultural Heritage Commissioner made it compulsory not to demolish anything, because they were all historical places so even the bell tower was unstable, still it was a XVII-XVIII century bell tower with decorations. Therefore, we had to intervene in critical conditions, even extremely critical precisely because demolishing was forbidden, the building had always to be saved even if it was extremely unstable' -Engineer, L'Aquila 'If there is a restricted building where you are not allowed to demolish, if you leave it in those conditions, not only it becomes a danger and you can't, you can't enter it, this applies even to those who are in the red zone, to the firefighters, and we had to move anyways when we wanted to visit and if we wanted to move we had to secure as we were moving forward' -Engineer, L'Aquila Shoring of buildings was done in stages and it changed over time in terms of the methods and materials used. Initial shoring was done by the firefighters, and mostly consisted of wooden structures as provisional support systems. The required shoring was at such a great extent [START_REF] Rossetto | The value of multiple earthquake missions: The EEFIT L'Aquila earthquake experience[END_REF] that, to facilitate it, a special unit was developed called the Coordination of Provisional Works (NCP) within the national fire department (CNVVF) [START_REF] Grimaz | Management of urban shoring during a seismic emergency: Advances from the 2009 ĹAquila (Italy) earthquake experience[END_REF]. Although, limited in its strength and durability, the initial shoring systems in place allowed fire fighters and other relevant personnel to access the red zone and carry out the initial disaster response activities. As buildings were being secured, it allowed the authorities to reduce the spatial extent of the red zones as explained by the authorities:

'The first safety measures were made by the firefighters who used wood, but wood does not guarantee durability, but well, they could not do more than that at that time' -Council Representative, L'Aquila 'As long as the shoring was done, I was making the red zone smaller, but of course, the shoring had to be done first' -Politician, L'Aquila

The shoring of buildings also brought its own challenges. The initial shoring was done without pre-planning and often done invasively which meant that removing them without affecting the structural integrity and/or architectural heritage became difficult. Subsequently, given the complexity of damage to buildings and an array of building failures at a large scale across the city, initially, there was dearth of engineers with the necessary technical skills and capacity. To overcome this challenge many agencies such as Civil Protection, Universities and Ministry of Cultural and Architectural heritage, along with the fire fighters collaborated to design, develop and implement an alternative urban shoring system. Over time, however, it became difficult to coordinate these efforts [START_REF] Grimaz | Management of urban shoring during a seismic emergency: Advances from the 2009 ĹAquila (Italy) earthquake experience[END_REF]. The lack of public oversight for contracting the shoring activities to various companies [START_REF] Imperiale | Top-down reconstruction and the failure to "build back better" resilient communities after disaster: lessons from the 2009 L'Aquila Italy earthquake[END_REF] also highlighted the issues of transparency and potential corruption. However, the upgraded metal shoring systems were more secure and durable, as evident by the continued use of these systems at the time of writing. Even when the main structure was secured, there is still a possibility of non-structural parts falling which meant that the risk was not completely averted. Further challenges arose in maintaining the shoring systems in places which required technical and financial resources which were not always available.

'Or maybe the same company that followed that specific shoring system isn't there anymore because it was responsible for it only for a temporary moment for that specific shoring and not for others and it's very likely that some companies aren't participating in the reconstruction anymore, they set up the securing and they left, which is quite common' -ANCE Representative, L'Aquila 'Because the problem following the shoring was not the collapse of the building, but rather the detachment of parts of it. Therefore, we just had to monitor that it was all right, we had no concern that the building could fall on the road' -Council Representative, L'Aquila

The shoring system nevertheless supported the reconstruction process by allowing a safe working space for reconstruction to begin and continue. Similar to Christchurch, the red zone was a transitional space that was free from logistical obstacles and had simplified bureaucratic processes which allowed physical and administrative works to be carried out faster. PECs also provided a less stressful environment for the construction workers by eliminating the presence of the public. Furthermore, it also supported the finances of the reconstruction projects through fee waivers of large sums of money for occupying public land (street such as via dell' Arcivescovado and plaza such as Santa Maria Paganica) necessary to setup a construction site. It should be noted that in both cities, authorities wanted to bring people into the city as soon as possible. To this end, the Christchurch red zone bus tours [START_REF] Dally | Red zone bus tour draws mixed reaction | Stuff.co.nz, Stuff[END_REF] and opening of the Re:Start shopping mall were attempts made by authorities to bring the public back to the city centre.

Similarly, in L'Aquila some businesses and bars were given temporary permits and few Piazzas were opened so that the citizens could have some degree of social life. The desire to reduce PECs and return life to normalcy will always be there. And even when safety is of limited concern, the reduction of cordons may be dependent on administrative, technical, and resource challenges. As observed in L'Aquila, the rebuilding of the city has been an extremely complicated process [START_REF] Imperiale | Top-down reconstruction and the failure to "build back better" resilient communities after disaster: lessons from the 2009 L'Aquila Italy earthquake[END_REF].

The private reconstruction has been prioritised over public buildings to enable citizens to get back into the city as soon as possible, yet the completion rate for reconstruction is still low considering it has been more than a decade since the earthquake disaster. This has caused a lot of discontent among the citizens of L'Aquila.

