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Outline

Cryptography

Past, Present, and Future

Presenter: Group 3

Ahmed Abdalla,Troy Brant, Gabe Campbell, Ana Lim, Saudamini Zarapkar

Outline

A Brief History of Cryptography

Symmetric Encryption

Asymmetric Cryptography

Politics in Cryptography

Quantum Cryptography

Summary

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Ancient times
- Substitution ciphers - method of encrypting by which units of plaintext are substituted with cipher text according to a regular system.
- EX: Atbash cipher (circa 500 BC)
- based on Hebrew alphabet,
- where the first letter is substituted by the last letter, the second letter by the second to last letter and so on.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Frequency analysis - where one examines the frequency of substituted letters, from which they can estimate certain letters which appear repeatedly in the plaintext language.
- First recorded use in 9th century.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Polyalphabetic Cipher
- Based on substitution, but used multiple substitution alphabets.
- Invented by Leon Battista

Alberti in 1467.Alberti would

use a common Caesar cipher

to encrypt messages, but

would switch alphabet keys,

indicating switch by

capitalizing the first letter of

the new alphabet.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Cryptanalysis of Polyalphabetic Cipher
- Charles Babbage
- 1854 – He found that the critical weakness in a polyalphabetic was the short and repetitive nature of the key.
- Freidrich Kasiski
- 1863 – published Die Geheimschriften und die Dechiffrierkunst that was first published account of deciphering polyalphabetic ciphers, especially the Vigenère cipher.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Babbage/Kasiski Test

Ciphertext: DYDUXRMHTVDVNQDQNWDYDUXRMHARTJGWNQD

- Look for repeated groups of letters and count the number of letters between the beginning of each group.
- Factor the numbers. If there are similarities, that is the length of the key.
- If the keyword is N letters long, then every Nth letter must be enciphered using the same letter of the keytext. Grouping every Nth letter together, it is possible to use frequency analysis to decipher message.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- WWII Innovations
- Electromechanical

rotor machines that

worked with any

combination rotors

- Enigma famous for

its messages that

were decrypted by

Allied forces –

intel known as ULTRA.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- One-Time Pads
- Developed in 1917 by Gilbert Vernam, an AT&T Bell Labs engineer.
- OTP is an encryption algorithm where the plaintext is combined with a random key that is as long as the plaintext so that it’s used only once.
- OTP proven unbreakable by Claude Shannon, a fellow engineer at Bell Labs who provided a proof in his information theory.

Outline

- A Brief History of Cryptography
- Symmetic Encryption
- Asymmetic Cryptography
- Politics in Cryptography
- Quantum Cryptography
- Summary

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Overview
- The Serpent Algorithm
- The TwoFish Algorithm

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Overview
- DES
- Invented by IBM
- In 1976 became an official Federal Information Processing Standard (FIPS) NIST
- Effective key length 56-bit
- Double DES, Triple DES

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

NIST contest

- the First AES Conference
- August 20, 1998
- 15 candidate algorithms
- 5 US, 10 international

- the Second AES Conference
- March 22, 1999
- Technical Analysis
- Announcement of 5 finalists
- Mars, RC6, Rijndeal,

Serpent, and TwoFish

- the Third AES Conference
- April 13, 2000
- Winner: Rijndeal

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Serpent Algorithm
- Second place
- Designed by Ross Anderson, Eli Biham and Lars Knudsen
- Substitution-Permutation Network
- S-boxes: transform input bits into output bits
- P-boxes: permute or transpose bits across S-box inputs.

Symmetric Encryption

- The Serpent Algorithm
- a block size of 128 bits
- key length vary from 128 to 256 bits long
- 33 128-bit subkeys
- 32 rounds

Symmetric Encryption

- The Serpent Algorithm
- Algorithm:
- initial permutation
- 32 rounds of Key Mixing, pass through S-boxes,
- and linear tranf ormation
- a final permutation

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Serpent Algorithm
- Hardware
- Elbird and Paar use Field Programmable Gate Array (FPGA) , encryption rate 4Gbit/s
- Can be implemented in satellite TV, HDTV

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Serpent Algorithm
- Strength:
- 32 rounds, probability < 2^-120
- 33 128 bits key
- Different rounds use different S-boxes
- No weak keys, no semi-weak keys

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Serpent Algorithm
- Weakness:
- Fixed substitution table
- Key distribution
- Key management

Symmetric Encryption

- The TwoFish Algorithm
- Designed by Bruce Schneier, John Kelsey, Doug Whiting, David Wagner, Chris Hall, and Niels Ferguson
- block size 128 bits
- 128 to 256 bits key length
- 16 rounds

Symmetric Encryption

- The TwoFish Algorithm
- Split plaintext into 32-bit words
- Input whitening:
- XORed with four words of key
- 16 rounds
- Output whitening

Symmetric Encryptoin

- The TwoFish Algorithm
- Hardware:
- Smart Card
- Very-large-scale integration (VLSI)

