Here are my 100 interesting things to learn about cryptography: For a 128-bit encryption key, there are 340 billion billion billion billion possible keys. [Calc: 2**128/(1e9**4)] For a 256-bit encryption key, there are 115,792 billion billion billion billion billion billion billion billion possible keys. [Calc: 2**256/(1e9**8)] To crack a 128-bit encryption with brute force using a cracker running at 1 Teracracks/second, will take — on average — 5 million million million years to crack. Tera is 1,000 billion. [Calc: 2**128/100e9/2/60/60/24/365/(1e6**3)] For a 256-bit key this is 1,835 million million million million million million million million million years. For the brute force cracking of a 35-bit key symmetric key (such as AES), you only need to pay for the boiling of a teaspoon of energy. For a 50-bit key, you just need to have enough money to pay to boil the water for a shower. For a 90-bit symmetric key, you would need the energy to boil a sea, and for a 105-bit symmetric key, you need the energy to boil and ocean. For a 128-bit key, there just isn’t enough water on the planet to boil for that. Ref: here. With symmetric key encryption, anything below 72 bits is relatively inexpensive to crack with brute force. One of the first symmetric key encryption methods was the LUCIFER cipher and was created by Horst Feistel at IBM. It was further developed into the DES encryption method. Many, at the time of the adoption of DES, felt that its 56-bit key was too small to be secure and that the NSA had a role in limiting them. With a block cipher, we only have to deal with a fixed size of blocks. DES and 3DES use a 64-bit (eight-byte) block size, and AES uses a 128-bit block size (16 bytes). With symmetric key methods, we either have block ciphers, such as DES, AES CBC and AES ECB, or stream ciphers, such as ChaCha20 and RC4. In order to enhance security, AES has a number of rounds where parts of the key are applied. With 128-bit AES we have 10 rounds, and 14 rounds for 256-bit AES. In AES, we use an S-box to scramble the bytes, and which is applied for each round. When decrypting, we have the inverse of the S-box used in the encrypting process. A salt/nonce or Initialisation Vector (IV) is used with an encryption key in order to change the ciphertext for the same given input. Stream ciphers are generally much faster than block cipers, and can generally be processed in parallel. With the Diffie-Hellman method. Bob creates x and shares g^x (mod p), and Alice creates y, and shares g^y (mod p). The shared key is g^{xy} (mod p). Ralph Merkle — the boy genius — submitted a patent on 5 Sept 1979 and which outlined the Merkle hash. This is used to create a block hash. Ralph Merkle’s PhD supervisor was Martin Hellman (famous as the co-creator of the Diffie-Hellman method). Adi Shamir defines a secret share method, and which defines a mathematical equation with the sharing of (x,y), and where a constant value in the equation is the secret. With Shamir Secret Shares (SSS), for a quadratic equation of y=x²+5x+6, the secret is 6. We can share three points at x=1, x=2 and y=3, and which gives y=12, y=20, and y=20, respectively. With the points of (1,12), (2,20), and (3,20), we can recover the value of 6. Adi Shamir broke the Merkle-Hellman knapsack method at a live event at a rump session of a conference. With secret shares, with the highest polynomial power of n, we need n+1 points to come together to regenerate the secret. For example, y=2x+5 needs two points to come together, while y=x²+15x+4 needs three points. The first usable public key method was RSA — and created by Rivest, Shamir and Adleman. It was first published in 1979 and defined in the RSA patent entitled “Cryptographic Communications System and Method”. In public key encryption, we use the public key to encrypt data and the private key to decrypt it. In digital signing, we use the private key to sign a hash and create a digital signature, and then the