'But they go with two very different speeds: we have reached between 70% and 75% of the private reconstruction, while with the public we are generally at 10%, considering the whole seismic crater 6 and not only the city of L'Aquila' -ANCE representative, L'Aquila 'Human and social times are different from construction times, from administrative ones' -ANCE Representative, L'Aquila

As discussed above, PECs and their purpose evolve from their initial, safety focused, police/army controlled red zone into a transitional space focused on reconstruction and are sensitive to people's wellbeing. Accordingly, people's perceptions and acceptance of PECs also evolves as described by one participant below:

'I think that the acceptance of the red zone and today's barriers are two very different things, in the sense that ... because when you are told that that thing is a red zone and you are outside the red zone and there are soldiers and you live elsewhere and you don't know if you will come back to live in L'Aquila, if a reconstruction will ever start, you think the red zone will be forever. Today we hardly notice it anymore because even though the red zone is still there, it seems that it doesn't' exist anymore, because we go everywhere. The 'barriers' are gone, the soldiers are gone' -Community Leader, L'Aquila

Considering the impacts of cordons in both case studies, it can be argued that establishing and maintaining cordons have had a positive effect on recovery of these cities. In case of Christchurch, this conclusion has been supported by other studies as well [START_REF] Shrestha | To cordon or not to cordon: The inherent complexities of postearthquake cordoning learned from Christchurch and Wellington experiences[END_REF][START_REF] Brown | The role of insurance in organisational recovery following the 2010 and 2011 Canterbury earthquakes[END_REF]. However, it is difficult to ascertain to what degree PECs were influential in supporting recovery and even more difficult to conclude if PECs were appropriate (for such a long time) given their overarching imposition over various aspects of people's lives and livelihoods. Undoubtedly, PECs are useful, but by virtue of their restrictiveness, they can be detrimental to civil liberties [START_REF] Underwood | Post-earthquake cordons and their implications[END_REF]. It is understandably controversial to exclude people from their own homes, own streets, own city for an extended timeframe (years) when that geographic area is not perceived to have risks. If the awareness of risks differs, then there will be observed differences in the public's willingness to accept those risks, which might be in contrast/conflict with the degree of risk that the authorities deem appropriate to allow. As such, it is necessary to properly communicate the actual risk posed by the buildings within the cordons so that varying perceptions of risks among the public and the authorities can be aligned.

Conclusion

Post-earthquake cordons are a necessary response tool to ensure the safety of people against risks posed by structurally unsafe buildings as well as non-structural elements that may fall due to aftershocks. However, as the level of risk subsides the continued presence of cordons can have a range of potentially unintended consequences, both positive and negative. Nevertheless, this research has demonstrated that cordons can evolve from being a safety-focused response tool to reconstruction-focused transitional tool. To this end, it is necessary to understand that, even though there are similar factors driving PEC establishment, it is equally important to recognize that the contextual realities of each case will undoubtedly affect how cordons are managed and how they impact response and recovery. As observed from the two case studies of Christchurch and L'Aquila, insurance, recovery strategies (demolitions vs shoring) and temporary housing needs are some of the major context-driven realities that directly affect PECs and their extended establishment. Effective communication about PECs will foster understanding of the reasons why PECs are necessary, initially, for life safety purposes and later, can be beneficial to support recovery over extended time periods.

Ethics Statement

The University of Otago Human Ethics Committee has approved this study under category 'A'.

Excerpts from the interviews are anonymized for privacy.

Figure 1

 1 Figure 1 Evolution of cordons in Christchurch CBD (among 22 changes).

Figure 2

 2 Figure 2 Evolution of cordons over the years in L'Aquila city Source: a) [34] b)[START_REF] Mastropietro | cartografia della Zona Rossa[END_REF] c), d), e)[START_REF] Commune | Ordinances : Red Zone of the city[END_REF]

Table 1

 1 Details of participant's profession and respective interview durations

	S.N. Profession	Total number	Avg. duration
			Christchurch
	1.	Business Representative	1	47 mins
	2.	Communication Manager	2	1hr 20 mins
	3.	Council Representative	2	36 mins
	4.	Demolition Manager	2	1 hr 57 mins
	5.	Emergency Managers	3	1 hr 18 mins
	6.	Insurance Representative	2	23 mins
	7.	Police	1	47 mins
			L'Aquila
	1.	Academic	1	1 hr 14 mins
	2.	ANCE 1 representative	2	41 mins
	3.	Community Leader	1	1 hr 4 mins
	4.	Council Representative	2	1 hr 13 mins
	5.	Emergency Manager	1	1 hr 54 mins
	6.	Engineer	2	50 mins
	7.	Politician	1	1 hr 28 mins

  'The shoring issue was useful because knowing the Italian timing, the reconstruction of this palace … for example started after 7 years, after 7 years if you don't shore this up, it continues to open up and grow more and more until it collapses as it happened in some cases' -Engineer, L'Aquila 'It was much better for the businesses to work when there was the red zone, because it meant that only businesses could enter, and we had all the space we needed to set up the construction site' -Engineer, L'Aquila 'For the workers, yes, because the work was limited to an area of a building that he knew was free from other people, only the ones linked to the construction site. Imagine, if, in such a vulnerable area with narrow streets it was possible to have children or old people it would be an aggravating circumstance from the point of view of risk and safety. Let's imagine a crane truck which is installing a steel beam as security system but there's a child with his grandfather in the nearby' -ANCE Representative, L'Aquila

'When the red zone was here, they didn't pay for the public land, now in a normal situation they are really working like any other city in the world, so they pay for the occupation of public land and it's extremely expensive, like here they can pay €100.000 euro for two years. It is a cost in the reconstruction' -Engineer, L'Aquila

ANCE is the Italian Association of private construction contractors which represents

regional organisations, 101 provincial associations and 20,000 construction companies in Italy. It safeguards the construction industry through engagement with political, cultural, social institutions and lobbying efforts. ANCE, L'Aquila was and still is, an important organization that overlooks reconstruction work in L'Aquila

Jackal, translated from 'Sciacallo' means a dishonest person who takes advantage of other people's tragedies, usually by stealing goods from their properties.