Symmetric Encryptoin

- The TwoFish Algorithm
- Strenght:
- 1-bit rotation
- no Equivalent key
- lacks simplicity

Symmetric Encryptoin

- The TwoFish Algorithm
- Weakness:
- vulnerable to divide-and-conquer attack of the key space.
- lacks simplicity
- Key distribution
- Key management

Outline

- A Brief History of Cryptography
- Symmetric Encryption
- Asymmetric Cryptography
- Politics in Cryptography
- Quantum Cryptography
- Summary

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- First proposed in 1976
- "New Directions in Cryptography" Diffie and Hellman
- Proposed Public Key encryption
- Did not produce an algorithm
- Discussed Digital Signatures
- Outlined a method of key exchange

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The RSA Algorithm
- “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems” published in 1978
- Proposed by Rivest, Shimar, and Adleman
- Called RSA after the authors
- Used a computationally difficult problem
- C = Me( mod N )
- Breaking requires factoring of large numbers

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Elgamal Algorithm
- "A public key cryptosystem and a signature scheme based on discrete logarithms" -- 1985
- Proposed by Taher Elgamal
- More accurately followed Diffie-Hellman's suggestion
- Key Exchange
- Digital Signatures
- Based around discrete logarithms
- C = ek mod p
- Better mathematical foundation than RSA

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- RSA being first...
- Was used for all public key applications
- Secure Socket Layer (SSL)
- Pretty Good Privacy (PGP)
- Elgamal later...
- Replaced RSA in PGP
- Better implementation of Diffie-Hellman
- Key exchange
- Signatures

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- RSA vs. Elgamal
- RSA uses longer keys
- Elgamal creates longer cipher text
- RSA encryption less computationally intensive
- Elgamal completely open
- RSA key creation very computationally intensive
- Elgamal based on better math
- RSA offers less security per bit
- Elgamal uses evanescent (ephemeral) keys

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The present
- RSA still used for ssl
- SSL Requires few key generations
- Elgamal
- Selected as the Digital Signature Standard (DSS)
- Replaced RSA as default in PGP
- Implementation of PKI
- Public Key Infrastructures (PKI) becoming popular
- Generally uses RSA
- Provides secure communications across networks

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Future
- Continued deployment of PKI
- Development of Elliptic Curve algorithms
- Still theoretical
- Already allowed for in standards

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- The Problems
- Not provably secure
- Considered computationally secure
- Will require larger and larger keys
- Increasing computational power
- Theoretical attacks possible
- RSA bad key generation
- Quantum computing
- Will probably obsolesce public key technology
- Easy factoring of large numbers

Outline

- A Brief History of Cryptography
- Symmetric Encryption
- Asymmetric Cryptography
- Politics in Cryptography
- Quantum Cryptography
- Summary

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Introduction
- The National Security Agency
- NSA influence
- Government export control on cryptography
- Current crypto-political status

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Introduction
- World War II - Cryptography major force
- Cryptography - Government strictly regulates public development and deployment
- 1970s - No big issues with government control over cryptography until 1970s and DES

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- National Security Agency (NSA)
- Officially established on December 9, 1952
- President Harry Truman authorizes creation
- Agency in the Department of Defense
- Purpose to monitor international communications enhance US security
- Must use cryptanalysis to read intercepted messages

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- NSA (Continue)
- Highly secretive
- Believed to be largest employer of mathematicians and cryptographers in the world
- Publicly or commercially developed cryptographic materials must be approved by the NSA before export or publication

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- NSA Influence
- Data Encryption Standard (DES)
- 1972 - 1975
- IBM winning algorithm sent to NSA
- NSA “suggested” 2 changes:
- Changes to substitution boxes (“s-boxes”)
- Key length reduced from 128 bits to 56 bits
- Trap-door fear

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- NSA Influence
- Khufu and Khafre block ciphers
- 1989
- Ralph Merkle, current Georgia Tech professor
- Request to publish papers denied by NSA
- Copies sent to John Gilmore
- Gilmore published the papers on a newsgroup
- NSA miffed, but no legal action

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- NSA Influence
- Pretty Good Privacy (PGP)
- 1991
- Phil Zimmerman
- Released PGP to the public on the Internet
- NSA and government criminally investigate Zimmerman and battle him in court
- In 1996, government drops case and result is seen as victory for computer industry

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Government Export Control
- Cryptography classified as “munitions”
- Joint export control by 2 US Departments
- Department of State
- Handles most cryptography export regulations
- Department of Commerce
- Jurisdiction over technology exports
- Concedes issues involving crypt. to State Dept.
- Key length limited to 40 bits (until recently)

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Government Export Control
- Applied Cryptography Case
- 1994
- Phil Karn vs. government export laws
- Applied Cryptography by Bruce Schneier
- Book exportable, but floppy disk not
- Case dropped in 2000
- Due to a new law relaxing export regulations

