This document provides an introduction to public key cryptography. It explains that public key crypto uses two keys - a public key that can be shared and a private key that is kept secret. The document discusses how public key crypto works using RSA encryption as an example. It also covers other common public key crypto algorithms like Diffie-Hellman key exchange and elliptic curve cryptography. The document discusses key sizes and their relationship to security strength and provides examples of public key crypto implementations in Python.

2. 🔒 Practical Cryptography 🔐
Introduction to Public Key Cryptography

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Kelley Robinson
@kelleyrobinson

4. Meet Alice and Bob
🔐 🔐
💬🤷

6. What is Public Key Crypto?
Each entity has 2⃣ keys
Public Key - to be shared
Private Key - to be kept secret

8. Asymmetric Crypto == Public Key Crypto == PKC

9. RSA algorithm
(there are other algorithms, we'll get to that)

10. What is Public Key Crypto?
Two major use cases (for RSA):
1. Encrypt with Public Key
2. Sign with Private Key

11. ...only Bob can decode the cyphertext
Encrypting with Public Key

12. Signing with Private Key
...only Alice can be the author

13. How are keys generated?
TL;DR: math
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14. How are keys generated?

15. Trapdoor Functions

16. Trapdoor Functions
Which is easier?
1. Find the two prime factors of 4,757
2. Multiply 67 and 71

17. RSA Algorithm Example# Chosen inputs
p, q, e = 67, 71, 37
https://github.com/robinske/rsa-example
# Calculated
n = p*q
x = (p - 1)*(q - 1)
d = inverse_mod(e, x) # modular multiplicative inverse
public_key = (e, n)
private_key = (d, n)
message = 123
encrypted = pow(message, e, n)
decrypted = pow(encrypted, d, n) # == message 🤯
These are all trapdoor functions!

18. Other Common
Algorithms

19. Diffie-Hellman Key Exchange

20. Elliptic-Curve Cryptography (ECC)
y2 = x3 + ax + b
Elliptic Curve Addition (Image By SuperManu [GFDL or CC BY-SA 3.0], via Wikimedia Commons)

21. What is Key Size?
https://xkcd.com/538/

22. Impacts security strength, measured in bits of security
What is Key Size?
RSA key size of 2048
RSA key size of 3072
ECC key size of 256
112 bits of security
128 bits of security
128 bits of security

23. What is Security Strength?
- NIST Recommendation for Key Management
“a number associated with the amount of
work that is required to break a
cryptographic algorithm or system.
”

24. PKC in Python

25. PKC in Python
# pip install cryptography
from cryptography.hazmat.primitives.asymmetric import rsa
private_key = rsa.generate_private_key(
public_exponent=65537,
key_size=2048,
...
)

26. PKC in Python
https://cryptography.io/en/latest/hazmat/primitives/asymmetric/rsa/

27. Encrypting
public_key = private_key.public_key()
ciphertext = public_key.encrypt(message, ...)
plaintext = private_key.decrypt(ciphertext, ...)
# returns True
message == plaintext

28. Signing
public_key = private_key.public_key()
signature = private_key.sign(message, ...)
# throws exception if not verified
public_key.verify(signature, message, ...)

29. Everyday Uses of Public Key Cryptography
Authy
PGP and GPG
JWTs (with RS256)
TLS (HTTPS)
Bitcoin
SSH

30. ]

31. @kelleyrobinson
]
Public key
on the Authy
servers

32. @kelleyrobinson
]
Private key
on your
device

33. @kelleyrobinson
]
Your device
signs with your
private key

35. Algorithm

36. Key SizeAlgorithm

37. https://xkcd.com/1181/

38. @kelleyrobinson
__________________
| |
Don't roll
your own crypto!
|__________________|
(__/) ||
(•ㅅ•) ||
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39. @kelleyrobinson
twilio.com/blog/what-is-public-key-cryptography
Further Reading

40. astonishinglegends.com
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Further Listening

41. @kelleyrobinson
THANK YOU!
@kelleyrobinson