Re:Start: It was a temporary shopping mall built from shipping contaners which accommodated 27 shops. It was opened on 29 October, 2011 and remained opened until January 2018.

EQC as in the Earthquake Commission is a New Zealand Crown entity that provides insurance to residential property owners and also invests in natural disaster research.

Shoring of buildings: It is an engineering process to temporarily support damaged buildings against collapse usually done through timber or metal props.

Seismic Crater denotes broader areas affected by the L'Aquila earthquake. It contains 57 municipalities of which 42 are from L'Aquila province, 8 are from Termano province and

are from Pescara Province

Acknowledgements

This project was (partially) supported by QuakeCoRE, a New Zealand Tertiary Education Commission-funded Centre. This is QuakeCoRE publication number 0679

Appendix

The following are some of the general questions that were asked during the interviews.

Time frame

General Questions

Shortterm

• Who took the decision to establish initial cordon/s? • What were the underlying reasons for the decisions?

• What type of information is necessary during initial cordon establishment?

• What were the major challenges during the initial period of cordon establishment and management?

Midterm

• The cordon was reduced gradually [in Christchurch]. What were the major considerations taken for reducing cordons?

• How did the extended timeframe of the cordons impact businesses, transport, and temporary housing?

• Was the extent and management of cordon flexible? Could it have been more flexible, both in terms of the spatial extent and access?

• How was the information related to cordons communicated to the public? Do you think the public should be involved [if so, when?] in decision making and cordon implementation?

• What type of information do you need for effective cordon management during this timeframe? Long term

• How did the cordons impact recovery of the city?

• What was the effectiveness of the cordon, especially if you consider the long-term implications? In hindsight, was having the cordon in place for such a long period necessary?

• Do you think cordoning should be a part of a disaster recovery framework?


Hamed Nazim Mamache
email: hamednazim.mamache@etu.sorbonne-universite.fr

Gabin Mazué
email: gabin.mazue@etu.sorbonne-universite.fr

Osama Rashid
email: osama.rashid@etu.sorbonne-universite.fr

Gewu Bu
email: gewu.bu@uca.fr

Maria Potop-Butucaru
email: maria.potop-butucaru@lip6.fr

Resilience of IOTA Consensus

Keywords: Consensus, Byzantine fault, IOTA

Blockchains are appealing technologies with various applications ranging from banking to networking. IOTA blockchain is one of the most prominent blockchain specifically designed for IoT environments. In this paper we investigate the convergence of two Consensus proposed by IOTA: Fast Probabilistic Consensus and Cellular Consensus, when run on top of various topologies. Furthermore, we investigate their resilience to various types of adversaries. Our extensive simulations confirm that both Fast Probabilistic Consensus and Cellular Consensus have poor convergence rates even under low power adversaries and have poor scaling performances except for the case of Watts Strogatz topologies. Our study points out that the design of IOTs dedicated blockchains is still an open research problem and gives hints design. This why the foundation IOTA works on a complete version of consensus, Coordicide, for the new IOTA, while regarding these two as components of.

I. INTRODUCTION

Internet of Things (IoT) devices are used in a large range of applications such as smart grids, smart foraging, smart buildings, smart supply chains or smart medical applications and the IoT environment [START_REF] Ijaz | Enabling massive iot in 5g and beyond systems: PHY radio frame design considerations[END_REF] is expected to further expand even more ubiquitous deployment thanks to the fifth generation of networks (5G) [START_REF] Andrews | What will 5g be?[END_REF] and beyond.

Due to the vulnerabilities of IoT to various attacks and the very harmful potential consequences, the currently dominating approach in the management of IoT devices is centralizing control operations at IoT gateways, which are considered as the natural function to absolve access control, data filtering and mixing operations. However, centralization does not appear viable when one envisions hundreds of thousands of devices per km2 or per cell [START_REF] Ijaz | Enabling massive iot in 5g and beyond systems: PHY radio frame design considerations[END_REF], especially when those devices can be constrained in size and power supply.

The use of Distributed Ledger Technologies (DLT) can respond to both security and decentralization needs in the management of IoT devices. Distributed Ledger Technologies (DLT) such as blockchains provide a secure way to share information between a high number of independent nodes operating under different authorities, while ensuring high availability and immutability. Distributed Ledger Technology pioneered by Bitcoin technology created a new design philosophy for executing and storing transactions in a decentralized and secure fashion [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF].

