How do Machines Keep Secrets II
Ryan: FYS Computational Reasoning Fall 2025
Lecture content licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Playlist
REFERENCES/RESOURCES
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IMAGES
Outline
CH 3 Asymmetric encryption
What did we learn from Eddy Woo?
RSA starts by generating a "key pair" - one private or secret and one public. So we sometimes write SK and PK
We can encrypt with either one.
We can decrypt with the "other" one only.
RSA (Rivest–Shamir–Adleman) is an asymmetric cryptographic algorithm algorithm used to encrypt and decrypt messages.
Asymmetric means one key is used to encrypt and another is used to decrypt.
Generate RSA Keys
(5,14) \\(11,14) \\\text{encrypt(b): }2^5 \text{ mod } 14 = 4\\ \text{decrypt(4): }4^{11} \text{ mod } 14 = 2
\text{Pick 2 primes: } p = 2, q = 7\\
N = pq = 14
\text{Compute number of coprimes N has with p and q}\\
\phi(N) = (p-1)(q-1)
\text{Choose e (first encryption element) such that} \\
0 \lt e \lt \phi(N) \text{ and } e { is coprime with } N, \phi(N) \\
e = 5 \\
\text{Find d for decription such that } d e \text{ mod } \phi(N) = 1\\
Why "public" and "private"?
Two kinds of "secret keeping"
I want to create something that only you can read
I want to create something that you can be certain came from me.
RSA DEMO
ONLINE RSA
"Public Key Cryptography Standards"
CONFIDENTIALITY
-
You generate public and private key
- You tell me your public key
- I encrypt message with your public key
- I send you the encrypted message
- You decrypt message with your private key
Sending a message for your eyes only
For your eyes only
AUTHENTICATION
-
I generate public and private key
- I encrypt message with my private key
- I tell you my public key
- I send you the encrypted message
- You decrypt message with my public key
Sending a message you know comes from me
Anyone can read it and know it is from me
I'd like a secure session
Here is SPUBKEY
Here is ESPUBKEY(CPUBKEY)
ECPUBKEY("READY")
ESPUBKEY("REQUEST")
ECPUBKEY("RESPONSE")
DCPRIVKEY("READY")
process
DSPRIVKEY("REQUEST")
process
hacker
hacker
Server private key not available to hacker
Client private key not available to hacker
With What We Have So Far
Certificates
Start with information about yourself
Ask a trustee to validate and confirm
Trustee signs certificate with private key
Recipient uses trustee's public key to decrypt
If result matches certificate then it's valid.
I am Dan.
This IS Dan.
45ab98de7ff7ced213198005adfe
Skey(trustee)
Web connection receives certificate
Secure Web Exchange
Browser generates keys and sends public as "session" key, encrypted with server's public key.
Server encrypts web page content with session key.
Browser encrypts content to send with private session key.
Browser decrypts content with private key.
Server decrypts content with session key.
Certificate includes server's public key.
Hashing
Quick Interlude: Hashing
Hashing
- a hash function maps or converts arbitrary data (meaning data of any size) to a fixed sized piece of data in a more or less unique way
- that is, no two things will have the same hash
- in general it is a one way operation
- that is, you can't unhash the hash to find out what the original data was
HASHING REFERENCES
Example
Example
Example
1st letter of first name
3rd letter of first name
3rd letter of last name
1st letter of last name
length of first name
length of last name
dnracdgg
month of birth
date of birth mod 26*
* 1=a, 2=b, ..., 27=a, 28=b, 29=c, 30=d, 31=e
Cryptographic Hash
A cryptographic hash (sometimes called ‘digest’) is a kind of ‘signature’ for a text or a data file.
Cryptographic Hash
aa58b21b01d6b8a99c1a5856962dbac36c758a79dc0a77c2e013ce2c39ecdc8a
da
ec4f2dbb3b140095550c9afbbb69b5d6fd9e814b9da82fad0b34e9fcbe56f1cb
dan
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30293f4f02f784c4166a3e17109f01625bd1bfe97de2e017eebf9d23a55d9caf
We just learned two things
- Different sized inputs produce same size output
- Similarity in input does not mean similarity in output
Cryptographic Hash
A cryptographic hash (aka ‘digest’) is a transformation of a text or a data file into an almost-unique fixed length block of data.
A hash is not ‘encryption’ insofar as it cannot be decrypted back to the original text.
As a ‘one-way’ cryptographic function it can be used on a copy of a document and then compared to a hashed version of an original to verify that the copy is accurate to the original.
SHA-256
an algorithm that generates an almost-unique 256-bit (32-byte) signature for a text input.
Secure Hashing Algorithm 256 bit
SHA256 Pseudocode
SHA-256 Implemented in JS
DIGITAL SIGNATURE
-
I generate public and private key
- I create a hash of my document.
- I encrypt the hash with my private key (the signature)
- I tell you my public key
- I send you the message and the encrypted hash
- You hash the message and decrypt the signature with my public key
- If the two hashes match then you have the same document that I signed
HOW do I guarantee that I signed THIS document?
only you can read it
Information Security
- confidentiality: secrecy is maintained
- authenticity: it is from who it says
- integrity: it is what it says
How to operate on lots of data? Break it up into blocks. Blocks always same size. Padding.
How Machines Keep Secrets II
By Dan Ryan
How Machines Keep Secrets II
Asymmetric Encryption and Sending Secrets in Public