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Current Crypto-Political Status
- In 2000, Dept. of Commerce relaxed cryptography laws
- Publicly available source code freely exportable
- Custom cryptographic software still requires a license for export
- Exportable everywhere (except 7 nations)

- A Brief History of Cryptography
- Symmetric Encryption
- Asymmetric Cryptography
- Politics in Cryptography
- Quantum Cryptography
- Summary

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Introduction to quantum theory
- Overview of quantum computing
- Implications of quantum computing on current encryption algorithms
- The BB84 Algorithm
- The E91 Algorithm
- Limitations and the Future

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Heisenberg Uncertainty Principle
- Certain quantum properties are intrinsically related (ex. position and momentum)
- Knowing the exact details of both is impossible
- Measuring one introduces some level of randomness to the other.
- This will be used in quantum cryptography to detect interception.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Superposition
- Before being observed, a particle can exist as the superposition of multiple states.
- When the particle is observed, it collapses into only one of those states.
- Traditional bits exist as either a 0 or 1.
- Quantum bits (qubits) can exist in both states simultaneously.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Entanglement
- Two or more particles can have properties that are linked, even when they are spatially separated
- Ex. Two entangled particles exist with entangled spin (spin can be up or down).
- Measuring the spin on one particle ensures that the other will have the opposite spin.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Shor's Algorithm is a method for factoring prime numbers and solve discrete logarithms
- RSA and Elgamal assume complexity in solving these problems.
- Shor's utilizes superposition to evaluate multiple states simultaneously and factor the number in polynomial time.
- RSA and Elgamal are theoretically broken.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- DES
- Grover's quantum search algorithm allows for enhanced database searching, again using superposition.
- This allows for a significantly faster brute for attack on the DES algorithm.
- Speed increase is “only” quadratic and increasing key length still provides extra security.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Proposed by Bennett and Brassard

in 1984.

- Utilizes the uncertainty principle to ensure secure quantum key distribution (QKD).
- Key is based upon polarizations of single photons sent between source (Alice) and receiver (Bob)

90° for a 0 and 0° for a 1 OR 135° for 0 and 45° for a 1

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Alice chooses a random string of

bits and random sequence of bases.

- She sends Bob a train of single photons.
- Bob measures each photon with a randomly chosen polarization
- Bob tells Alice what polarizations he chose.
- Alice tells Bob which were correct
- Bob and Alice pick a few random bits to verify the keys integrity.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- What if there was an eavesdropper (Eve)?
- Eve could only get the polarization correct half the time and half of those would be measured wrong.
- An incorrect choice would destroy the actual information due to the uncertainty principle.
- So if Eve measured every bit, he would see an error rate of 25%.
- When Bob and Alice compare bits, any inconsistency would indicate Eve's presence.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Need to send exactly ONE photon for each bit.
- An extra would theoretically allow Eve to intercept.
- Lasers this precise are hard and expensive to produce.
- Single photon receptors are difficult as well.
- Susceptible to a specific man in the middle attack.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Proposed by A. Ekert in 1991.
- Similar to the BB84 algorithm, but utilizing entanglement as well as uncertainty.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- A third party or Alice creates a

pair of polarized, entangled photons.

- The polarization and bit value for each photon is random.
- Alice receives one photon, Bob the other.
- Each measures their photons using random bases.
- They exchange which were used. If they used the same basis, the resulting measurements will be correlated.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- What if ever persistent Eve

eavesdrops again?

- As before, incorrect measurement of the photon's value destroys the information.
- Additionally, should Eve try and generate photons of her own, checks can be run to be sure the photons were entangled.
- Overall more secure than BB84.
- Main disadvantage is higher cost compared to BB84.

- History
- Symmetric
- Asymmetric
- Politics
- Quantum
- Summary

- Challenges
- Dedicated fiber run between Bob and Alice
- High cost of equipment.
- Implementations still somewhat untested.
- Future of QKD
- Transmission distances are steadily increasing. Current max is 150km.
- New algorithms and implementations are being proposed regularly.
- Quantum physics developments will continue to provide more options.

Summary

- History of Cryptography
- Symmetric Encryption
- Asymmetric Encryption
- Political in Cryptography
- Quantum Cryptography

Image Sources

- AJ Elbirt, C. Paar. “An FPGA Implementation and Performance Evaluation of the Serpent Block Cipher.” The Association for Computer Machinery. International Symposium on Field Programmable Gate Arrays. Pg 33-40. 2000.

http://portal.acm.org/citation.cfm?id=329176&coll=portal&dl=ACM

- A. Poppe, A. Fedrizzi, H. Hübel, R. Ursin, A. Zeilinger, “Entangled State Quantum Key Distribution and Teleportation”, 31st European Conference on Optical Communication, 2005, pt. 5, 61 vol.5
- B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall, and N. Ferguson. “Twofish: A 128-Bit Block Cipher.”
- cipher wheel: http://www.practicalturkish.com/ottoman-present-day-codewheel.jpg
- SIGABA: http://encyclopedia.quickseek.com/images/Sigaba.jpg

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