A blockchain is a distributed ledger that mimics the functioning of a classical traditional ledger (i.e. transparency and falsification-proof of documentation) in an untrusted environment where the computation is distributed. Traditional blockchain systems such as Bitcoin [START_REF] Nakamoto | Bitcoin: A peer-to-peer electronic cash system[END_REF] or Ethereum [START_REF] Wood | Ethereum: A secure decentralised generalised transaction ledger[END_REF] maintain a continuously-growing list of ordered blocks that include one or more transactions that have been verified by the members of the system, called miners. Blocks are linked using cryptography and the order of blocks in the blockchain is the result of a form of agreement (consensus) among the system participants. Bitcoin technology and similar proposals (e.g Ethereum) came with several drawbacks that prevent them from being used as standards for IoT industry. Therefore, alternative solutions have been opened by IOTA [START_REF] Popov | The tangle[END_REF]. IOTA's data structure is a Directed Acyclic Graph (DAG) based distributed ledger, also known as the Tangle, aimed to overcome limitations of Bitcoin-like distributed ledgers when used in IoT environment while preserving equivalent security levels. Transactions are continuously appended to the tangle. Similar approaches have been proposed by Spectre or Phantom [START_REF] Sompolinsky | SPECTRE: A fast and scalable cryptocurrency protocol[END_REF], [START_REF] Sompolinsky | PHANTOM: A scalable blockdag protocol[END_REF]. However, IOTA and similar approaches have not yet been adopted by the IoT industry because of 1) lack of strong consistency guarantees and 2) unclear resistance to attacks. In order to respond to these criticism IOTA proposed recently in [START_REF] Serguei | The coordicide[END_REF] attacks resilient consensus mechanisms that plugged into the IOTA Tangle will offer strong consistency guarantees. Two consensus algorithms are proposed: Fast Probabilistic Consensus (FPC) and Cellular Consensus (CC). These two proposals have been partially evaluated in [START_REF] Popov | Fpc-bi: Fast probabilistic consensus within byzantine infrastructures[END_REF], [START_REF] Capossele | Robustness and efficiency of leaderless probabilistic consensus protocols within byzantine infrastructures[END_REF].

In this work we investigate the performances of IOTA consensus in several aspects. First, we run Fast Probabilistic Consensus (FPC) and Cellular Consensus (CC) on top of various topologies, from theoretical to practical (2D Grid, Torus and Watts-Strogatz model [START_REF] Watts | Collective dynamics of 'smallworld'networks[END_REF]) then we evaluate their resilience to adversarial behavior. Our evaluation is conducted with OMNET++ simulator enriched with three adversarial models introduced in [START_REF] Serguei | The coordicide[END_REF]. Even though most of the results reported in our study are negative they contain hits in order to design an efficient IoT dedicated blockchain.

II. IOTA DISTRIBUTED CONSENSUS

In this section, we briefly describe the operating principles of the two consensus mechanisms proposed by IOTA [START_REF] Serguei | The coordicide[END_REF]. The basic idea is all honest nodes in the system should agree dynamically with a commun opinion by a distributed way, so that this opinion cannot be changed by others easily.

Consider a connected network composed of N nodes, enumerated as {1. . . i. . . N }. Some lossless links connect nodes in the network. Nodes connected directly are neighbors.

We follow the setting proposed in [START_REF] Popov | Fpc-bi: Fast probabilistic consensus within byzantine infrastructures[END_REF], [START_REF] Capossele | Robustness and efficiency of leaderless probabilistic consensus protocols within byzantine infrastructures[END_REF], assuming that the time is discrete and divided into rounds.

Each node has an opinion status, O i (r) ∈ {0, 1} at the round r. Consensus is achieved, if ∀i, j ∈ N, O i (r end ) = O j (r end ), where r end is the last round of simulation.

An opinion held by most of the nodes is a major opinion. The convergence rate is the percentage of runs leading to a consensus stage given P 0, where P 0 is the probability that a node has opinion 0 at round 0. If a node does not have opinion 0 at round 0 it will have opinion 1.

A. Fast Probabilistic Consensus (FPC)

The idea of Fast Probabilistic Consensus algorithm is based on the query/reply of opinion from nodes in the network. Algorithm executed by each node is as follows:

• Query randomly a number of nodes in network at each discrete time round t; • Wait for the chosen nodes to respond and give their opinions; • Calculate the mean of the received opinions. Once the node executing Fast Probabilistic Consensus algorithm has calculated the mean, if it is the first round, he will compare it to a threshold τ , if the mean is bigger than τ , then its opinion becomes 1, otherwise becomes 0. If it is not the first round, the node will generate a random variable U t following a uniform law in function of τ between [β, 1 -β] (where β is the uniform low parameter). If the mean is bigger than U t , the opinion becomes 1, if it is smaller, the opinion becomes 0 and if they are equal, the opinion stays the same as the previous round.

In [START_REF] Popov | Fpc-bi: Fast probabilistic consensus within byzantine infrastructures[END_REF], FPC has two special assumptions. The first is that all nodes in the network have a common random values sequences. This random values sequences should theoretically be provided by a trusted third party in other network layer. Through this common sequence, all nodes will "randomly" select the same threshold, U t , at each execution round t. The second assumption is that each node has the complete view of all N nodes in network, and can freely query Q nodes among them. Although the experiments in the [START_REF] Capossele | Robustness and efficiency of leaderless probabilistic consensus protocols within byzantine infrastructures[END_REF] show that even if nodes have only 50% of the network view, the algorithm still works.

