SHA-512 Coins
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Xerox Sha512 bitcoin restoration, IC reverse engineering, chargers, and sha512 bitcoin Mining Bitcoin with pencil and paper: I decided to see how practical it would be to mine Bitcoin with pencil and paper. It turns out that the SHA algorithm used for mining is pretty sha512 bitcoin and can in fact sha512 bitcoin done by hand. Not surprisingly, the process is extremely slow compared to hardware mining and is entirely impractical. But performing the algorithm manually is a good way to sha512 bitcoin exactly how bitcoin sha works.
The idea is that Bitcoin miners group a bunch of Bitcoin transactions into a block, then repeatedly perform a cryptographic sha512 bitcoin called hashing zillions of times until someone finds a special extremely rare hash value.
At this point, the block has been mined and becomes part of the Bitcoin block chain. The hashing task sha512 bitcoin doesn't accomplish bitcoi useful in itself, but because finding a successful block is so difficult, it ensures that no individual has the resources to take over the Bitcoin system. For more details on mining, see my Bictoin mining article.
A cryptographic hash sha512 bitcoin takes a block of input data and creates a smaller, unpredictable output. The hash function is designed so there's no "short cut" bitcoin sha get the desired output - you just have to keep hashing blocks until you find one by brute force that works. But Bitcoin is exponentially harder. Currently, a successful hash must start with approximately 17 zeros, so only one out of 1.
In other words, finding a successful hash is harder than finding a particular grain of sand out of all the grains of sand on Earth. The following diagram shows a block in the Bitcoin sha512 bitcoin along with its hash.
The yellow bytes are hashed to generate the block hash. In this case, the resulting hash starts with enough zeros so sha512 bitcoin successful. However, the hash will almost always be unsuccessful. In that case, the miner changes the nonce value or other block contents and tries again. The SHA algorithm consists of a sha512 bitcoin simple round repeated 64 times. The diagram below shows one round, which takes eight 4-byte inputs, A through H, performs a few operations, and generates new bitciin of A through H.
One round of the SHA algorithm showing bitcojn 8 input blocks A-H, the processing steps, and the new blocks. The blue boxes mix up the values in non-linear ways that are hard to analyze cryptographically. Since the shaa uses several different functions, bitcoin sha an attack is harder.
If you could figure out a mathematical shortcut to generate successful hashes, you could take over Bitcoin mining. The Ma majority box looks at the bits of A, B, and C. For each position, if the majority of the bits are 0, it outputs 0. Otherwise sha512 bitcoin outputs 1. That bitcoin shafor each position in A, B, and C, look at the number of 1 bits.
Bittcoin it is zero or one, output 0. If it bircoin two or three, output 1. In other words, if the number of 1 bits is odd, the sum is 1; otherwise, it is 0. The three values in the sum are A sha512 bitcoin right by 2 bits, 13 bits, and 22 bits. The Ch "choose" box chooses output bits based on the value of bitcoon E. If a bit of E is 1, the output bit is the corresponding bit of F. If bircoin bit of E is 0, the output bit is the corresponding bit of G. In this way, the bits of F and G are shuffled together based on the value of E.
The red boxes perform bit addition, generating new values for A and E. The input Wt is based on the input data, slightly processed. This is where the input block gets fed into the algorithm.
The Kt is a constant bitcoib for each round. The other bicoin pass through unchanged, with the old A value becoming the new B value, the old B value becoming the new C value and so forth. Although each round of SHA doesn't change the data much, after 64 rounds the input data will be completely scrambled. I perform the first round of hashing to mine a block.
Completing this round took me 16 minutes, 45 seconds. To explain what's on the paper: I've written each block A through H in hex on a separate row and put bitcoin sha binary value below. In the lower right, a bunch of terms are added together, corresponding to the first three red sum boxes. In the upper sha512 bitcoin, this sum is used to generate the new Just click for source value, and in the middle right, this sum is used to generate the new E value.
These steps all correspond to the ssha and discussion above. I also manually performed another hash sha512 bitcoin, the last round to finish hashing the Bitcoin block. In the image below, the hash result is highlighted in yellow. The zeroes in this hash show that it is a successful hash. Note that the zeroes are at the end of bittcoin hash.
The reason is that Bitcoin inconveniently reverses all the bytes generated by SHA What this means for mining hardware Each step sha512 bitcoin SHA is very easy to implement sha512 bitcoin digital logic - simple Boolean "bitcoin sha " and bit addition. If you've studied electronics, you can probably visualize the circuits already. For this reason, custom ASIC chips can implement the SHA algorithm very efficiently in hardware, putting hundreds of rounds on a chip in parallel.
It stores different hash values into memory, and sha512 bitcoin combines them in unpredictable ways to get the final shx. As a result, much more circuitry and memory is required for scrypt than for SHA hashes.
You can see the impact by looking at mining hardwarewhich is thousands of times slower bitcoin sha scrypt Litecoin, etc than for SHA Bitcoin.
Conclusion The SHA bitcoin sha is surprisingly simple, easy enough to do by hand. The elliptic curve algorithm for signing Bitcoin transactions would be very painful to do by hand since it has lots sha512 bitcoin multiplication of byte integers.
Doing one round of SHA by hand took me 16 minutes, 45 seconds. At this rate, hashing a full Bitcoin block rounds [3] would take 1. In comparison, current Bitcoin mining hardware does several terahashes per second, about a quintillion sha512 bitcoin faster than my manual hashing. Needless to say, sha512 bitcoin Bitcoin mining is not at all practical.
The next question is the energy cost. Thus my energy cost per hash is about 67 quadrillion times that of mining hardware. It's clear I'm not going to make my fortune off manual mining, and I haven't even included the cost of all the paper and pencils I'll need.
Notes [1] It's not exactly sha512 bitcoin number of zeros at the start of sha512 bitcoin hash that matters. Sha512 bitcoin be precise, the hash must be less than a particular value that depends on the current Bitcoin difficulty level. The NSA designed the SHA algorithm link picked the values for these constants, so how do you know they didn't pick special values that let them break sha512 bitcoin hash?
To avoid suspicion, the initial hash values come from the square roots of the first 8 primes, and the Kt values come from the cube roots of the first 64 primes. Since these constants come from a simple formula, you can trust that the NSA bitcoin sha do anything shady at least with the constants.
Thus, a second set of 64 SHA hash rounds is required on the second half sha512 bitcoin the Bitcoin block. Adding this up, hashing an arbitrary Bitcoin block takes rounds in total. However there is a shortcut. Mining here hashing the same block over and over, bitcoin sha changing the nonce which appears in the second 52 of the block. Thus, mining can reuse the sha512 bitcoin of hashing the first bits, and hashing a Bitcoin block typically only requires rounds.
I sha512 bitcoin the hashing "bitcoin sha " with sha512 bitcoin block that had already been successfully mined.
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