How Quantum Cryptography Quantum . . . and Quantum Computing How - PowerPoint PPT Presentation

What Are Cyber- . . . For Cyber-Physical . . . How Cyber-Security Is . . . Quantum Challenge to . . . How Quantum Cryptography Quantum . . . and Quantum Computing How Quantum . . . How to Deal with This . . . Can Make Cyber-Physical Quantum Computing . . . What About Optimization Systems More Secure Home Page Title Page Deepak Tosh, Oscar Galindo, Vladik Kreinovich, and Olga Kosheleva ◭◭ ◮◮ ◭ ◮ University of Texas at El Paso El Paso, Texas 79968, USA Page 1 of 43 dktosh@utep.edu, ogalindomo@utep.edu, vladik@utep.edu, olgak@utep.edu Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 1. What Are Cyber-Physical Systems: A Brief How Cyber-Security Is . . . Reminder Quantum Challenge to . . . • Many modern complex systems include both computa- Quantum . . . tional parts and physical parts. How Quantum . . . How to Deal with This . . . • E.g., a power station includes: Quantum Computing . . . – actual electricity generators and transformers, as What About Optimization well as Home Page – computational devices that control the generators, Title Page transformers, and communications. ◭◭ ◮◮ • A city-wide system includes computers on all levels: ◭ ◮ – from microprocessors controlling individual devices Page 2 of 43 – to computers providing, e.g., city-wide optimiza- Go Back tion of transportation flows. Full Screen • Such systems are known as cyber-physical systems. Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 2. For Cyber-Physical Systems, Cyber-Security Is How Cyber-Security Is . . . Vital Quantum Challenge to . . . • Many computing system have been successfully attacked, Quantum . . . with information stolen or corrupted. How Quantum . . . How to Deal with This . . . • In general, cyber-security is an important problem. Quantum Computing . . . • This problem is especially vital for cyber-physical sys- What About Optimization tems, since: Home Page – by hacking into these systems, Title Page – an adversary can cause catastrophic damage: e.g., ◭◭ ◮◮ blow up a nuclear power station. ◭ ◮ Page 3 of 43 Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 3. How Cyber-Security Is Provided Now How Cyber-Security Is . . . • In general, there are two main directions in providing Quantum Challenge to . . . cyber-security of the current cyber-physical systems. Quantum . . . How Quantum . . . • On the one hand: How to Deal with This . . . – there are consistent efforts to educate users, Quantum Computing . . . – so that adversaries will not use social engineering What About Optimization (as they do now) to penetrate systems. Home Page • For this purpose, users should create strong passwords, Title Page avoid disclosing them, never send them by email, etc. ◭◭ ◮◮ • On the technical side, cyber-security is (or at least ◭ ◮ should be) provided by making sure that: Page 4 of 43 – all communications between sensors and computers Go Back (and between computers themselves) – are encrypted. Full Screen • This encryption is usually based on the RSA algorithm. Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 4. Cyber-Security Now (cont-d) How Cyber-Security Is . . . • An agent selects two very large (up to 100 decimal Quantum Challenge to . . . digits long) prime numbers p and q . Quantum . . . How Quantum . . . • He sends their product n = p · q openly to everyone How to Deal with This . . . interested. Quantum Computing . . . • Once a recipient knows the value n , he/she can encrypt What About Optimization any message. Home Page • Any agent who knows the values p and q can decrypt Title Page this message. ◭◭ ◮◮ • However, without knowing p and q , decryption does ◭ ◮ not seem possible. Page 5 of 43 Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 5. Cyber-Security Now (cont-d) How Cyber-Security Is . . . • This algorithm is secure since no efficient algorithm is Quantum Challenge to . . . known for factoring large integers: Quantum . . . How Quantum . . . – other than trying all possible prime factors from 1 to √ n , How to Deal with This . . . Quantum Computing . . . – but this would require about 10 50 computational What About Optimization steps, Home Page – this is more than the number of moments of time Title Page in the Universe. ◭◭ ◮◮ ◭ ◮ Page 6 of 43 Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 6. Quantum Challenge to Cyber-Security How Cyber-Security Is . . . • A quantum algorithm designed by Peter Shor enables Quantum Challenge