However, in an IOT network environment where millions of devices can join and exit at any time, neither of these assumptions is realistic. In order to adapt FPC to distributed IOT environment, we made the following adjustments: 1) Remove the assumption about the common random values sequence.

2) The node only knows the nodes directly connected to it, the neighbors. In order to represent the process of randomly querying Q nodes of original FPC, we use the Random Walk method. Through random walks, nodes that only know its neighbors can still query other nodes within the range of random walks that are not directly connected.

When a node need to query nodes in each round, it launches a number of random walks of distance D. When a random walk stops at a node, this node will be chosen as a node to be queried. When a node launches a random walk within distance D, it will choose randomly one of its neighbors and send a message containing a list of visited nodes and a positive distance value, D -1, as the distance decremented of 1. At this point, the list of visited nodes will only have the node that launched the random walk. Once one node receives that message, it will verify whether the distance remaining is greater than 0. If so, it adds itself in the list of visited nodes, decreases the distance value and sends the message to one of its neighbors. This neighbor is chosen uniformly between the neighbors that have not already been visited so that no random walk can go through the same node twice. If all of the neighbors have already been visited, no random walk will be launched. A node stops launching the random walk if the remaining distance value reaches 0.

B. Cellular Consensus(CC)

In Cellular Consensus(CC), each node acts as an individual agent, that changes its opinion in case of conflict with its neighbors and adopts the major opinion among its neighbors.

At the beginning of each round, every node sends a "heartbeat" of its signed current opinion and the opinions from the previous round of his neighbors, each one signed by the issuing node.

When a node receives an opinion given by one of its neighbors, it will evaluate this opinion by a "proof" accompanying the opinion. This "proof" is materialized by the opinions of the neighbor's neighbors. That will allow nodes to monitor each other and to detect if someone is lying independently of its neighbors. If this "proof" shows that the neighbor is lying, it will immediately be blacklisted by the node and none of his opinions will be taken into account.

Since the previous opinions of the neighbors cannot be faked, every node can validate that the received opinion is indeed correct.

In detail, the cellular consensus algorithms work as follows. At each step of the algorithm, each node holds an opinion, which can be 0, 1 or a temporary opinion state -1.

If the major opinion among neighbors of node i in round r is:

• 0, then the opinion of node i in round r + 1 will be 0,

• 1, then the opinion of node i in round r + 1 will be 1,

• non-existent (i.e. there is no majority opinion), then the opinion of node i in round r + 1 will be -1.

III. TOPOLOGY PRESENTATION

In this section we introduce three network typologies that used in our experimentation: 2D Grid, Torus , two topologie theoretical often used as reference topologie in algorithm analyzing, and Watts-Strogatz [START_REF] Watts | Collective dynamics of 'smallworld'networks[END_REF], a realistic network model which is well-suitable for IoT.

A. 2D Grid

The first topology studied is the simplest of all. We consider a grid or matrix, which contains nodes. Each nodes' neighbors will be those adjacent to them. Their number therefore varies according to the position of the node in the grid. Indeed, if a node ends up in a corner, it will only have 2 neighbors. Also, if it ends up on an edge, it will have 3 neighbors. Finally, if this one is in the center of the grid, it will have 4 neighbors.

B. Torus

The second topology studied is an improvement of the 2D grid and avoids getting stuck in the corners and on the edges. To do this we will transform our grid into a torus [START_REF] Contrepoints | John nash, un mathématicien d'exception (1928-2015[END_REF]. We therefore connect the top and bottom edges together, and repeat the same process for the right and left edges. By connecting the edges between them, we add neighbors to the nodes which are in the corners and on the edges. Indeed, if we are in the top left corner, we add the bottom left corner and the top right corner to the list of our neighbors. If we are on an edge, we add the node which is on the opposite edge. Finally, if we are located in the center, nothing changes. The number of neighbors is therefore equal to 4 for any node in the network.

C. Watts-Strogatz model graphs

The Watts-Strogatz model [START_REF] Watts | Collective dynamics of 'smallworld'networks[END_REF] is a graph generation model, possessing the small world property (the computation of the shortest path between two nodes is logarithmic). This method takes in parameters N the number of nodes, K the average degree of the nodes in the network and P the probability allowing to change the edges. The goal of the process is to start from a ring graph in order to process every edge of a node. Indeed, each edge can change recipient with the probability P passed as a parameter.

IV. BYZANTINES ADVERSARIES

In order to simulate possible attacks and predict critical security cases, three mentioned byzantine adversaries [START_REF] Capossele | Robustness and efficiency of leaderless probabilistic consensus protocols within byzantine infrastructures[END_REF] were implemented: These nodes are able to lie on every round of the process with a probability P lying . However, the opinion sent during the same round is always the same even though the queries come from different nodes.

B. Semi-Cautious adversaries

These nodes will not lie, however, they may not respond to a query, with a probability P silence . Thus delaying the process of convergence and reducing the number of accessible nodes in the network.

C. Berserk adversaries

This adversary is stronger than the previous two adversaries. It behaves similar to Cautious, except that it is able to provide different responses to different queries received in the same round. Thus, during the same round, it can send his true opinion, then lie and respond with a wrong opinion.

V. SIMULATION RESULTS

In this section we will present a selection of our extensive simulations related to the resilience of IOTA consensus algorithms with various adversaries and different network topologies. We use OMNet++ simulator enriched with the three topologies and the three adversaries models. We run our simulations on a physical machine with 8 cores 16 threads and 16 GB RAM. We also run simulations in a virtual machine with 6 VCPU cores and 16 GB RAM.

