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IBM Storage
Why new off-chain storage is required for
blockchains
Document version 4.1
© Copyright International Business Machines Corporation 2018.
US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule
Contract with IBM Corp.
Why new off-chain storage is needed for blockchains
1
Contents
Why new off-chain storage is required for blockchains...................................................... i
Contents............................................................................................................................ 1
List of figures..................................................................................................................... 3
Introduction ....................................................................................................................... 4
1 What a blockchain is, and what it is not ................................................................ 4
1.1 Costs of blockchain technologies .............................................................. 4
1.1.1 Hyperledger costs.....................................................................................4
1.1.2 Non-permissioned blockchain costs .........................................................5
1.1.3 Results......................................................................................................5
1.2 What then is Offchain Data?...................................................................... 5
1.3 All of this data must be shared .................................................................. 5
1.4 On-chain storage calculations ................................................................... 6
1.4.1 On-chain blockchain assumptions ............................................................6
1.4.2 Calculation ................................................................................................6
2 The issues with using existing data stores ............................................................ 7
2.1 Access issues............................................................................................ 7
2.2 Security issues .......................................................................................... 7
2.3 Cryptographic issues................................................................................. 7
2.4 Performance issues................................................................................... 7
2.5 Success issues.......................................................................................... 7
2
2.5.1 Off-chain data assumptions ......................................................................8
2.5.2 Calculation ................................................................................................8
2.5.3 Storage required to save documents........................................................8
2.6 New businesses ........................................................................................ 9
2.7 New business processes require new data organization .......................... 9
2.8 GDPR and granulation of data .................................................................. 9
3 The solution........................................................................................................... 9
Why new off-chain storage is needed for blockchains
3
List of figures
Figure 1: Example blockchain structure............................................................................................ 4
Figure 2: Cost per month for blockchains......................................................................................... 5
Figure 3: Example off-chain data...................................................................................................... 5
Figure 4: Example blockchain data flows ......................................................................................... 6
4
INTRODUCTION
In pursuing the storage point of view for blockchain technology, the test team has come up against a
recurrent theme. This recurrent theme is that no new storage is needed for off-chain data as most
companies are already using the data to be utilized by the blockchain. Because the companies are
already using the data, it already exists somewhere in their storage environment and only needs to
be referenced by the blockchain application programming interface (API). This paper examines this
to see if it is valid.
1 What a blockchain is, and what it is not
A blockchain is a distributed ledger that is utilized by a consortium of related users. These users
might be a group of banks, a group of lending institutions, or a polyglot of food providers. Each will
have a full copy of the distributed ledger with its links to any off-chain data. The off-chain data must
be sharable and accessible for the concept of a distributed ledger to work.
Figure 1: Example blockchain structure
1.1 Costs of blockchain technologies
The same calculation to deliver the amount of storage can also be applied to the cost of various
blockchain technologies. Using published cost per transaction data for bitcoin and Ethereum, you
can compare this to a five-node IBM Hyperledger system.
1.1.1 Hyperledger costs
The current base enterprise-level cost for an IBM Hyperledger is USD 1000 per month plus an
additional USD 1000 per active node bringing the cost to USD 6000 per month. This does not
include other software as a service (SaaS) costs that the project may incur as those will vary
between projects.
Why new off-chain storage is needed for blockchains
5
1.1.2 Non-permissioned blockchain costs
At the time of this writing, the cost per transaction for bitcoin is USD 1.30 per transaction. However,
this might change based on the cost of the underlying bitcoin cryptocurrency. The cost per Ethereum
transaction is USD 0.25 per transaction, and this again depends on the cost of the underlying Ether
cryptocurrency.
1.1.3 Results
The costs for non-permissioned blockchain vary by transaction rate and the current value of the
underlying cryptocurrency. The cost of the permissioned blockchain such as Hyperledger vary by
number of nodes and the amount of SaaS used in the application. This results in a fixed cost per
month for permissioned blockchain, but costs per month for non-permissioned could vary widely.
Based on these charges per transaction, the cost for using the various blockchain platforms at the
current cost per transaction is easily calculated.
Figure 2: Cost per month for blockchains
As shown in Figure 2, the cost of the various non-permissioned blockchains such as bitcoin and
Ethereum get excessive beyond, or even at, a low transaction per second rates.
