Quantum Cryptography Quantum Cryptography Quantum Quantum Crypto - PDF document

Quantum Cryptography Quantum Cryptography Quantum Quantum Crypto ?? Crypto ?? or or How Alice Outwits Eve How Alice Outwits Eve Cani Cani Samuel J. Lomonaco, Jr. Samuel J. Lomonaco, Jr. Dept. of Comp. Sci Dept. of Comp. Sci. & Electrical Engineering . & Electrical Engineering University of Maryland Baltimore County University of Maryland Baltimore County Baltimore, MD 21250 Baltimore, MD 21250 Email: Email: Lomonaco@UMBC.EDU Lomonaco@UMBC.EDU WebPage: WebPage : http:// http://www.csee.umbc.edu/~lomonaco www.csee.umbc.edu/~lomonaco L L- -O O- -O O- -P P & Bob This work is supported by: Introducing Alice Introducing Alice & Bob This work is supported by: ! Throb ! Throb The Defense Advance Research Projects • Alice Alice Bob Bob Agency (DARPA) & Air Force Research Laboratory (AFRL), Air Force Materiel Command, USAF Agreement Number F30602-01-2-0522. The National Institute for Standards • Sender Sender and Technology (NIST) Receiver Receiver • The Mathematical Sciences Research Eve Eve Bah ! Bah ! Institute (MSRI). Humbug ! Humbug ! • The L-O-O-P Fund. L- L -O O- -O O- -P P • The Institute of Scientific Interchange Eavesdropper Eavesdropper Introducing Alice & Bob & Bob Introducing Alice Key Idea Key Idea Throb ! ! Throb Alice Roberto Bob Alice Roberto Bob Quantum cryptography provides a new Quantum cryptography provides a new mechanism enabling the parties mechanism enabling the parties communicating with one another to: communicating with one another to: Sender Sender Receiver Receiver Automatically detect eavesdropping. . Automatically detect eavesdropping Eve Eve Pia Pia Consequently, it provides a means of Consequently, it provides a means of Bah ! Bah ! Humbug ! Humbug ! determining when an encrypted determining when an encrypted Spia Spia communication has been compromised. communication has been compromised. Eavesdropper Eavesdropper 1

The Dilemma The Dilemma Alice Takes a Cryptography Course Alice Takes a Cryptography Course How can I How can I outwit Eve outwit Eve How do I prevent How do I prevent ??? ??? Eve from Eve from eavesdropping ??? eavesdropping ??? ? ? ? ? ? ? ? ? ? ? ? ? Alice Alice Alice Alice Classical Classical Shannon Shannon The The Bit Bit Classical Classical Decisive World World Individual 0 or 1 Classical Bits Bits Can Can Be Be Copied Copied Classical Cryptographic Cryptographic In In Out Out Copying Copying Systems Systems Machine Machine 2

Catch 22 A Classical Cryptographic Communication System A Classical Cryptographic Communication System Catch 22 Il cane che Il cane che si si morde morde la coda la coda Eavesdropper Eavesdropper Eve Eve Receiver Receiver Transmitter Transmitter Bob Bob Alice Alice There are perfectly good ways to There are perfectly good ways to Info Insecure Info Info Insecure Info Encrypter Encrypter Decrypter Decrypter Source Source Channel Channel Sink Sink communicate in secret provided provided communicate in secret Key Key we can already communicate in we can already communicate in P = Plaintext P = Plaintext C = Ciphertext C = Ciphertext P = Plaintext P = Plaintext secret … secret … Secure Secure Channel Channel Classical Crypto Systems Classical Crypto Systems Types of Communication Security Types of Communication Security • Practical • Practical Secrec Secrecy y (Circa 106 BC) (Circa 106 BC) Ciphertext breakable after Ciphertext breakable after x x years years CHECK LIST CHECK LIST • Catch 22 Solved ? • Examples: : Data Encryption Standard (DES), Data Encryption Standard (DES), Examples Catch 22 Solved ? NO NO Advanced Data Encryption Standard (AES) Advanced Data Encryption Standard (AES) • Authentication ? • Authentication ? NO NO • Eavesdropping Detection ? • • Perfect • Eavesdropping Detection ? NO NO Perfect Security Security (Shannon, 1949) (Shannon, 1949) Ciphertext Ciphertext C C without key gives no without key gives no information about plaintext information about plaintext P P ( ( ) ) ( ) Prob P|C Prob P = An Example of Perfect Security An Example of Perfect Security Difficulties Difficulties The Vernam The Vernam Cipher Cipher, a.k.a., , a.k.a., the One the One- -Time Time- -Pad Pad • PROBLEM: Long random bit sequences • Consider a random sequence of bits Consider a random sequence of bits PROBLEM: Long random bit sequences must be sent over a secure channel must be sent over a secure channel Key K K K � K � = = = = 1 2 n • CATCH 22: There are perfectly good ways • Encrypting algorithm Encrypting algorithm CATCH 22: There are perfectly good ways to communicate in secret provided we can to communicate in secret provided we can C P K mod 2 = = + + i i i communicate in secret … communicate in secret … P 0110 0101 1101 = • KEY PROBLEM in CRYPTOGRAPHY: • K 1010 1110 0100 = KEY PROBLEM in CRYPTOGRAPHY: ⊕ ⊕ C = = 1100 1011 1001 We need some way to securely We need some way to securely • Perfectly secure if key • communicate key communicate key Perfectly secure if key K K is unknown is unknown • Easy to decode with • Easy to decode with Key = K Key = K 3