to . . . us to factor large integers in feasible time. Quantum . . . How Quantum . . . • Thus, it can break the RSA encryption. How to Deal with This . . . • Similar algorithms can break all similar encryptions Quantum Computing . . . algorithms. What About Optimization Home Page • This result practically guaranteed that this challenge has to be taken seriously. Title Page • Before this result, quantum computing was mostly an ◭◭ ◮◮ academic topic close to science fiction; but: ◭ ◮ – once it turned out that a quantum computer will Page 7 of 43 enable to us to read all the messages sent so far, Go Back – all the governments and all big companies have in- Full Screen vested billions of dollars into quantum computing. Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 7. Quantum Challenge (cont-d) How Cyber-Security Is . . . • Whoever gets there first will be the first to read all the Quantum Challenge to . . . information. Quantum . . . How Quantum . . . • Thus, this person will gain a tremendous advantage How to Deal with This . . . over others. Quantum Computing . . . • Thousands of researchers and practitioners all over the What About Optimization world are working on designing a quantum computer. Home Page • This practically guarantees that it will be eventually Title Page built. ◭◭ ◮◮ • It may take 5 years, it may take 20 years, but it will ◭ ◮ be built. Page 8 of 43 • And so, we must be ready for this challenge. Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 8. Quantum Cryptography: A Secure Alternative How Cyber-Security Is . . . to RSA Encoding Quantum Challenge to . . . • The situation with cyber-security is not as gloomy as Quantum . . . it may seem at first glance. How Quantum . . . How to Deal with This . . . • Yes, quantum algorithms make RSA vulnerable. Quantum Computing . . . • However, quantum algorithms also provide an unbreak- What About Optimization able (so far) alternative to RSA. Home Page • It is called quantum cryptography . Title Page • Another good news is that: ◭◭ ◮◮ – while general quantum computing algorithms can- ◭ ◮ not yet be practically implemented Page 9 of 43 – quantum cryptography is perfectly practical, and it Go Back has been implemented. Full Screen • There is a quantum computing-protected communica- tion line between the White House and the Pentagon. Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 9. Quantum Cryptography (cont-d) How Cyber-Security Is . . . • China used quantum cryptography it to communicat- Quantum Challenge to . . . ing with a satellite. Quantum . . . How Quantum . . . • Yet another good news is that: How to Deal with This . . . – not only the current quantum cryptography algo- Quantum Computing . . . rithm unbreakable; What About Optimization – this algorithm is also, in some reasonable sense, the Home Page best possible. Title Page • Not only it is the best possible for two-agent commu- ◭◭ ◮◮ nication. ◭ ◮ • It is also clear how to use it in the most efficient way Page 10 of 43 for multi-agent communications. Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 10. What We Do in This Talk How Cyber-Security Is . . . • First, we provide a brief description of quantum cryp- Quantum Challenge to . . . tography. Quantum . . . How Quantum . . . • Our main objective is to use quantum cryptography How to Deal with This . . . for making cyber-physical systems more secure. Quantum Computing . . . • We will also analyze how quantum computing can help What About Optimization in the design of cyber-physical systems. Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 11 of 43 Go Back Full Screen Close Quit

What Are Cyber- . . . For Cyber-Physical . . . 11. Basic Facts From Quantum Mechanics: A Brief How Cyber-Security Is . . . Reminder Quantum Challenge to . . . • In quantum mechanics: Quantum . . . How Quantum . . . – in addition to the usual classical states s 1 , . . . , s n , How to Deal with This . . . – we also have superpositions , i.e., states of the type Quantum Computing . . . s = c 1 · | s 1 � + . . . + c n · | s n � . What About Optimization Home Page • Here c 1 , . . . , c n are complex numbers for which Title Page | c 1 | 2 + . . . + | c n | 2 = 1 . ◭◭ ◮◮ • These states can be viewed as vectors ( c 1 , . . . , c n ) in ◭ ◮ the n -dimensional complex-valued vector space C n . Page 12 of 43 • In particular, each of the original states s i corresponds Go Back to a vector (0 , . . . , 0 , 1 , 0 , . . . , 0) with 1 in the i -th place. Full Screen Close Quit