1.2 What then is Offchain Data?
Off-chain data is any non-transactional data that is too large to be stored in the blockchain efficiently,
or, requires the ability to be changed or deleted. Figure 3 shows examples of offchain data types.
Figure 3: Example off-chain data
1.3 All of this data must be shared
For example, a blockchain is not a silo application where business A sees only business A’s data.
This is where the belief that data reuse from existing systems seems to have root. To be on the
blockchain, or referenced by the blockchain, the data must be shared among other members of the
consortium. Figure 4 is a graphic representation of an extended data set of offchain data on various
peer-nodes.
6
Figure 4: Example blockchain data flows
1.4 On-chain storage calculations
Given a basic understanding of storage and some basic understanding of how blockchain stores
data, you can derive a back-of-the-envelope calculation on how much storage is required for
Hyperledger blockchain.
1.4.1 On-chain blockchain assumptions
The following assumptions are made in the on-chain storage calculations:
1. All calculations will be in actual bytes, that is 1024 is 1 KB.
2. All hyperledger blocks are 1 megabyte (MB)
3. Only hash, signature, or key data is stored in the blockchain
4. The company works 8 hour per day
5. The company has roughly 240 processing days per year and the number of transactions per
second is averaged over those days only (allows for holidays and weekends.)
6. Currently bitcoin is storing about 1400 basic transactions per MB block. Hyper ledger has
larger headers and a more robust transaction size so 1000 transactions per block was
selected. Blockchain transactions currently run about 5 KB each which equates to 205 TPS.
1.4.2 Calculation
Using the above assumptions, the calculation to find out the amount of storage required per TPS
becomes:
(1 TPS/1000 TB)*1024 KB*3500 sec/hr*8 hr/day*240 days/year=
7,077,888 KB of data per transaction per year
Why new off-chain storage is needed for blockchains
7
6,912 MB = 6.75 GB = .00659 TB/transaction/yr
Because the transaction sizes might change according to the type of transaction being stored in the
blockchain, the chart has been prepared using various transaction sizes.
2 The issues with using existing data stores
There are several key issues with using existing data stores with new blockchain-based projects.
2.1 Access issues
What would happen if instead of providing an isolated data store that holds the off-chain reference
data, each of the consortium members had to provide links to their existing data stores? Each
consortium member would have to finance the programming of the various data connectors,
encryption, and security applications needed. While it might be perfectly okay for fellow consortium
members to see document XYZ, it is not for them to possibly see document ZZX which is not on the
blockchain.
2.2 Security issues
When using existing data stores, there is a high probability of accidental disclosure of confidential
data. You must also consider that the very shared nature of the blockchain environment might lead
to deliberate hacking into the consortium members individual data stores by a malicious actor
facilitated by the blockchain access paths.
2.3 Cryptographic issues
Even if an existing data store could be used, it needs to be modified to store the required hash,
cryptographic codes, and keys needed to provide proof to the blockchain that the data has not been
modified since last access. For already active data stores that are modified frequently, this
recalculation and storing of hash and cryptographic keys could become onerous.
2.4 Performance issues
Another issue with using existing data stores is the problem with getting uniform response times from
multiple, independent, data stores using different database technologies, storage hardware, and
server capabilities across the consortium. A unification of hardware, software, and data store
technology is required at the consortium level to meet the needed service levels.
2.5 Success issues
Sometimes, a project’s biggest problem is that it succeeds too well. A recent blockchain
development in the Hyperledger environment went live and it exceeded its planned growth by 300%
leading to performance and storage issues. The need for successful projects to have elastic storage
(that is scalable and secure) is clear. If existing data stores are used, how will the success of a
blockchain application that is parasitic on a data store affect the existing application and its
performance? How will the influx of new data, possibly not linked in the same manner as far as
foreign keys and other relationships affect the existing data store? These questions must be
8
addressed before they cause existing applications to fail or give incorrect results caused by the
encroachment of the blockchain data.
Let’s look at a simple calculation to see what the effect on storage volume of a successful blockchain
project using offchain storage would entail. Our definition of success would be an increase in the
transactions per second, so going from 1 to 10 to 100 or higher means the project is more
successful. For this example, we will assume that every third transaction results in the generation of
an offchain document. We will use an average document size, so the type of document doesn’t
matter for this example. We will also assume that the business is not a 24x7 operation open 364
days a year, however, it is a simple extrapolation should you iwsh to see the results form that type of
operation.
