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      "body": "This article is about seeds. A seed can help you organizing the great number of public/privat key pairs you may need.\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Seed\n\nWhen using crypto currencies, then we quickly need to deal with a growing number of public/private key pairs. With a seed (random seed) we can avoid remembering all the used key pairs. \n\nA seed is a character string, for example:\n\"a90dcxvuw34df74cxl246o345qweratwemzesdfseszdfw332843sfmsacx\"\n\nNobody can keep in mind such a character string. Hence we use a mnemonic like:\n\"dog cat elephant first ape third Jim horse salamander ninth mouse rat\"\n\nFrom such a mnemonic we derive a seed. For example, by calculating a hash value from this character string. \n\nNow we have a seed. We use this seed and an additional number, let's take \"1\", as base number when creating a key pair. Another key pair we create bases on the seed and the number \"2\". And so on. This way we could, for example, create 100 key pairs. We do not need to remember the created key pairs. Neither the public nor the private keys. Both we can recreate from the seed and the numbers 1 to 100. And the seed we can derive from the mnemonic. We only need to remember the mnemonic.\n\nInstead of simply incrementing a number in practice some more complicate algorithm are used. For example, we could derive some number or string from the aimed intended use of the key pair. This result and the seed and maybe again incrementing numbers lead to our key pairs. Sometime this procedure is called a derivation path.\n\nThe application of a seed is described in the next chapter.\n\n# HD Wallet\n\nA HD wallet (hierarchical deterministic wallet) is not really a wallet but a technique to be used together with one of the different forms of wallets. With a HD wallet we can create key pairs based on a seed phrase. These key pairs we then use to receive cryptocurrency. \n\nExample: If we want to receive Bitcoins using the Bitcoin Core wallet we must create a new pair of public address and private key each time. The public address we tell the sender of the Bitcoins. We should make a backup of the private key instantly. We also could generate 100 pairs of public addresses and private keys at once. These we could use sequentially. Then we only need to make a backup of the keys after generating the 100 keys. But we still have to backup every used key. \n\nWith a HD wallet this is easier. A HD wallet generates the keys for us. And we do not need to memorize or note all private keys. We only need to memorize a seed phrase. From this seed phrase the HD wallet generates the private keys. The needed private keys we can import in our wallet. \n\nA HD wallet usually is a hardware wallet.",
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      "body": "This article is about seeds. A seed can help you organizing the great number of public/privat key pairs you may need.\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Seed\n\nWhen using crypto currencies, then we quickly need to deal with a growing number of public/private key pairs. With a seed (random seed) we can avoid remembering all the used key pairs. \n\nA seed is a character string, for example:\n\"a90dcxvuw34df74cxl246o345qweratwemzesdfseszdfw332843sfmsacx\"\n\nNobody can keep in mind such a character string. Hence we use a mnemonic like:\n\"dog cat elephant first ape third Jim horse salamander ninth mouse rat\"\n\nFrom such a mnemonic we derive a seed. For example, by calculating a hash value from this character string. \n\nNow we have a seed. We use this seed and an additional number, let's take \"1\", as base number when creating a key pair. Another key pair we create bases on the seed and the number \"2\". And so on. This way we could, for example, create 100 key pairs. We do not need to remember the created key pairs. Neither the public nor the private keys. Both we can recreate from the seed and the numbers 1 to 100. And the seed we can derive from the mnemonic. We only need to remember the mnemonic.\n\nInstead of simply incrementing a number in practice some more complicate algorithm are used. For example, we could derive some number or string from the aimed intended use of the key pair. This result and the seed and maybe again incrementing numbers lead to our key pairs. Sometime this procedure is called a derivation path.\n\nThe application of a seed is described in the next chapter.\n\n# HD Wallet\n\nA HD wallet (hierarchical deterministic wallet) is not really a wallet but a technique to be used together with one of the different forms of wallets. With a HD wallet we can create key pairs based on a seed phrase. These key pairs we then use to receive cryptocurrency. \n\nExample: If we want to receive Bitcoins using the Bitcoin Core wallet we must create a new pair of public address and private key each time. The public address we tell the sender of the Bitcoins. We should make a backup of the private key instantly. We also could generate 100 pairs of public addresses and private keys at once. These we could use sequentially. Then we only need to make a backup of the keys after generating the 100 keys. But we still have to backup every used key. \n\nWith a HD wallet this is easier. A HD wallet generates the keys for us. And we do not need to memorize or note all private keys. We only need to memorize a seed phrase. From this seed phrase the HD wallet generates the private keys. The needed private keys we can import in our wallet. \n\nA HD wallet usually is a hardware wallet.",