Objective of All Crypto Systems: Safety Safety Objective of All Crypto Systems: Safety Safety Objective of All Crypto Systems: Objective of All Crypto Systems: Old Idea: Old Idea: New Idea: New Idea: Unconditional Security Unconditional Security Computational Security Security Computational The crypto system can resist any The crypto system can resist any The crypto system is unbreakable The crypto system is unbreakable cryptanalitic attack no matter cryptanalitic attack no matter because of the computational cost of because of the computational cost of how much computation is involved. how much computation is involved. cryptanalysis, but would succumb to , but would succumb to cryptanalysis an attack with unlimited computation. an attack with unlimited computation. Computational Security Computational Security Computational Security Computational Security (Diffie ( Diffie- -Hellman Hellman, circa 1970) , circa 1970) For example, the crypto system: For example, the crypto system: Public Key Crypto Systems … Example: RSA Public Key Crypto Systems … Example: RSA • Requires • 30 years to be broken on the Requires 10 10 30 years to be broken on the Public Phone Public Phone E B E fastest known computer fastest known computer Directory Directory B • Or, requires • C C C C 100 bits of memory to break Or, requires 10 10 100 bits of memory to break Insecure Insecure • Or, requires • Channel Channel 30 euros to break Or, requires 10 10 30 euros to break Encrypter Encrypter Decrypter Decrypter D D B C C B P P P P System computationally safe implies safe for System computationally safe implies safe for Eavesdropper Eavesdropper Eve all practical purposes all practical purposes Eve Info Info Info Info Source Sink Source Sink Idea comes from a field in computer science called Idea comes from a field in computer science called Transmitter Transmitter Receiver Receiver Computational Complexity. Computational Complexity . Alice Bob Alice Bob Public Key Crypto Systems Public Key Crypto Systems Alice Takes a Quantum Mechanics Course Alice Takes a Quantum Mechanics Course CHECK LIST CHECK LIST • Catch 22 Solved ? • Catch 22 Solved ? Yes & No Yes & No • • Authentication ? Yes Authentication ? Yes • Eavesdropping Detection ? • No No Eavesdropping Detection ? Alice Alice 4

Introducing the Quantum Bit … … The The Qubit Qubit Introducing the Quantum Bit The The Look Here Look Here Indecisive Indecisive Quantum Quantum Individual Individual World World Can be both 0 0 & 1 1 Can be both & at the same time ! at the same time ! Quantum Representations of Quantum Representations of Qubits Qubits Quantum Representations of Qubits Quantum Representations of Qubits 1 Example 1 Example 1. . A spin A spin- - particle particle Example 2 Example 2. . The polarization state of a photon The polarization state of a photon 2 Horizontal Horizontal Vertical Vertical Polarization Polarization Polarization Polarization 1 = � 0 = ↔ = ↔ Spin Up Spin Down Spin Up Spin Down 1 0 1 0 H = Where does a Where does a Qubit Qubit live ? live ? Def. A Hilbert Space is a vector A A Qubit Qubit is a is a quantum quantum space over together with an inner H � Home product such that , : H H → � − − − − × system whose whose state state is is system 1) u u v , u v , u v , & vu u , v u , vu , + + = = + + + = = + 1 2 1 2 1 2 1 2 represented by a Ket Ket represented by a 2) u , v u v , λ λ = λ λ lying in a 2 lying in a 2- -D Hilbert D Hilbert ∗ = 3) u v , v u , Space H Space ∀ lim u H 4) Cauchy seq u u … , , in , H ∈ n 1 2 n →∞ →∞ The elements of will be called kets The elements of will be called H kets, and , and will be denoted by label will be denoted by 5