Because non-transaction data, such as pictures, contracts, PDF, personal information and so on
should not be stored in the actual blockchain, some form of off-chain or sideDB storage is required.
Generally, off-chain data is unstructured. A hash or signature for the off-chain item is generated and
that is what is stored in the blockchain. The actual item is either stored in the cloud or in near-cloud
storage. It is expected that the required storage for off-chain data will exceed the needs of
blockchain storage.
2.5.1 Off-chain data assumptions
The following assumptions are made in the off-chain storage calculations:
1. Each transaction does not produce a document. For calculation, a ratio of three
transactions for each document is used so a figure of 0.3 is used.
2. 8 hours per day is the workday.
3. 240 days per year are actual processing days.
4. Indexing and other storage requirements are not included.
2.5.2 Calculation
Using the assumptions made in the previous section, the calculation becomes:
1 TPS*0.3 doc/transaction*3600 sec/hr*8 hr/day*240 day/yr=DPY (documents per year)
= 0.3*3600*8*240=814,301 DPY for 1 TPS
2.5.3 Storage required to save documents
According to current references, 1,000,000 documents (of mixed formats) requires 333 GB of
storage. This means, 814,301 documents will require:
1000000X/(333*814301) = GB/year/TPS
X = (333*814,301)/1,000,000
= 271 GB/TPS/year = 0.264 TiB/year/TPS
So, as expected, you can see that if the transactions produce one document for every three
transactions recorded, as the transactions per second increase, the storage required soon exceeds
those required for the primary blockchain by a couple orders of magnitude.
Why new off-chain storage is needed for blockchains
9
2.6 New businesses
All new disruptive technologies bring new businesses. New businesses do not have existing data
stores. So new storage is required for them to participate in the blockchain revolution.
2.7 New business processes require new data organization
Blockchain business application solutions often lead to re-engineering of business processes. For example,
in payments (multi-industry), the business workflow might change to take advantage of the potential
streamlining available in a blockchain community of participants. This could significantly transform an
institution's payment systems, many of which have been in place for decades. Re-engineering may also be
required to meet new performance standards, such as near real-time objectives. Most of the existing data
stores are based (usually loosely) on the relational model of interrelated tables of data connected by
primary and secondary key values. The tables are arranged in a way that the current application can
quickly and easily access it. The blockchain requires a different form of data model which is more
data warehouse-like than relational where the blockchain acts as the central fact table and the off-
chain storage acts as the dimension table. The blockchain only stores the facts (totals, aggregations,
transaction details), that result from or generate the intersection of data (documents, pictures, PDF
files, tabular data) stored offchain. This new data organization requirement results in inefficiencies,
need for re-organization, and changes to the way existing data stores store information.
2.8 GDPR and granulation of data
General Data Protection Regulation (GDPR) in Europe and companies doing business in Europe will
also drive the need for new off-chain storage in blockchain applications. It is recommended to store
sensitive information offchain so that you can delete if need be.
3 The solution
The only way to fully, uniformly, and securely control access to off-chain data and mitigate all of the
issues mentioned earlier, is to create a shared network of storage and server resources that is
designed to provide the required security and shared environment for the blockchain consortium
members. Each time a data object is accessed it must be verified using stored hash values proving
that it is the same object as the one that was stored initially. Each object should be stored in more
than one data store to make sure that loss of one node does not result in significant data loss as
long as the node is down. Also, once a node rejoins the consortium after recover, a mechanism to
synchronize the off-chain references and rebalance the off-chain data is also be required. These
requirements and few others drive the need for new blockchain dedicated off-chain storage assets
and new storage access paradigms.
The storage calculations show that unless the blockchain is being used for low volume,
cryptocurrency-based transactions, it is recommended that a permissioned blockchain (such as IBM
Hyperledger) with a fixed price per month be utilized.
10
®
© Copyright IBM Corporation 2018
IBM United States of America
Produced in the United States of America
US Government Users Restricted Rights - Use, duplication or disclosure restricted by GSA ADP Schedule Contract with
IBM Corp.