Our extensive simulations show that there is no difference between Berserk adversaries and Cautious adversaries in terms of convergence rate. That is because, in long runs, both malicious nodes will give the same quantity of false information to their neighbors in average. If we consider M the number of rounds and X the number of queries that the malicious node will receive per round on average, a Cautious adversary will lie in M 2 rounds which makes an average quantity of lies of

M ×X 2 .
As for the Berserk adversary, it will lie in average of X 2 regardless of the round which also makes a total of M X 2 lies. In the following, we will detail only the resilience of Fast Probabilistic Consensus and Cellular Consensus to cautious and semi-cautious adversaries.

A. Fast Probabilistic Consensus resilience

We list here the basic parameters involved in Fast Probabilistic Consensus. We first studied the impact of the number of nodes, N , and the initial opinion distribution, P 0 on the convergence rate. In Figure 3, we show the convergence rate function to the initial division probability P 0 in each topology and for different network sizes from N = 49 to N = 1024. In Torus, with small network sizes, the convergence rate is 100% regardless of the value of P 0 . While in Grid, even with small network sizes, the convergence rate drops drastically when P 0 ∈ [0.35, 0.75]. In terms of network size, for the Grid and the Torus topologies, the more nodes are in network, the lower convergence rate is. Hence, Fast Probabilistic Consensus is not scalable. On the contrary, the Watts-Strogatz topology seems to converge well regardless of the number of nodes change. 2) Convergence rate according to the initial division probability P 0 for different average number of neighbors k in a Watts-Strogatz graph without malicious nodes: In Figure 4, we adjust the average number of neighbors of each node, K, from 4 to 20. As we can see, if a node has more neighbors, it should converge more easily towards the majority opinion of the network. For K = 20, the network always converges, however, the network had already a good convergence rate with K = 4. This implies that the number of direct neighbors of a node in FPC does not mainly affect the convergence rate. 3) Convergence rate according to the initial division probability P 0 for different number of rounds M without malicious nodes: Figure 5 shows how the number of rounds can affect the convergence rate by setting M from 10 to 50. We can observe that from 20 rounds to 50 rounds, there is no noteworthy difference, that means that for all topologies, 20 rounds is enough to get convergence. In further simulations, we kept 30 rounds just to be sure that the network will have enough time to converge (if it converges). Interestingly, for the rest of simulations, even we introduce adversaries, increasing the execution round will not help at all. ) Convergence rate according to the initial division probability P 0 for different network sizes, with 33% Cautious Adversaries: We inspected first the Fast Probabilistic Consensus resilience when 33% of total nodes in the network (N/3) are Cautious adversaries. This is motivated by the fact that N/3 resilience is the upper bound in terms of Byzantine resilience for consensus protocols.

we observed that in Figure 6, the convergence rate drops below 5% for all studied topologies regardless of the initial opinion distribution P 0 or the network size N . This is due to the fact that the Cautious adversaries can spread freely their lies across the network when nodes ask their opinions via the Fast Probabilistic Consensus queries. Honest nodes therefore cannot make a correct decision. In the following simulations, we fix the network size by choosing a reasonable medium network size, N = 225 and study the resilience of Fast Probabilistic Consensus to various percentages of Cautious adversaries. ) Convergence rate according to the initial division probability P 0 for different percentages of Cautious adversaries P malicious : In Figure 7, we vary the percentage of malicious nodes from 10% up to 50%. We can clearly notice a huge difference between P malicious = 0% and P malicious = 10%. When the network is corrupted with only 10% of Cautious adversaries for both Grid and Torus, the convergence rate drops to 10% and 20%, respectively. Watts-Strogatz resists up to 10 % Cautious adversaries with a convergence rate of around 80%. Even though Watts-Strogatz has a better resilience to Cautious than Grid and Torus, the convergence rate is catastrophic for all topologies starting with 20% of malicious nodes.

6) Convergence rate according to the initial division probability P 0 for different network sizes, with 33% Semi-Cautious Adversaries: We an observe from Figure 8 that for each topology, Semi-Cautious adversaries do not have an important impact. It seems that the curves are the same as when there is no malicious nodes. This can be explained by the fact that Semi-Cautious adversaries do not lie, they just do not answer sometimes which does not corrupt the network. In theory, it should only slow down the network so the next graphs that we will see are going to make the percentage of Semi-Cautious vary and see if a big amount makes a difference or not.

7) Convergence rate according to the initial division probability P 0 for different percentages of Semi-Cautious adversaries P malicious : When the percentage of Semi-Cautious adversaries increases from 10% to 50%, we do not see any notable difference in terms of convergence rate in Figure 9, apart from a slight decrease. This means that the number of Semi-Cautious adversaries in the network does not affect the convergence, hence we can conclude on the fact that these types of malicious nodes are the least dangerous for the network. It also shows that if some devices are slow and they can't respond to the queries in time (this type of behavior is similar to being a Semi-Cautious adversary), the network will not be put at disadvantage because of these devices.