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      "body": "Encryption and digital signature are important foundations of the blockchain concept. This article explains the asymetric encryption and the digital signature used with blockchains.\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Encryption and Digital Signature\n\nBlockchain uses asymmetric encryption. There are different terms like asymmetric cryptography, public key cryptography or public/private key cryptography. These all address the approach explained now:\n* Hans wants to send a message to Katja. He wants to ensure only Katja to read the message.\n* First, they need to agree on an encryption method. This encryption method must be able to encrypt a message using the public key and to allow only the holder of the private key to decrypt the message. And the method must be able to generate the needed key pairs consisting of a public and a private key.\n* Usually the encryption method is given by the used application.\n* Katja generates a key pair and publishes her public key. The private key she keeps a secret. For the key generation a random private key is created first. The public key will be derived from the private key by a one-way function. To derive the private key from the public key is practically impossible.\n* Hans uses Katja's public key to encrypt the message and sends the encrypted message to Katja.\n* Katja receives the encrypted message and uses her private key to decrypt the message. \n\nWe can encrypt a message using the public key of someone else and only the holder of the matching private key is able to decrypt this message. Vice versa we can sign a message using our private key and anyone else can check the message for being unchanged by using our public key.\n\nBlockchain uses asymmetric encryption for example for crypto currencies.\n\nThis time Hans wants to send 0,25 Bitcoin to Katja instead of the text message. \n* The encryption technique used for Bitcoin is Elliptic Curve Digital Signature Algorithm (ECDSA). It is not important to understand the algorithm itself. Hence the algorithm is not explained in this book. For us is important that it is a cryptographic one-way algorithm. It derives a public key from a private key and it is not possible to derive the private key from the public key. \n* Katja generates a key pair. This way she gets a public Bitcoin address and the corresponding private key. This public Bitcoin address is not derived directly from the private key. It is an address resulting from the public key derived from the private key and further processing. \n* Her public Bitcoin address she sends to Hans. \n* Hans now sends the Bitcoins to this public Bitcoin address.\n* Hans sends a message to Katja to tell her that he transferred the Bitcoin amount to the Bitcoin address she told him. Or Katja checks her Bitcoin address to find out if the Bitcoin amount already has been booked on this address.\n* The only one who can use the Bitcoin amount available on this public Bitcoin address is the holder of the corresponding private key. In this case this is Katja. To transfer these Bitcoins to someone else she needs to sign the transaction with her private key. With this signature and the corresponding public key, for the blockchain software it is possible to check if it is the holder of the private key who tries to use the Bitcoins. This way nobody else can use the Bitcoins tied to this Bitcoin address. \n\nThis was a simplified explanation. Effectively Hans creates a Bitcoin transaction sending the Bitcoins to an address. This information then is available in the blockchain and everyone can see it. But Katja is the only one being able to use the Bitcoins bound to this address. She owns the necessary private key for doing this. This private key she may not really see but it is stored in a wallet and the wallet uses the private key to sign the transaction that uses the Bitcoins. \n\nIt is important to know that we send our crypto coins to a public address and only the owner of the corresponding private key can use the Bitcoin bound to this address. Check digits at the end of the address help to avoid typing errors when sending crypto coins to an address. \n\nIn detail each crypto currency has an own procedure and differently structured address. If we are going to deal with a cryptocurrency then we should find out how the encryption and addressing is designed for this currency.",
      "title": "Blockchain Foundations Part 7: Encryption and Digital Signature",
