Encryption basics
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The document provides an overview of encryption basics, detailing various methods from ancient steganography to modern cryptographic algorithms. It covers key concepts such as symmetric and asymmetric encryption, along with specific algorithms like RSA and AES, emphasizing their functionalities and challenges. The text also discusses key distribution issues and introduces hybrid approaches for secure communication.
Encryption basics
- 1. Encryption Basics Kevin O'Brien Washtenaw Linux Users Group
- 2. Ancient History ● Wax tablets – Herodotus ● Shaved head – Herodotus ● Both examples of Steganography (hidden writing) – Steganos (Greek) = hidden – Graphei (Greek) = writing ● Essentially security by obscurity ● More modern version = microdots
- 3. Encryption ● Kryptos (Greek) = hidden ● A message should be unreadable to someone who finds it ● Employs a cipher ● Substitutes one symbol for another ● Not the same as a code!
- 4. Codes ● Codes do not try to obscure the message ● Examples: – Morse code – ASCII ● Codes transform one set of symbols into another without trying to hide the meaning
- 5. Caesar Cipher ● Moved each letter a fixed number of spaces ● Same as ROT13 ● HAL = IBM ● Not very secure, but then Caesar was dealing with barbarians :) ● Trivial to break since there are only 25 schemes to try.
- 6. Substitution Cipher ● Better than Caesar Cipher ● No fixed pattern to how symbols are substituted ● Think of the “brain teaser” puzzles in the newspaper ● Obviously, these can be broken by ordinary people with small effort
- 7. Statistical analysis ● The weakness of Substitution Ciphers is that they are susceptible to statistical analysis ● First shown by Al-Kindi in the 9th century ● In English, letters have a certain frequency – e,t,a,o,i,n,s,h,r,d,l,u.... ● Letter q almost always followed by u, “the” is most common three-letter word, and so on
- 8. Vigenere Square ● Uses a key word or phrase to create a different substitution for each letter of the message ● But if reused could also be analyzed ● Charles Babbage showed that it could be attacked statistically
- 9. One-Time Pads ● A series of unique Vigenere Squares ● Each one is used only once ● Absolutely secure ● But pain the butt to create ● And distribution is an issue ● If enemy gets it, no security
- 10. Mechanical solutions ● Captain Midnight Decoder Ring ● Rotate one disk against another ● Essentially just another Caesar Cipher
- 11. Enigma ● Decoder ring on steroids ● Multiple disks ● Settings change after each letter ● Poles figured out how to analyze ● Passed to Brits ● Bletchley Park & Turing
- 12. Enigma flawed ● First, essentially mechanical means there is a way to attack ● Mechanical cannot be truly random ● No letter could be encrypted as itself ● Key turned out to be mathematics
- 13. Computers ● Originally created to break ciphers ● Collosus used against German Lorenz Cipher ● But computers could be used to create ciphers as well ● By the 1960s it was clear that computers could create unbreakable encryption schemes as long users did not make a mistake
- 14. Key distribution ● But how to distribute keys securely? ● Same issue as with one-time pads ● Whitfield Diffie, Martin Hellman, and Ralph Merkle solved that and created Diffie-Hellman- Merkle Key Exchange ● Diffie later realized that publicly distributed keys could be asymmetric
- 15. RSA ● Ron Rivest, Adi Shamior, and Leonard Adelman first figured out how to do it practically ● Based on one-way function ● Easy to compute, impractical to reverse ● They used large prime numbers which they multiplied together to get an even larger number ● Extremely large numbers are hard to factor, hence the one-way
- 16. Key Pair ● RSA procedure creates two keys ● Each key can decrypt what the other key has encrypted ● But no key can decrypt what it itself has encrypted
- 17. Other Algorithms ● In addition to the RSA prime number algorithm there are two well-known alternatives ● Discrete Logarithm ● Elliptical Curve ● Both are also “one-way” functions that are easy to compute but impractical to reverse
- 18. Symmetric vs. Asymmetric Encryption ● Symmetric means the same key that encrypted the message will also decrypt it ● Very efficient = can easily and quickly encrypt and decrypt ● Key distribution is a problem ● Alice has to send Bob the key before sending the encrypted message ● Eve can listen in and get the key
- 19. Public Key ● This is Asymmetric ● A key pair is generated ● One of the keys is designated as private, the other public ● Arbitrary which is which
- 20. Key Distribution ● Public key gets around the key distribution problem ● The Public key can be freely distributed ● But only the Private key can decrypt what the Public key has encrypted ● But also requires a lot more resources
- 21. Symmetric Standard DES ● Data Encryption Standard (DES) developed by IBM for the U.S. Government ● Employed several techniques still in use today – Block Cipher – XOR ● http://en.wikipedia.org/wiki/Data_Encryption_St andard
