Thrilled to see that my book Mastering blockchain - the third edition is a best-seller at Amazon! 

https://www.amazon.com/Mastering-Blockchain-distributed-consensus-cryptocurrencies/dp/1839213191/

 Ethereum 2.0 architecture

Mastering Blockchain: Third edition

Very pleased to announce a new edition of my book with four new chapters on consensus, tokenization, Ethereum 2.0 and enterprise blockchains. 

Available here:

https://www.packtpub.com/product/mastering-blockchain-third-edition/9781839213199

and on Amazon

Mastering Blockchain: A deep dive into distributed ledgers, consensus protocols ... https://www.amazon.com/dp/1839213191/ref=cm_sw_r_tw_dp_x_CguuFb4KFCPT6

Mastering Blockchain book review 2nd edition

https://youtu.be/DWJSa7EKGO8?t=120

Top 5 Cryptocurrency and Blockchain Books - (2018)

How SHA256 works

SHA-256

SHA-256 has the input message size < 2^64-bits. Block size is 512-bits and has a word size of 32-bits. The output is a 256-bit digest.

The compression function processes a 512-bit message block and a 256-bit intermediate hash value. There are two main components of this function: compression function and a message schedule.

The algorithm works as follows:

Pre-processing:

1.   Padding of the message, which is used to make the length of a block to 512-bits if it is smaller than the required block size of 512-bits.

2.   Parsing the message into message blocks that ensure that the message and its padding is divided into equal blocks of 512-bits.

3.   Setting up the initial hash value, which is the eight 32-bit words obtained by taking the first 32-bits of the fractional parts of the square roots of the first eight prime numbers. These initial values are randomly chosen to initialize the process and gives a level of confidence that no backdoor exists in the algorithm.

Hash computation:

1.   Each message block is processed in a sequence and requires 64 rounds to compute the full hash output. Each round uses slightly different constants to ensure that no two rounds are the same.

2.  First, the message schedule is prepared.

3.  Then, eight working variables are initialized.

4.  Then, the intermediate hash value is calculated.

5.  Finally, the message is processed, and the output hash is produced:

one round of SHA256 compression function

In the preceding diagram, a, b, c,d, e, f, g, and h are the registers. Maj and Ch are applied bitwise.   performs the bitwise rotation. Round constants are Wjand Kj, which are added mod 2^32.

How Advanced Encryption Standard (AES) works

Advanced Encryption Standard

In 2001 after an open competition an encryption algorithm named Rijndael that was invented by cryptographers Joan Daemen and Vincent Rijmen was standardized as AES with minor modifications by NIST in 2001. So far there is no attack found against AES that is better than brute force method.  Original Rijandaeil allows different key and block sizes of 128,192 and 256 bits but in AES standard only 128-bit block size is allowed. However key sizes of 128, 192 and 256 bit are allowed.

AES Steps

During AES Algorithm processing a 4 by 4 array of bytes knows as state is modified using multiple rounds. Full encryption requires 10 to 14 rounds depending on the size of the key. Following table shows the key sizes and required number of rounds.

Key Size	Number of rounds required
128 bit	10 rounds
192 bit	12 rounds
256 bit	14 rounds

Once the state is initialized with the input to the cipher, four operations are performed in four stages in order to encrypt the input. These stages are AddRoundKey, SubBytes, ShiftRows, and MixColumns.

1.    In AddRoundKey step, the state array is XORed with a subkey which is derived from the master key.

2.    This is the substitution step where a lookup table (S-box) is used to replace all bytes of the state array.

3.    This step is used to shift each row except the first one in the state array to the left in a cyclic and incremental manner.

4.    Finally, all bytes are mixed in this step in a linear fashion column-wise.

The steps above describe one round of AES. In the Final round (either 10, 12 or 14 depending on the key size), Stage 4 is replaced with Addroundkey to ensure that first three steps cannot just be simply inverted back.

AES block diagram, showing 1^stround, in last round mixing step is not performed

Various cryptocurrency wallets use AES encryption to encrypt locally stored data. Especially in bitcoin wallet, AES 256 in CBC mode is used.