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      "body": "This article focuses the radix tree (radix trie, PATRICIA trie). The concept is used for example in Ethereum to store the state.\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Radix Tree (PATRICIA trie)\n\nA radix tree (radix trie, prefix tree, PATRICIA trie) is a search tree and an ordered data structure. Common prefixes are stored only once. Hence data stored in a radix tree is compressed. \n\nThe subsequent figure shows edges and nodes. Each edge represents a character. Starting at root strings are stored this way. Characters of strings starting with the same characters are stored only once.\n\n![](https://cdn.steemitimages.com/DQmaKYiGD8o81MNrcTLcHL1iAHWa4Gvupiq7MptEgJRJ9FF/image.png)\nFigure 8: Trie (prefix tree)\n\nA radix tree is a more compact form of this search tree. We can see it in the subsequent figure. The number of edges is reduced distinctly.\n\n![](https://cdn.steemitimages.com/DQmPYNKNiFA8XzvSdtSbLPkGvcR7tC2XySPEudSWDddzTFF/image.png)\nFigure 9: Radix tree (PATRICIA trie)\n\nThe term trie is derived from information retrieval. Often tree is used instead of trie. PATRICIA is an acronym for Practical Algorithm to Retrieve Information Coded in Alphanumeric.\n\nEthereum uses the radix tree to store the state. This is explained later in this article series.",
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      "body": "This article talks about Merkle Tree and Merkle Root. The concept is used in many blockchains, for example in the Ethereum or Bitcoin blockchain. Merkle tree is often mentioned when talking about blockchain, Bitcoin or similar topics. Hence it is useful to know what a Merkle tree is\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Merkle Tree and Merkle Root\n\nThe Merkle tree is a hash tree. Ralph Merkle specified it in 1979. It is a tree consisting of hash values. \n- All leaves of the tree represent the hash values of data blocks\n- All intersections of the tree represent the hash value derived from 2 to n subjacent hash values. In a binary hash tree an intersection hash value always is derived from exactly 2 subjacent hash values\n\nFor building the Merkle tree in the subsequent example in the first step of all strings (like \"A sends 0,01 BTC to C\") on the lowest level the SHA-256 hash value was derived. To build the nodes the hash value for each node was derived from the concatenated two hash values below the node.\n\n![](https://cdn.steemitimages.com/DQmRGq22MGCByLJaaRiL95FrhWtrU5deGUo8TnfJftoBU5P/image.png)\nFigure 5: Merkle tree\n\nWhat to do if there are not exactly 4, 8, 16, … transactions? There are different methods. One method for a node with only one leave is to duplicate the existing leave. That is the way Bitcoin does it. \n\n![](https://cdn.steemitimages.com/DQmf7TiaWQSGfxJzSFCHGkJVQx1hjPt7ZgnS6fUTeWzm4Cu/image.png)\nFigure 6: Merkle tree with an uneven number of leaves\n\nWe use the Merkle tree to check data blocks being unchanged since they have been stored. For this we only need to store the root hash value. A new calculation of the Merkle tree bases on the stored data blocks will lead to the same root hash value, if the data blocks are unchanged. \n\nWith a Merkle tree we can check data blocks with little costs. Assume we want to check data block 4 shown in the figure above for being unchanged. Then we need for the check beside data block 4 and its corresponding hash value only the hash value of data block 3, the hash value 12 and the hash value 5555. The hash values 34, 1234 and 12345555 we calculate from these inputs to check for data block 4 being unchanged.\n\nIf we add a new data block to a Merkle tree, we do not need to recalculate the whole tree. We only need to recalculate the hash value of the new data block and the hash values of the nodes above the new data block. Then our Merkle tree is consistent once again.\n\n![](https://cdn.steemitimages.com/DQmTkJyGacUqjhocGQZGUxUg1ZENQhBAdyBV5uMJm2rRifw/image.png)\nFigure 7: Do a change to a Merkle tree\n\nIn the figure the light blue elements (data block 6 and hash value data block 6) where added and calculated. The yellow elements (hash values 56, 5656 and 12345656) we need to recalculate. All the other elements with the white background remain unchanged.\n\nBlockchain uses Merkle tree for example for:\n- For storing the transactions within a block as Merkle tree\n- Bitcoin calculates a hash value for each block. Because the transactions are stored in a Merkle tree the Merkle root hash value represents all transactions in the block. Hence for the calculation of the block hash value it is not necessary to derive a hash value from all the data contained in the block. It is enough to derive the block hash value from the block header containing the root hash value of the Merkle Tree\n\nMerkle tree is often mentioned when talking about blockchain, Bitcoin or similar topics. Hence it is useful to know what a Merkle tree is. On the other hand, Merkle tree is located deep in the details of implementation. You will understand blockchain without knowing details about the Merkle tree or even knowing how to build one. It is enough to know that a Merkle root hash can unambiguously represent the complete data structure it stands for.",
