This document provides an overview of cryptography concepts including various ciphers like the Caesar cipher, Vigenère cipher, Playfair cipher, and the one-time pad. It discusses stream ciphers using techniques like the middle squares method. Asymmetric encryption techniques like elliptic curve cryptography are covered as well as the impact of quantum computing. Additional topics include hashing, block ciphers, mixing services/onion routing, zero-knowledge proofs, and scriptless scripts. Recommended further reading on applied cryptography is also provided.

2. Intro
◦ Roy Wasse
◦ Co Founder OpenValue
◦ Dutch JUG leader
◦ Love technochange
◦ Disclaimer: no heavy math
2

3. ΚΡΥΠΤΕΙ
ΓΡΆΦΩ

4. CAESAR CIPHER

7. ◦ Invented by Leon Battista in 1467
◦ Uses multiple alphabets (polyalphabetic)
◦ Circumvents frequency analysis
A T T A C K A T D A W N
L E M O N L E M O N L E
L X F O P V E F R N H R
Vigenère cipher

8. Repetition is deadly

10. Playfair
◦ Key PLAYFAIR EXAMPLE
◦ Plaintext HI DE TH EG OL DI NT HE TR EX ES TU MP
◦ Ciphertext BM OD ZB XD NA BE KU DM UI XM MO UV IF

12. Image http://kerryb.github.io/enigmaa/

13. tps://hackaday.com/2016/04/29/centennial-birthday-of-claude-e-shannon-the-math-and-ee-pioneer/

14. One time pad
◦ If and only if:
◦ Key length >= Source text
◦ Key is generated randomly
◦ Any key is used only once
◦ Only sender and receiver have key

15. One time function
Source T H I S I S S E C R E T
Position 20 8 9 19 9 19 19 5 3 18 5 20
KEY X V H E U W N O P G D L
+ 23 21 7 4 20 22 13 14 15 6 3 12
Result 43 29 16 23 29 41 32 19 18 24 8 32
Mod 26 17 3 16 23 3 15 6 19 18 24 8 6
Ciphertext R D Q X D P G T S Y 9 G

17. Disadvantages
One time pad
Works fine in some use cases (pen &
paper)
1 GB file requires 1 GB random key
No access to true random input
Key can only be used once, how to
guarantee

18. Semantic
security
Shorter key
Pseudo random generator
Ciphers for varying message length
Safe enough for vast amount of computing power
Practical encryption != Mathematical safe

19. STREAM CIPHER

20. Middle Squares
method
◦ Take random input number (11)
◦ Square number (11 * 11 = 121)
◦ Select # middle chars (0121)
◦ add trailing zero if needed
◦ Square those (12 * 12 = 144)
◦ Repeat until key is long enough

21. ATTACK AT NOON
◦ Key needed consisting of 12 chars (spaces removed)
Sum Outcome Key Length PRG key
11 * 11 0121 12 2
12 * 12 0144 1214 4
14 * 14 0196 121419 6
19 * 19 0361 12141936 8
36 * 36 1296 1214193629 10
84 * 84 7056 121419362905 12
Position 1 2 3 4 5 6 7 8 9 10 11 12
Input A T T A C K A T N O O N
Key 1 2 1 4 1 9 3 6 2 9 0 5

22. Pseudo Random is hard

23. Nonce
◦ Cipher algorithm that uses a Nonce next
to a Seed
◦ Seed * Nonce => ~Cipher text
◦ Reuse key because s1*n0 != s1*n1
◦ IV = Initialization Vector, example of
Nonce
◦ In WPA Nonce reuse was predictable

24. C M V H
F R O M M O L L Y
Position 6 18 15 13 13 15 12 12 25
KEY X V H U W N O P G
+ 23 21 7 20 22 13 14 15 6
Result 29 39 22 33 35 28 26 27 31
Mod 26 3 13 22 7 9 2 0 1 5
Ciphertext C M V H J C A B X
F R O M A L I C E
Position 6 18 15 13 1 12 9 3 5
KEY D B J E L L M W A
+ 4 2 10 13 1 12 9 3 5
Result 10 20 25 26 2 24 18 6 10
Mod 26 10 20 25 0 2 24 18 6 10
Ciphertext K U Z A C Y S G K
C Y S G KK U Z A
J C A B X