B. Cellular Consensus results

Cellular Consensus (CC) has been evaluated using the same base configuration as Fast Probabilistic Consensus (FPC): 1) Convergence rate according to the initial division probability P 0 for different network sizes N , without malicious nodes: Through Figure 10, for the three topologies, we observe that the number of nodes, N , is still an important parameter for the convergence of the network as in the case of Fast Probabilistic Consensus. Indeed, when the number of nodes increases, the convergence rate decreases for both Grid and Torus topologies. However, in terms of initial option distribution P 0 , Cellular Consensus on Grid and Torus become more sensitive compared with Fast Probabilistic Consensus. Convergence rates decrease drastically when P 0 ∈ [0.25, 0.85] and never pass 50%. In Watts-Strogatz model, Cellular Consensus has similar behavior as Fast Probabilistic Consensus and has a good scalability. We conclude here that without malicious nodes, the higher the average number of neighbors is, the better the convergence rate will be.

3) Convergence rate according to the initial division probability P 0 for different network sizes N , with 33% Cautious Adversaries: First we study the convergence rate when N/3 (33%) nodes are Cautious adversaries. When we introduce Cautious adversaries in Cellular Consensus, we observe, in Figure 12, the same tendency as without malicious nodes by adjusting network size N however, the convergence rate is much lower. Indeed when the malicious nodes are detected, they are immediately blacklisted which means that some nodes lose neighbors, which leads to this decrease. However, compared with Fast Probabilistic Consensus, Cellular Consensus has a better resilience to Cautious Adversaries since it can detect malicious nodes and block them once detected. In the sequel, we fix the network size N = 225 as in Fast Probabilistic Consensus. 5) Convergence rate according to the initial division probability P 0 for different percentages of Cautious adversaries P malicious : When P malicious varies, we observed in 14 a decrease in the convergence rate. We observe that the results obtained with Torus are better than those in Grid. As for the results obtained with the Watts-Strogatz topology, they are consistently good and sometimes even excellent with K = 20.

6) Convergence rate according to the initial division probability P 0 for different network sizes N , with 33% Semi-Cautious Adversaries: When we introduce Semi-Cautious adversaries in the network, we observe in Figure 15 that when 0, 3 ≤ P 0 ≤ 0, 7, the convergence rate is the same than the case without malicious nodes for 2D Grid and Torus topologies. In addition, for Watts-Strogatz topology, when P 0 is in this interval, we have better results that without byzantines nodes. This phenomenon is explained by the fact that when a network is in disagreement, the nodes which do not respond, make it possible to take a decision on the opinion, and therefore to promote convergence. It seems that this process, appears only when the average number of neighbors is high. However, when 0 ≤ P 0 < 0, 3 or 0, 7 < P 0 ≤ 1, the convergence rate is lower than normal, which seems quite logical. Indeed, when the network is in agreement, the Semi-Cautious adversaries disturb him and cause a drop of the convergence rate. The results in Figure 16 show that when the average number of neighbors is low, K <= 4, the convergence rate is relatively low for 0 ≤ P 0 < 0, 3 or 0, 7 < P 0 ≤ 1 and similar to a network without malicious nodes for 0, 3 ≤ P 0 ≤ 0, 7. When the average number of neighbors is higher, the results can be better. Same as in Cautious case, by adjusting K, Watts-Strogatz might have a good resilience to this type of attack.

8) Convergence rate according to the initial division probability P 0 for different percentages of Semi-Cautious adversaries P malicious : When we vary the P malicious of Semi-Cautious adversary in Figure 17, we observe a decrease in convergence which seems quite logical. By comparing the different topologies, we observe that the results obtained with the Torus are better than those obtained with the 2D grid. As for the results obtained with the Watts-Strogatz topology, they are consistently excellent with k = 20. As we have seen in the case of Cautious adversaries, we see that when the number of byzantines nodes is low (0% ≤ P malicious ≤ 10%) or high (30% ≤ P malicious ≤ 50%) the convergence rate does not evolve a lot.

VI. CONCLUSION

In this paper we extensively evaluate the resilience of Fast Probabilistic Consensus and Cellular Consensus (two agreement building blocks introduced for IOTA blockchain [START_REF] Serguei | The coordicide[END_REF]). Our evaluation focused on the impact of the underlying network topology on the convergence rate of the algorithms and their resilience to various adversaries (cautious, semicautious and Berserk). We showed that the initial opinion state distribution of each node and the total number of nodes in the network will seriously affect the convergence results, especially in 2D Grid and Torus topologies. These effects will not be alleviated by increasing the run time.

In Fast Probabilistic Consensus, Cautious and Berserk adversaries will cause serious convergence issues even with low power adversaries. However, semi-cautious adversaries seem to not be a menace.

In the Cellular Consensus, all three adversaries have an impact on the convergence, but none of them is as serious as in the case of Fast Probabilistic Consensus.

Interestingly, the Watts-Strogatz topology when the density is properly adjusted can even eliminate the effects of adversaries.

We plan to continue this work by giving mathematical modeling and explaining our results formally.

Fig. 1 .

 1 Fig. 1. Transformation of a 2D grid into a torus

Fig. 2 .

 2 Fig. 2. Watts-Strogatz method process

•Fig. 3 .