IBM may not offer the products, services, or features discussed in this document in other countries. Consult your local IBM
representative for information on the products and services currently available in your area. Any reference to an IBM
product, program, or service is not intended to state or imply that only that IBM product, program, or service may be used.
Any functionally equivalent product, program, or service that does not infringe any IBM intellectual property right may be
used instead. However, it is the user's responsibility to evaluate and verify the operation of any non-IBM product, program,
or service.
IBM may have patents or pending patent applications covering subject matter described in this document. The furnishing of
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Why new off-chain storage is needed for blockchains
11
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0045cbf22d80b68f

  • 1. IBM Storage Why new off-chain storage is required for blockchains Document version 4.1
  • 2. © Copyright International Business Machines Corporation 2018. US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp.
  • 3. Why new off-chain storage is needed for blockchains 1 Contents Why new off-chain storage is required for blockchains...................................................... i Contents............................................................................................................................ 1 List of figures..................................................................................................................... 3 Introduction ....................................................................................................................... 4 1 What a blockchain is, and what it is not ................................................................ 4 1.1 Costs of blockchain technologies .............................................................. 4 1.1.1 Hyperledger costs.....................................................................................4 1.1.2 Non-permissioned blockchain costs .........................................................5 1.1.3 Results......................................................................................................5 1.2 What then is Offchain Data?...................................................................... 5 1.3 All of this data must be shared .................................................................. 5 1.4 On-chain storage calculations ................................................................... 6 1.4.1 On-chain blockchain assumptions ............................................................6 1.4.2 Calculation ................................................................................................6 2 The issues with using existing data stores ............................................................ 7 2.1 Access issues............................................................................................ 7 2.2 Security issues .......................................................................................... 7 2.3 Cryptographic issues................................................................................. 7 2.4 Performance issues................................................................................... 7 2.5 Success issues.......................................................................................... 7
  • 4. 2 2.5.1 Off-chain data assumptions ......................................................................8 2.5.2 Calculation ................................................................................................8 2.5.3 Storage required to save documents........................................................8 2.6 New businesses ........................................................................................ 9 2.7 New business processes require new data organization .......................... 9 2.8 GDPR and granulation of data .................................................................. 9 3 The solution........................................................................................................... 9
  • 5. Why new off-chain storage is needed for blockchains 3 List of figures Figure 1: Example blockchain structure............................................................................................ 4 Figure 2: Cost per month for blockchains......................................................................................... 5 Figure 3: Example off-chain data...................................................................................................... 5 Figure 4: Example blockchain data flows ......................................................................................... 6
  • 6. 4 INTRODUCTION In pursuing the storage point of view for blockchain technology, the test team has come up against a recurrent theme. This recurrent theme is that no new storage is needed for off-chain data as most companies are already using the data to be utilized by the blockchain. Because the companies are already using the data, it already exists somewhere in their storage environment and only needs to be referenced by the blockchain application programming interface (API). This paper examines this to see if it is valid. 1 What a blockchain is, and what it is not A blockchain is a distributed ledger that is utilized by a consortium of related users. These users might be a group of banks, a group of lending institutions, or a polyglot of food providers. Each will have a full copy of the distributed ledger with its links to any off-chain data. The off-chain data must be sharable and accessible for the concept of a distributed ledger to work. Figure 1: Example blockchain structure 1.1 Costs of blockchain technologies The same calculation to deliver the amount of storage can also be applied to the cost of various blockchain technologies. Using published cost per transaction data for bitcoin and Ethereum, you can compare this to a five-node IBM Hyperledger system. 1.1.1 Hyperledger costs The current base enterprise-level cost for an IBM Hyperledger is USD 1000 per month plus an additional USD 1000 per active node bringing the cost to USD 6000 per month. This does not include other software as a service (SaaS) costs that the project may incur as those will vary between projects.
