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🔒 Practical Cryptography 🔐
Introduction to Public Key Cryptography
© 2020 TWILIO INC. ALL RIGHTS RESERVED.
krobinson@twilio.com
👋👩💻🔐
Kelley Robinson
@kelleyrobinson
Meet Alice and Bob
🔐 🔐
💬🤷
What is Public Key Crypto?
Each entity has 2⃣ keys
Public Key - to be shared
Private Key - to be kept secret
Asymmetric Crypto == Public Key Crypto == PKC
RSA algorithm
(there are other algorithms, we'll get to that)
What is Public Key Crypto?
Two major use cases (for RSA):
1. Encrypt with Public Key
2. Sign with Private Key
...only Bob can decode the cyphertext
Encrypting with Public Key
Signing with Private Key
...only Alice can be the author
How are keys generated?
TL;DR: math
@kelleyrobinson
How are keys generated?
Trapdoor Functions
Trapdoor Functions
Which is easier?
1. Find the two prime factors of 4,757
2. Multiply 67 and 71
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!
Other Common
Algorithms
Diffie-Hellman Key Exchange
Elliptic-Curve Cryptography (ECC)
y2 = x3 + ax + b
Elliptic Curve Addition (Image By SuperManu [GFDL or CC BY-SA 3.0], via Wikimedia Commons)
What is Key Size?
https://xkcd.com/538/
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
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.
”
PKC in Python
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,
...
)
PKC in Python
https://cryptography.io/en/latest/hazmat/primitives/asymmetric/rsa/
Encrypting
public_key = private_key.public_key()
ciphertext = public_key.encrypt(message, ...)
plaintext = private_key.decrypt(ciphertext, ...)
# returns True
message == plaintext
Signing
public_key = private_key.public_key()
signature = private_key.sign(message, ...)
# throws exception if not verified
public_key.verify(signature, message, ...)
Everyday Uses of Public Key Cryptography
Authy
PGP and GPG
JWTs (with RS256)
TLS (HTTPS)
Bitcoin
SSH
]
@kelleyrobinson
]
Public key
on the Authy
servers
@kelleyrobinson
]
Private key
on your
device
@kelleyrobinson
]
Your device
signs with your
private key
Algorithm
Key SizeAlgorithm
https://xkcd.com/1181/
@kelleyrobinson
__________________
| |
Don't roll
your own crypto!
|__________________|
(__/) ||
(•ㅅ•) ||
/   づ
@kelleyrobinson
twilio.com/blog/what-is-public-key-cryptography
Further Reading
astonishinglegends.com
@kelleyrobinson
Further Listening
@kelleyrobinson
THANK YOU!
@kelleyrobinson

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