 3 Fig.3. Convergence rate ccording to the initial division probability P 0 for different network sizes, without malicious nodes 1) Convergence rate according to the initial division probability P 0 for different network sizes without malicious nodes: We first studied the impact of the number of nodes, N , and the initial opinion distribution, P 0 on the convergence rate. In Figure3, we show the convergence rate function to the initial division probability P 0 in each topology and for different network sizes from N = 49 to N = 1024. In Torus, with small network sizes, the convergence rate is 100% regardless of the value of P 0 . While in Grid, even with small network sizes, the convergence rate drops drastically when P 0 ∈ [0.35, 0.75]. In terms of network size, for the Grid and the Torus topologies, the more nodes are in network, the lower convergence rate is. Hence, Fast Probabilistic Consensus is not scalable. On the

Fig. 4 .

 4 Fig. 4. Convergence rate according to the initial division probability P 0 for different average number of neighbors K in a Watts-Strogatz without malicious nodes

Fig. 5 .

 5 Fig. 5. Convergence rate according to the initial division probability P 0 for different number of rounds M without malicious nodes

Fig. 6 .

 6 Fig.6. Convergence rate according to the initial division probability P 0 for different network sizes, with 33% Cautious Adversaries

4

 4

Fig. 7 .

 7 Fig. 7. Convergence rate according to the initial division probability P 0 for different percentages of Cautious adversaries P malicious

5

 5

Fig. 8 .

 8 Fig. 8. Convergence rate according to the initial division probability P 0 for different network sizes, with 33% Semi-Cautious Adversaries

• K = 10 ,Fig. 10 .

 1010 Fig. 10. Convergence rate according to the initial division probability P 0 for different network sizes N , without malicious nodes

Fig. 11 .

 11 Fig. 11. Convergence rate according to the initial division probability P 0 for different average number of neighbors K, in Watts-Strogatz graph without malicious nodes2) Convergence rate according to the initial division probability P 0 for different average number of neighbors K, in Watts-Strogatz graph without malicious nodes: Contrary to Fast Probabilistic Consensus, in Figure11, we show that adjusting K for Watts-Strogatz topology impacts clearly the convergence rate in Cellular Consensus: when K gets smaller, Watts-Strogatz topology becomes more sensitive to the initial opinion distribution P 0 and networks size N . We therefore test different K values for the Watts-Strogatz model to evaluate the resilience of Cellular Consensus to Cautious and Semi-Cautious Adversaries. Recall that Cellular Consensus is based on the communication between neighbors and that we have the average number of neighbors K < 4 for Grid, K = 4 for Torus and K = 10 for Watts-Strogatz in our simulations. We conclude here that without malicious nodes, the higher the average number of neighbors is, the better the convergence rate will be.3) Convergence rate according to the initial division probability P 0 for different network sizes N , with 33% Cautious Adversaries: First we study the convergence rate when N/3 (33%) nodes are Cautious adversaries. When we introduce Cautious adversaries in Cellular Consensus, we observe, in Figure12, the same tendency as without malicious nodes by adjusting network size N however, the convergence rate is much lower. Indeed when the malicious nodes are detected, they are immediately blacklisted which means that some nodes lose neighbors, which leads to this decrease. However, compared with Fast Probabilistic Consensus, Cellular Consensus has a better resilience to Cautious Adversaries since it can detect malicious nodes and block them once detected. In the sequel, we fix the network size N = 225 as in Fast Probabilistic Consensus.4) Convergence rate according to the initial division probability P 0 for different average number of neighbors K, in Watts-Strogatz graph with 33% Cautious adversaries: In the following we study the convergence rate of Cellular Consensus in Watts-Strogatz model when varying K and considering N/3 (33%) Cautious adversaries. In Figure13, the results

4 )

 4 Fig. 12. Convergence rate according to the initial division probability P 0 for different network sizes N , with 33% Cautious Adversaries

Fig. 14 .

 14 Fig. 14. Convergence rate ccording to the initial division probability P 0 for different percentages of Cautious adversaries P malicious

Fig. 16 .

 16 Fig. 16. Convergence rate according to the initial division probability P 0 for different average number of neighbors K, in Watts-Strogatz graph with Semi-Cautious adversaries 7) Convergence rate according to the initial division probability P 0 for different average number of neighbors K, in Watts-Strogatz graph with 33% Semi-Cautious adversaries:The results in Figure16show that when the average number of neighbors is low, K <= 4, the convergence rate is relatively low for 0 ≤ P 0 < 0, 3 or 0, 7 < P 0 ≤ 1 and similar to a network without malicious nodes for 0, 3 ≤ P 0 ≤ 0, 7. When the average number of neighbors is higher, the results can be better. Same as in Cautious case, by adjusting K, Watts-Strogatz might have a good resilience to this type of attack.8) Convergence rate according to the initial division probability P 0 for different percentages of Semi-Cautious adversaries P malicious : When we vary the P malicious of Semi-Cautious adversary in Figure17, we observe a decrease in convergence which seems quite logical. By comparing the different topologies, we observe that the results obtained with the Torus are better than those obtained with the 2D grid. As for the results obtained with the Watts-Strogatz topology, they are consistently excellent with k = 20. As we have seen in the case of Cautious adversaries, we see that when the number of byzantines nodes is low (0% ≤ P malicious ≤ 10%) or high (30% ≤ P malicious ≤ 50%) the convergence rate does not evolve a lot.

Fig. 17

 17 Fig. 17. Convergence rate according to the initial division probability P 0 for different percentages of Semi-Cautious adversaries P malicious

  Fig. 17. Convergence rate according to the initial division probability P 0 for different percentages of Semi-Cautious adversaries P malicious