  • 7. Why new off-chain storage is needed for blockchains 5 1.1.2 Non-permissioned blockchain costs At the time of this writing, the cost per transaction for bitcoin is USD 1.30 per transaction. However, this might change based on the cost of the underlying bitcoin cryptocurrency. The cost per Ethereum transaction is USD 0.25 per transaction, and this again depends on the cost of the underlying Ether cryptocurrency. 1.1.3 Results The costs for non-permissioned blockchain vary by transaction rate and the current value of the underlying cryptocurrency. The cost of the permissioned blockchain such as Hyperledger vary by number of nodes and the amount of SaaS used in the application. This results in a fixed cost per month for permissioned blockchain, but costs per month for non-permissioned could vary widely. Based on these charges per transaction, the cost for using the various blockchain platforms at the current cost per transaction is easily calculated. Figure 2: Cost per month for blockchains As shown in Figure 2, the cost of the various non-permissioned blockchains such as bitcoin and Ethereum get excessive beyond, or even at, a low transaction per second rates. 1.2 What then is Offchain Data? Off-chain data is any non-transactional data that is too large to be stored in the blockchain efficiently, or, requires the ability to be changed or deleted. Figure 3 shows examples of offchain data types. Figure 3: Example off-chain data 1.3 All of this data must be shared For example, a blockchain is not a silo application where business A sees only business A’s data. This is where the belief that data reuse from existing systems seems to have root. To be on the blockchain, or referenced by the blockchain, the data must be shared among other members of the consortium. Figure 4 is a graphic representation of an extended data set of offchain data on various peer-nodes.
  • 8. 6 Figure 4: Example blockchain data flows 1.4 On-chain storage calculations Given a basic understanding of storage and some basic understanding of how blockchain stores data, you can derive a back-of-the-envelope calculation on how much storage is required for Hyperledger blockchain. 1.4.1 On-chain blockchain assumptions The following assumptions are made in the on-chain storage calculations: 1. All calculations will be in actual bytes, that is 1024 is 1 KB. 2. All hyperledger blocks are 1 megabyte (MB) 3. Only hash, signature, or key data is stored in the blockchain 4. The company works 8 hour per day 5. The company has roughly 240 processing days per year and the number of transactions per second is averaged over those days only (allows for holidays and weekends.) 6. Currently bitcoin is storing about 1400 basic transactions per MB block. Hyper ledger has larger headers and a more robust transaction size so 1000 transactions per block was selected. Blockchain transactions currently run about 5 KB each which equates to 205 TPS. 1.4.2 Calculation Using the above assumptions, the calculation to find out the amount of storage required per TPS becomes: (1 TPS/1000 TB)*1024 KB*3500 sec/hr*8 hr/day*240 days/year= 7,077,888 KB of data per transaction per year
  • 9. Why new off-chain storage is needed for blockchains 7 6,912 MB = 6.75 GB = .00659 TB/transaction/yr Because the transaction sizes might change according to the type of transaction being stored in the blockchain, the chart has been prepared using various transaction sizes. 2 The issues with using existing data stores There are several key issues with using existing data stores with new blockchain-based projects. 2.1 Access issues What would happen if instead of providing an isolated data store that holds the off-chain reference data, each of the consortium members had to provide links to their existing data stores? Each consortium member would have to finance the programming of the various data connectors, encryption, and security applications needed. While it might be perfectly okay for fellow consortium members to see document XYZ, it is not for them to possibly see document ZZX which is not on the blockchain. 2.2 Security issues When using existing data stores, there is a high probability of accidental disclosure of confidential data. You must also consider that the very shared nature of the blockchain environment might lead to deliberate hacking into the consortium members individual data stores by a malicious actor facilitated by the blockchain access paths. 2.3 Cryptographic issues Even if an existing data store could be used, it needs to be modified to store the required hash, cryptographic codes, and keys needed to provide proof to the blockchain that the data has not been modified since last access. For already active data stores that are modified frequently, this recalculation and storing of hash and cryptographic keys could become onerous. 2.4 Performance issues Another issue with using existing data stores is the problem with getting uniform response times from multiple, independent, data stores using different database technologies, storage hardware, and server capabilities across the consortium. A unification of hardware, software, and data store technology is required at the consortium level to meet the needed service levels. 2.5 Success issues Sometimes, a project’s biggest problem is that it succeeds too well. A recent blockchain development in the Hyperledger environment went live and it exceeded its planned growth by 300% leading to performance and storage issues. The need for successful projects to have elastic storage (that is scalable and secure) is clear. If existing data stores are used, how will the success of a blockchain application that is parasitic on a data store affect the existing application and its performance? How will the influx of new data, possibly not linked in the same manner as far as foreign keys and other relationships affect the existing data store? These questions must be
