More Secrets of Cryptography

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More Secrets of Cryptography Chris Riley ConFoo 2018 1

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Introduction

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Why do we need cryptography? 1

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Modern cryptography • Confidentiality 2

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Modern cryptography • Confidentiality • Key exchange 2

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Modern cryptography • Confidentiality • Key exchange • Identity 2

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Modern cryptography • Confidentiality • Key exchange • Identity • Authentication 2

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Symetric vs Asymetric Cryptography

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Eliptic Curve Cryptography

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Eliptic Curve Equation • y2 = x3 + ax2 + b 3

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Eliptic Curve Equation • y2 = x3 + ax2 + b • y2 = x3 + 486662x2 + x 3

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An Eliptic Curve 4

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Eliptic curve dot function 5

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Eliptic curve multiplication function 6

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Eliptic curve for Cryptography 7

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Eliptic Curve Key Exchange • Agree a curve, modulus and generator point (G) 8

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Eliptic Curve Key Exchange • Agree a curve, modulus and generator point (G) • Select random integer d and compute P = dG 8

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Eliptic Curve Key Exchange • Agree a curve, modulus and generator point (G) • Select random integer d and compute P = dG • Exchange public keys (PA and PB) 8

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Eliptic Curve Key Exchange • Agree a curve, modulus and generator point (G) • Select random integer d and compute P = dG • Exchange public keys (PA and PB) • Compute a shared secret dBPA and dAPB 8

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Key Exchange protocol 9

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Man in the middle 10

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The Web of Trust

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Trent, the trusted third party 11

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Can you trust a web of trust? 11

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Cryptographic Hash functions

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Ideal hash function properties • It should be quick and easy to compute a hash for any given data. 12

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Ideal hash function properties • It should be quick and easy to compute a hash for any given data. • It should be difficult to compute data that has a given hash. 12

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Ideal hash function properties • It should be quick and easy to compute a hash for any given data. • It should be difficult to compute data that has a given hash. • It should be unlikely that two different messages will have the same hash. 12

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SHA-2

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Setup phase • Append a single ’1’ bit to the data • Pad the data with ’0’ so that the data + 64 bits is a multiple of 512 • Append the data length as a 64 bit integer 13

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Expansion phase • Split message into 512 bit blocks • Expand each block to 2048 bits • Expansion is done using shifts and rotates of the original block xor’d together 14

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Compression phase 1By User:kockmeyer (Own work) CC-BY-SA-3.0, via Wikimedia Commons 15

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Merkel Trees

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A Merkel Tree 16

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A Merkel Tree 17

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Bitcoin

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What is a blockchain? • A Merkle tree 18

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What is a blockchain? • A Merkle tree • No central authority 18

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What is a blockchain? • A Merkle tree • No central authority • Multiple ’forks’ may exist 18

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What is a blockchain? • A Merkle tree • No central authority • Multiple ’forks’ may exist • There exists a consensus algorithm to determine the correct fork 18

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What is a blockchain? • A Merkle tree • No central authority • Multiple ’forks’ may exist • There exists a consensus algorithm to determine the correct fork • The consensus algorithm only requires data contained on the blockchain to run 18

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Mining a bitcoin 19

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Why do bitcoins have value? 19

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Should I use a block chain for ... ? 19

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Thanks • @giveupalready • https://github.com/carnage • https://carnage.github.io 20