25. HASHING
VERSUS
ENCRYPTION

26. Checksum
◦ Based on hash function
◦ Small change in input, totally different
output
◦ Sender embeds a checksum in encrypted
message
◦ Receiver checks if he can reproduce the
checksum

27. Block ciphers
Plaintext A B C D E F
Ciphertext F A B C D E
Ciphertext E F A C
Source F A C E

29. Asymmetric encryption

30. Elliptic Curve
◦ Safer then RSA
◦ y2 = x3 + ax + b
◦ Bitcoin uses it
◦ SSL can use it
30

32. Quantum computing
◦ Sohr‘s algorithm mid 90’s showed RSA is vulnerable
◦ ECC even more vulnerable
◦ To guess Private key in reasonable amount of time few thousand qubits needed
◦ Currently best Quantum computer has 20-50 qubits
◦ Supersingular Isogeny Diffie-Hellman is post-quantum secure

33. Superencryption
◦ AKA Multi encryption
◦ Combine multiple encryption approaches

35. Mixing service & Onion Routing
◦ Implemented in TOR (The Onion Router)
◦ Alice want to send message to Bob’s forum anonymously
◦ Use proxy Carol ( A -> C -> B )
◦ Share a key with Carol and send cyphertext
◦ Use mixing service

36. Peeling the onion
◦ Use Multiple mixing services
◦ c1 := E(kd,m))
◦ c2 := E(kc, E(kd,m))
◦ Adding routing info: c2 := E(kc, <David, c1>) where c1 := E(kd, <Bob,m>)
◦ Carol doesn’t know she’s the entry point / Alice is a sender

37. Zero knowledge proof
CC BY 2.5, https://commons.wikimedia.org/w/index.php?curid=313648

38. ◦Sender’s address
◦Amount of coins sent
◦Receiver’s address

39. Exploiting multiplication to hide
information and verify ownership
Credit: https://medium.com/beam-mw/mimblewimble-explained-like-youre-12-d779a5bb483d

40. Hiding transaction amounts

41. Proving that money in = out

42. Schnorr Signatures
◦ Bitcoin uses script which signs several tx inputs for a single tx
◦ Signatures take up a lot of space.
◦ Schnorr allows aggregating signatures like:
◦ Output 1 -> ~Input A = Sig 1000
◦ Output 2 -> Input A= Sig 5000
◦ Just store 15000 (10000+15000)
◦ This enables scriptless transactions!
Image: https://bitcoinmagazine.com/articles/scriptless-scripts-how-bitcoin-can-support-smart-contracts-without-smart-contracts/

43. Scriptless scripts
◦ Smart contracts without use of a script
◦ No one can see the smart contract
◦ In this year maybe implemented in bitcoin

44. Unlock song with signature
Schnorr 8000
Schnorr 7000
Initiate transaction
Schnorr 1000
Zero knowledge proof
Calculate Song Schnorr 7000
Schnorr 8000
Finish transaction (streamer Schnorr)

45. Recommended
Reading
Dan Boney & Victor Shoup, A Graduate Course in Applied Cryptography
(September 2017, v0.4). https://crypto.stanford.edu/~dabo/cryptobook/
Applications of Modern Cryptography Technologies, applications and choices
(SURFNet, 2010)
https://www.surf.nl/binaries/content/assets/surf/en/knowledgebase/2010/rapport_20
1009_SNcryptoWEB.pdf
Decrypted secrets. Methods & Maixms of Cryptology byF.L Bauer. (2007).
Bitcoin magazine (November 2017)
https://bitcoinmagazine.com/articles/scriptless-scripts-how-bitcoin-can-support-
smart-contracts-without-smart-contracts/
https://medium.com/beam-mw/mimblewimble-explained-like-youre-12-
d779a5bb483d

46. Crypto erasure
◦ GDPR (AVG) requires option to erase all data (right to be forgotten)
◦ But how to keep track?
◦ And what if system crashes because record is deleted (in event sourcing
for instance)
◦ Crypto erasure, safe all sensitive records encrypted in data store.
◦ Just throw away key if you want to erase all data related to person x

47. Commitment Scheme
◦ Alice & Bob going on a date, but which movie to pick?
◦ Coin flip
◦ Bob make a choice (bit commitment), send to Alice
◦ Coin is flipped, outcome is known to Alice & Bob
◦ Alice can now open envelope

48. AMOUNT
PART
MUST BE
VANISHED!