  • 10. 8 addressed before they cause existing applications to fail or give incorrect results caused by the encroachment of the blockchain data. Let’s look at a simple calculation to see what the effect on storage volume of a successful blockchain project using offchain storage would entail. Our definition of success would be an increase in the transactions per second, so going from 1 to 10 to 100 or higher means the project is more successful. For this example, we will assume that every third transaction results in the generation of an offchain document. We will use an average document size, so the type of document doesn’t matter for this example. We will also assume that the business is not a 24x7 operation open 364 days a year, however, it is a simple extrapolation should you iwsh to see the results form that type of operation. Because non-transaction data, such as pictures, contracts, PDF, personal information and so on should not be stored in the actual blockchain, some form of off-chain or sideDB storage is required. Generally, off-chain data is unstructured. A hash or signature for the off-chain item is generated and that is what is stored in the blockchain. The actual item is either stored in the cloud or in near-cloud storage. It is expected that the required storage for off-chain data will exceed the needs of blockchain storage. 2.5.1 Off-chain data assumptions The following assumptions are made in the off-chain storage calculations: 1. Each transaction does not produce a document. For calculation, a ratio of three transactions for each document is used so a figure of 0.3 is used. 2. 8 hours per day is the workday. 3. 240 days per year are actual processing days. 4. Indexing and other storage requirements are not included. 2.5.2 Calculation Using the assumptions made in the previous section, the calculation becomes: 1 TPS*0.3 doc/transaction*3600 sec/hr*8 hr/day*240 day/yr=DPY (documents per year) = 0.3*3600*8*240=814,301 DPY for 1 TPS 2.5.3 Storage required to save documents According to current references, 1,000,000 documents (of mixed formats) requires 333 GB of storage. This means, 814,301 documents will require: 1000000X/(333*814301) = GB/year/TPS X = (333*814,301)/1,000,000 = 271 GB/TPS/year = 0.264 TiB/year/TPS So, as expected, you can see that if the transactions produce one document for every three transactions recorded, as the transactions per second increase, the storage required soon exceeds those required for the primary blockchain by a couple orders of magnitude.
  • 11. Why new off-chain storage is needed for blockchains 9 2.6 New businesses All new disruptive technologies bring new businesses. New businesses do not have existing data stores. So new storage is required for them to participate in the blockchain revolution. 2.7 New business processes require new data organization Blockchain business application solutions often lead to re-engineering of business processes. For example, in payments (multi-industry), the business workflow might change to take advantage of the potential streamlining available in a blockchain community of participants. This could significantly transform an institution's payment systems, many of which have been in place for decades. Re-engineering may also be required to meet new performance standards, such as near real-time objectives. Most of the existing data stores are based (usually loosely) on the relational model of interrelated tables of data connected by primary and secondary key values. The tables are arranged in a way that the current application can quickly and easily access it. The blockchain requires a different form of data model which is more data warehouse-like than relational where the blockchain acts as the central fact table and the off- chain storage acts as the dimension table. The blockchain only stores the facts (totals, aggregations, transaction details), that result from or generate the intersection of data (documents, pictures, PDF files, tabular data) stored offchain. This new data organization requirement results in inefficiencies, need for re-organization, and changes to the way existing data stores store information. 2.8 GDPR and granulation of data General Data Protection Regulation (GDPR) in Europe and companies doing business in Europe will also drive the need for new off-chain storage in blockchain applications. It is recommended to store sensitive information offchain so that you can delete if need be. 3 The solution The only way to fully, uniformly, and securely control access to off-chain data and mitigate all of the issues mentioned earlier, is to create a shared network of storage and server resources that is designed to provide the required security and shared environment for the blockchain consortium members. Each time a data object is accessed it must be verified using stored hash values proving that it is the same object as the one that was stored initially. Each object should be stored in more than one data store to make sure that loss of one node does not result in significant data loss as long as the node is down. Also, once a node rejoins the consortium after recover, a mechanism to synchronize the off-chain references and rebalance the off-chain data is also be required. These requirements and few others drive the need for new blockchain dedicated off-chain storage assets and new storage access paradigms. The storage calculations show that unless the blockchain is being used for low volume, cryptocurrency-based transactions, it is recommended that a permissioned blockchain (such as IBM Hyperledger) with a fixed price per month be utilized.
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