# OpenVMS Notes:Cryptography, etc.

Edit: 2019-12-08 (fixed a few typos)

## Introduction

For a quick bootstrap into cryptography I recommend reading The Code Book: The Science of Secrecy (2000) by Simon Singh

#### Substitution Basics

• Caesar Cipher
• https://en.wikipedia.org/wiki/Caesar_cipher
• Alphabetic fixed shift (e.g. each letter in your message is upper-cased then shifted by 3 letters)  Clear-text Message: WAIT FOR ME AT THE RUBICON Encrypted Message: ZDLW IRU PH DW WKH UXELFRQ
• Removing spaces and punctuation before you encrypt makes code-breaking somewhat harder
• Easy to hack with frequency analysis (e.g. the most frequent letter in English is "E"; the second is "T"; the third is "A", etc.)
• Download cryptool to see what I mean:
• Passphrases to encrypt and decrypt
• alphabetic (or whole character set) variable shift
• consider the passphrase: "THE QUICK BROWN FOX JUMPS THE LAZY DOGS BACK".
• If this phrase is repeatedly used to shift characters in your message...
• then your first character is shifted by 20 (because "T" is the twentieth letter in the alphabet)
• then your second character is shifted by 8 (because "H" is the eighth letter of the alphabet)
• then your third character is shifted by 5 (because "E" is the fifth letter of the alphabet)
• etc.
• Alternatively, if the message is in ASCII format then you might wish to XOR (exclusive OR) it with the ASCII value of the passphrase...
• then your first character is XOR'd with 84 which is the ASCII value of "T"
• then your second character is XOR'd with 72 which is the ASCII value of "H"
• then your third character is XOR'd with 70 which is the ASCII value of "E"
• etc.
• If you hit the end of your passphrase, just wrap around to the beginning (therefore longer phrases introduce more scrambling).
• If someone guesses your passphrase, then they will be able to decrypt your message
• You use the same passphrase to decrypt (shift back or just XOR a second time)

• Seemingly random passphrases
• in essence, this is what the Germans used with their Enigma Machine. Changing rotors (wiring), and starting settings (initialization value) produced a different code phrase every day. The standard machine only possessed three rotors while the Navy version possessed four.
• BTW, Enigma was a lot easier for British Intelligence to crack than the Lorenz Machine which was used by German high command. Almost everyone in common society has heard about Enigma whilst very few have heard about Lorenz.

#### Transposition Basics

• I won't waste too much time here exception to mention that substitution ciphers still have a common problem: the information still contains positional information which means cipher-text may still be subjected to certain kinds of frequency analysis.
• Transpositions change character position in order to hide positional information thus defeating most kinds of frequency analysis.

#### Keys and other stuff

• Symmetric Keys
• used to both encrypt and decrypt
• this means that either party can both encode or decode
• think of a mechanical lock with one physical key
• https://en.wikipedia.org/wiki/Symmetric_key
• think of these keys as really long passphrases (a 1024 bit key =  a single 128-character passphrase)
• Alternatively: think of each byte in the key acting as a pseudo CPU op-code with instructions like these:
• Substitute single character using polyalphabet X;
• Interchange characters between positions X and Y;
• XOR key character with clear-text character;
• left rotate (shift) bits of character;
• right rotate (shift) bits of character;
• and so on...

• Asymmetric Keys
• both public and private keys are two really large prime numbers
• one key encrypts while another decrypts
• if you encrypt with the private key then anyone with the public key can decrypt
• if you encrypt with the public key then anyone with a private key can decrypt
• think of a mechanical lock with two physical keys (one to close and another to open)
• https://en.wikipedia.org/wiki/Asymmetric_key
• in the case of SSL, each end maintains their own private key whilst the public key is distributed by a trusted third party like Verisign or Thawte to only name two of many.
• If I encrypt a message with my private key, and you then decrypt it with my public key, then you know the encrypted message came from me (electronic signature)
To continue...
• If I encrypt this signed message with your public key before I send it to you, then I will be sure that only you can read it (with your private key).
The message is now secured and verified in both directions

• Computational Load
• Due to a reliance upon a pair of large prime numbers, asymmetric keys require much more computer power to encrypt/decrypt than symmetric keys.
• So before each communication session:
• large random numbers are used to generate a set of symmetric keys (which are also known as session keys)
• asymmetric keys are used to encrypt then exchange (through the communications channel) these symmetric keys
• symmetric keys (session keys) are then used to encrypt/decrypt the message