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      "body": "This article contains basic about hash function.\n\nThe article is part of a series starting with this article: [Blockchain Foundations Part 1: Distributed, Decentralized and Centralized Computer Architecture](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture)\n\nThe articles are drawn from my book \"Blockchain and Crypto Currencies Easy to Understand for Everyone, Thomas Bauer\". Please refer to the [part 1 article](https://steemit.com/blockchain/@thomasoss/blockchain-foundations-part-1-distributed-decentralized-and-centralized-computer-architecture) for a introduction to the blockchain foundations series.\n\n# Hash Function\nFrom the point of view of its user a hash function is something very simple. We take any algorithm being able to calculate the so-called hash value from an arbitrary row of bits. This algorithm is free of any random. A certain row of bits always leads to the same hash value, as long we use the same hash algorithm. If the input is not an already existing file but readable text we have to watch for the encoding (UTF-8, ASCII, …) of the input. \n\nIf we change only one bit of the bit row the algorithm will lead to a completely different hash value. \n\nFor example, the Bitcoin blockchain uses the SHA-256 (SHA = secure hash algorithm).\n\ninput value (UTF-8 encoded) | SHA 256 hash value (hexadecimal)\n------------ | -------------\n1 | 6b86b273ff34fce19d6b804eff5a3f5747ada4eaa22f1d49c01e52ddb7875b4b\n2 | d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35\nI am an example | cf7e66b7c62562fb697576c1592a0787dffa4e542b770e28d330ca623f26c381\nI am an exampl | 151471b8dcd8d9e7f93282172c3fdab0d356cc6d32944253d062a8df31a5c59e\n3000000000000000000000000 | cdb72b05832ff97ffe86f6cf716d45dcd50fbb3b5c4999b6dbd182a8c3ffd0e9\n3000000000000000000000001 | 3b54c614f29d96ef8a3250fb56d581d96f19568659f9ee20ff0f660e21b8816e\n\nWe see that nearly similar input values lead to totally different hash values. The resulting hash value always has the same length independent of the input value length. SHA-256 always delivers a 256 bits hash value. A SHA-256 hash value of the complete Oxford English Dictionary has the same length as the SHA-256 hash value of the number 1.\n\nIt is important to know that the same input always leads to the same hash value. The hash algorithm is very sensible to every difference of the input value. But it will be deterministic if the input value is the unchanged. \n\nA hash value we can derive from everything which can be represented by bit row of any length consisting of 0-values and 1-values: pure text, encrypted text, pictures, file with tax information, pdf file, word file and much more.\n\nIf we derive a hash value from a content and store the hash value we later can use the hash value to check the content to unchanged. To do the check we again derive the hash value from the value and with an unchanged content we get the same hash value. \n\nA hash function is a one-way function. It is not possible to calculate the input value from the hash value. We may find the input value by trial and error. If we knew the input value being a number between 1 and 9, then we could derive the hash value for each of the numbers until we get one identically to the hash value we are searching the input value for.  \n\nPractically impossible is it to derive the input value from the hash value for example if the input value is a picture. Assumptions about the content are not possible. We even do not know the length of the picture file. \n\nThere is a chance to find the input value to a hash value if the input is a short row of bits or if we know some details about the input value reducing the possible range of input values considerably.\n\nIf we do know little about the input value, it is practically impossible to find the input value to a hash value by try and error. A hash value may be derived from a single digit or from the complete Oxford English Dictionary. \n\nOf course, small input values may be hacked faster. If the input value for the hash function is three bytes long and a hacker tries out every possible bit combination starting with 0, 1, 00, 01, 11, 000 … then at the latest with reaching 111111111111111111111111 (24 times 1) the hacker will have found the input value. These 24 times 1's equal to decimal 16.777.215. Hence the hacker needs at most about 16,8 million tries for 3 bytes input value. But with a 6 bytes input value we have already about 281 trillion (281.474.976.710.655) possible input values. \n\nAnother feature of hash functions is important for the blockchain. We cannot predict how a change to an existing bit row will affect the resulting hash value. As described in a later article of this series the Bitcoin mining \"puzzle\" is nothing else than finding a hash value derived from a block starting with a given number of zeros. The hash value must be the hash of the block content (the transactions enclosed and additional stuff) and an additional field. To this additional field we add a binary 1 until the resulting hash value meets the requirements. The rest of the block remains unchanged. Because there is no way to calculate which value of the additional number leads to a hash value with the required number of leading zeros, we need to add a binary 1 to this additional number until we find a matching hash value.\n\nLess important for understanding blockchain is how the hash value is calculated. Hence this is not described in this article series. We only need to know which algorithm is used in each environment. For example, Bitcoin uses among others the SHA-256 hash algorithm. \n\nWe need to know with which hash algorithm a hash value was calculated in the past if we want to use the hash value to check a content being unchanged.",
      "title": "Blockchain Foundations Part 4: Hash Function",
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