1 Cryptography Presenter: Group 3 Ahmed Abdalla, Troy Brant, Gabe Campbell, Ana Lim, Saudamini Zarapkar Past, Present, and Future

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Cryptography

Presenter: Group 3

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

Past, Present, and Future

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

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Brief History of Cryptography 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.

Outline History Symmetric Asymmetric Politics Quantum Summary

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History (continue)

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.


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History (continue) 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.


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History (continue)

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.


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History (continue) Babbage/Kasiski TestCiphertext: 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.


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History (continue) 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.


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History (continue) 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.


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

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Symmetric Encryption Overview The Serpent Algorithm The TwoFish Algorithm


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Symmetric (Continue) 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


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Symmetric (Continue)

the First AES Conference August 20, 1998 15 candidate algorithms

• 5 US, 10 international


NIST contest 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

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Symmetric Encryption 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.


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

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

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The Serpent AlgorithmOutline History Symmetric Asymmetric Politics Quantum Summary

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The Serpent Algorithm: Linear Transformation

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Hardware• Elbird and Paar use Field Programmable Gate

Array (FPGA) , encryption rate 4Gbit/s• Can be implemented in satellite TV, HDTV


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


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Weakness:• Fixed substitution table• Key distribution• Key management


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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

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Symmetric Encryption The TwoFish Algorithm

Split plaintext into 32-bit words Input whitening:

• XORed with four words of key 16 rounds Output whitening

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Symmetric Encryption

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Symmetric Encryptoin The TwoFish Algorithm

Hardware:• Smart Card• Very-large-scale integration (VLSI)

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Strenght:• 1-bit rotation• no Equivalent key• lacks simplicity

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Weakness:• vulnerable to divide-and-conquer attack of the key

space.• lacks simplicity • Key distribution• Key management

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Asymmetric Cryptography 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


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Asymmetric Cryptography 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


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Asymmetric Cryptography 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


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Asymmetric Cryptography

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


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Asymmetric Cryptography 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


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Asymmetric Cryptography 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


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Asymmetric Cryptography

The Future Continued deployment of PKI

Development of Elliptic Curve algorithms• Still theoretical

• Already allowed for in standards


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Asymmetric Cryptography 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


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Politics and Cryptography

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


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Politics and Cryptography 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


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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



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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



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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



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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



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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



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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)



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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



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Politics and Cryptography 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)


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Quantum Cryptography 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


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Quantum Theory 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.


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Quantum Theory 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.


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Quantum Theory 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.


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Breaking Current Algorithms

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.


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Breaking Current Algorithms

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.


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The BB84 Algorithm 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


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The BB84 Algorithm 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.


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The BB84 Algorithm

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.


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Disadvantages of BB84

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.


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Using Quantum Entanglement Proposed by A. Ekert

in 1991. Similar to the BB84

algorithm, but utilizing entanglement as well as uncertainty.


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The E91 Algorithm 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.


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The E91 Algorithm 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.


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Challenges and the Future 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.


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Summary

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

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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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Documents

1 Cryptography Presenter: Group 3 Ahmed Abdalla, Troy Brant, Gabe Campbell, Ana Lim, Saudamini Zarapkar Past, Present, and Future