• Diffie-Hellman key exchange
• this method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel while Eve watches. This key can then be used to encrypt subsequent communications using any cipher.
• Diffie-Hellman key exchange @ wikipedia
• Diffie-Hellman Description - which uses colors to represent a "shared secret" (randomly generated keys)
• Videos: http://www.khanacademy.org/science/brit-cruise/cryptography
• Example Math (Python demo): http://neilrieck.net/dh_demo.html
• Example Math (caveat: implemented in JavaScript with usual math limitations so this demo is restricted to smallish numbers)
Step Alice Bob Notes
1     Choose two random values then notify the other "in the clear"
Rules:
1) y must be smaller than p
2) p must be prime
Example Values: y= and p=
2 randomly picks
secret number A=
randomly picks
secret number B=
similar to starting colors in the video above
3 uses this formula:
a=y^A mod p
to compute public
number a=
uses this formula:
b=y^B mod p
to compute public
number b=
similar to mixed colors in the video above
4 send "a" to Bob send "b" to Alice Partial solutions are exchanged "in the clear"
5 uses Bob's "b" value
in this formula:
key=b^A mod p
to compute shared
secret key=
uses Alice's "a" value
in this formula:
key=a^B mod p
to compute shared
secret key=
both sides compute the same secret key

#### What do you want to do?

• If you want to encrypt a file or hard drive
• you encrypt with your asymmetric public key (which is publically available to everyone) and will decrypt with your private key (which is only known to you)

• If you want to prove who you are on the net (a good example is Secure DNS)
• then you encrypt with your private key.
• others will use your public key then say: "yes, he was the only one who could have encrypted that message"

• If Alice wants to send a message to Bob which can only be read by Bob
• then Alice encrypts using Bob's public key (only he will be able to decrypt with his private key)
• this is what happens during web banking (you use a password to prove who you are; by encrypting with your banks public key, only your bank will be able to decrypt)

• If Alice wants to send a message to Bob but also wants to prove it came from Alice
• then Alice encrypts using Alice's private key (Bob will decrypt using Alice's public key)
• Caveat: eves dropper "Eve" will also have access to Alice's public key so this communication is not considered secure; in fact, it is only known as a "digital signature"

• If Alice wants to send a message to Bob which can only be read by Bob but wishes to ensure that it only came from Alice
• Alice encrypts using Alice's private key ("digital signature")
• Alice encrypts again using Bob's public key
• Bob will decrypt using Bob's private key (only he can do this)
• Bob will decrypt again but this time will use Alice's public key (which only she could have encrypted)

• In SSL/TLS you would always encrypt with the other guys' public key (which everyone has access to via a trusted third party)

• In SSH/SSH2, you create a public/private pair, then copy the public key to the remote end. This means you would always encrypt with your private key. The far end always decrypts with your public key.

• The UNIX/Linux/Enterprise Server community sort of went the way of SSH2 while the public web went the way of SSL/TLS. Today, most systems employ both

• Today, encrypting with large asymmetrical keys is too computational intensive so they are only used to encrypt randomly generated asymmetric session keys. Session keys are then used to drive  cyphers (like TripleDES, BlowFish, TwoFish, etc.)

#### What's in a name?

• Usually, if "S" is the first character then the protocol employs SSH/SSH2:

 SCP secure copy SFTP secure FTP not a real FTP implementation since no ASC (text) mode FTP over SSH FTP over SSH not the same as SFTP SSH secure shell when used as a standalone app, can be used as a terminal emulatorwhen used as a technology, is the basis for other secure apps

• Usually, if "S" is the last character then the protocol employs SSL/TLS:

 FTPS FTP over SSL/TLS HTTPS HTTP over SSL/TLS DNSSEC DNS with security extensions

## External Links

Three Good Books (of many)
• The Code Book: The Science of Secracy (Simon Singh)
• this book is a must read for anyone bootstrapping into this profession
• Applied Cryptography: Protocols, Algorithms, and Source Code in C (Bruce Schneier)
• SSH: The Secure Shell The Definitive Guide (O'Reilly)
• second edition published in May of 2005

Introduction to Cryptography (web)

Tools and Toys

Links:

(mostly) Wikipedia Resources

• Public-key Cryptography
• RSA
• Elliptic Curve Cryptography (who needs prime number anyway?)
• OpenSSL
• OpenSSH
• OpenPGP
• Steganography (hiding information in plain sight (like inside GIFs and JPEGs)
comments:
• First consider a totally red pixel with the HTML color code of "255,0,0". Would your eye be able to see the difference between this color and "254,0,0"? (probably not)
• Now consider a picture in which all the colors have be pre-adjusted to have even color numbers
• A binary code (zeros and ones) could be serially inserted into the picture just by adjusting the color of each addressable pixel (binary 0 = even color; binary 1 = odd color)
• The code would be right before you eyes but you would not see it but a computer could

Back to Home
Neil Rieck
Waterloo, Ontario, Canada.