- 22. Block Cipher ● A Block Cipher operates on a fixed-length block of bits to transform them ● Plain text is turned into ciphertext block by block ● Generally the transformation is repeated a number times called rounds ● https://en.wikipedia.org/wiki/Block_cipher
- 23. XOR ● Most common transformation ● Stands for “Exclusive Or” ● In logic, means that either A is true or B is true, but not both ● In circuit design, if either A or B is sending a signal it is output, but if both are, nothing is output
- 24. XOR in Cryptography ● The message and the key are expressed in binary ● They are XORed together ● This essentially means adding without carrying the 1 ● If both A and B are 0, or both are 1, the result is 0. If one is zero and the other is 1, the result is 1
- 25. Coding ● Remember that a code is just a transparent transform of information from one scheme to another ● ASCII is such a code ● It takes letters and symbols and turns them into binary numbers ● http://en.wikipedia.org/wiki/ASCII
- 26. Coding Example 1 ● I want to send a message “cat” ● C=1100011 ● A=1100001 ● T=1110100 ● CAT=110001111000011110100 ● This is still transparent
- 27. Key ● Now I will choose a key to use, and I choose “dog” ● D=1100100 ● 0=1101111 ● G=1100111 ● DOG=110010011011111100111
- 28. XOR
- 29. XOR is reversible ● If you take the result text from the example, and XOR it with the key, you get back the original message
- 30. Encryption Algorithm ● Combines a number of transformations and combines them in rounds ● For symmetric encryption needs to be reversible ● XOR is always part of the process
- 31. DES ● Block size was initially 64-bits ● But one bit from each byte was devoted to parity checking ● Effective length 56-bits, therefore
- 32. DES role ● Bruce Schneier said about it “”DES did more to galvanize the field of cryptanalysis than anything else. Now there was an algorithm to study.” ● Standard against which all others were compared ● Key length just too small ● Cracked in 22 hours in 1999
- 33. Triple DES ● Uses 3 independent 56-bit keys in a repeated process ● Each block encrypted three times, once with each key ● Probably safe for now
- 34. AES ● Advanced Encryption Standard ● Adopted in 2001 by NIST ● Considered best symmetric algorithm available now
- 35. Rijndael Cipher ● Named for developers, Vincent Rijman and Joan Daeman ● Basis of AES ● Block size of 128-bits ● Key sizes of 128, 192, or 256 bits are allowed ● Called AES-128, AES192, or AES-256 ● As with all other algorithms, repeated rounds of transformations
- 36. Symmetric Summed Up ● Fast and efficient ● Relies on a single shared key ● Does not require entropy because the key needs only to be agreed, not random
- 37. Asymmetric Standards ● Solve the key distribution problem ● Requires entropy (randomness) along with one- way functions ● Three kinds – Multiplying large prime numbers – Discrete logarithm – Elliptic Curve
- 38. Prime Number Approach ● This is what RSA uses ● Two large prime numbers are multiplied together ● This is easy to do ● But factoring the result to get back the original primes is computationally infeasible with current technology ● But research into factorization is ongoing, it is an arms race
- 39. What numbers? ● Generally in the neighborhood of 1024 digits ● Must be randomly selected ● Should not be “near” each other ● Product is used to generate other prime numbers which help form the key pair ● One is arbitrarily made private, the other public
- 40. Discrete Logarithm ● Involves finding an integer that solves a logarithmic equation ● Used in Elgamal encryption and Diffie-Hellman- Merkle Key Exchange ● Choosing the particular numbers for the logarithmic equation is where the entropy comes in ● Diffie-Hellman-Merkle Key Exchange is used for Perfect Forward Secrecy
- 41. Elliptic Curve ● Builds on Discrete Logarithm approach ● A curve with the right properties is chosen, then a point on that curve ● Then you need to find the discrete logarithm of that point ● Entropy comes in when choosing the point on the curve
- 42. Issues with Elliptic Curve ● NIST has recommended 15 curves as suitable ● It appears NSA pushed one with weaknesses as the default ● But Elliptic Curve done right is faster and more efficient than RSA or general Discrete Logarithm approaches ● So it should be the future.
- 43. Symmetric vs. Asymmetric ● Symmetric is fast and efficient, but needs no entropy ● Symmetric has key exchange problems ● Asymmetric is resource-intensive, requires randomness ● Asymmetric solves key exchange
- 44. Hybrid Approach ● Most public key crypto uses Asymmetric encryption to distribute a Symmetric key ● So the inefficient algorithm is only used at the beginning ● Everything after that is done with the efficient Symmetric algorithm
- 45. Example: E-mail ● When you encrypt a message to someone, you use a Symmetric key to encrypt a message ● Then you use their Public key to encrypt the Symmetric key ● They get the message and use their Private key to decrypt the Symmetric key ● Then they use the Symmetric key to decrypt the message
- 46. See also ● SSL certificates ● SSH tunnels ● Generally, the same techniques are used over and over ● So learn it once and you can quickly learn other uses