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PUBLIC INFORMATION SECURITY IN A POST-QUANTUM WORLD Jessica R. Miller CSIT560 – Networking Security Montclair State Univeristy Dept. of Computer Science An analysis of quantum and post-quantum cr yptographic techniques WHAT WE WILL COVER Quantum Computing Overview & Analysis Current Systems & their Post-Quantum Weaknesses The Future: Are We Prepared? Conclusion A COUPLE OF IMPORTANT POINTS BEFORE WE START Quantum Cr yptography != Post-Quantum Cr yptography Quantum Computers != Smaller, Faster Conventional Computers SECTION I: QUANTUM COMPUTING OVERVIEW & ANALYSIS Qubit Quantum superposition Quantum entanglement Quantum annealing QUANTUM COMPUTING OVERLY SIMPLIFIED VO CA B? R E A L LY ? ? Quantum Computers: What’s going on? D-WAVE 2007: D-Wave Systems claimed to have a working 28-qubit quantum computer on the heels of a 16-qubit prototype. 2015: D-Wave Systems claims to have broken the 1000 qubit barrier G re at ex p lan at ion o f h ow q uan t um an n e alin g o n D - Wave wo rk s h e re : h t t p s :// www.yo ut ub e.c o m / wat c h?v = U V _RlCA c 5Zs Controversy: Are D-Wave Systems Computers really “Quantum”? Image credit: IBM Research https://www-03.ibm.com/press/us/en/photo/48259.wss SO WHAT HAVE WE ACTUALLY DONE? We have factored the number 15 using Shor’s Algorithm (more later) and five trapped ions as qubits h t t p :/ /p hys ic s world .c om / c ws / ar tic le /n ews / 2016/ m ar /0 4/ sh or s - algor ith m is - im p le m e nte d- us ing -f ive -trap pe d -io ns We have been able to factor the number 56,153 utilizing NMR quantum computing (and a minimization algorithm, similar to D-Wave’s method) h t t p :/ /ar xiv.o rg/ p df/ 141 1.6758 . pd f We have a way to solve optimization problems in a debatably quantum way h t t p :/ /www.dwave sys .c o m /d -wave -two -s ys tem SECTION II: CURRENT SYSTEMS AND THEIR POST-QUANTUM WEAKNESSES CURRENT SYSTEMS Cryptographic Algorithm Type Purpose Impact from large-scale quantum computer AES-256 Symmetric key Encryption Larger key sizes needed Hash functions Larger output needed Public key Signatures, key establishment No longer secure ECDSA, ECDH (Elliptic Public key Curve Cryptography) Signatures, key exchange No longer secure DSA (Finite Field Cryptography) Signatures, key exchange No longer secure SHA-256, SHA-3 RSA Public key Table credit: NISTIR 8105 Draft: Report on Post-Quantum Cryptography BREAKING THE SYSTEM: AN EXAMPLE BREAKING THE SYSTEM: AN EXAMPLE RSA’s Quantum Threat: Shor’s Algorithm “Given an integer N, find its prime factors p & q” Shor: “I got this in 5 steps .. And a quantum computer” Fo l l owi n g ex p l anat i on a d a p t e d f ro m A n a s tas i a M a rc h e n kova & S c o t t A a ro ns on: h t t p s : // m e di u m .c o m/ q u an t u m - b it s /b re ak - r s a - e n c r y pt i o n - wi t h - t h is - o n e - we i rd t r i c k - d 9 5 5 e 3 3 9 4 8 7 0 # . o d8 5 7 l 4 l 9 h t t p : / / www. s c o t t aaro n so n . c o m/bl o g/ ? p= 2 0 8 BREAKING THE SYSTEM: AN EXAMPLE Step 1: Back 2 Basics Greatest Common Divisor algorithm: choose random positive integers m, and if gcd(m, N) == 1, continue This will take forever .. we need something less random! Step 2: A Wild Sequence Appears! m mod N, m 2 mod N, m 3 mod N, m 4 mod N, … (Thanks, Euler) We want to find the per iod P of this sequence, which we can use to find non-tr ivial pr ime factors of N BREAKING THE SYSTEM: AN EXAMPLE We find the per iod P in Step 2, and then we just continue with the rest of the algor ithm: Step 3: If / Then If per iod P is odd, go back to Step 1; Else, continue Step 4: Checkpoint Check that m P/2 + 1 != 0 mod N Step 5: Solve gcd(m P/2 – 1, N) Spoiler alert: It’s always a non-trivial prime f actor of N WAIT. WAIT. WAIT. WHERE IS THE QUANTUM?? BREAKING THE SYSTEM: AN EXAMPLE PLOT TWIST: STEP 2 IS QUANTUM In Step 2, we r un into an issue: If our N is large it will also take forever and provide no real speedup over the classical GCD algor ithm. So, to get the period P, Shor uses the Quantum Fourier Transfor m, or QFT for shor t. STILL WITH ME? GREAT. Let’s look at something else. Something that isn’t headache inducing math. Please. SECTION III: THE FUTURE - ARE WE PREPARED? DON’T WORRY: NOT EVERYTHING IS BROKEN AES vs. Grover’s Classical Attack takes 2 n steps With Grover’s, br ute force attack takes 2 n/2 steps Now, onto some fun things we can do with quantum computing! (Actually Illidan, I think we might be alright) Remember Alice and Bob? THE ONGOING ADVENTURES OF BOB, ALICE, AND THEIR FRENEMIE EVE Image credit: Wikipedia https://en.wikipedia.org/wiki/Public-key_cryptography THE ONGOING ADVENTURES OF BOB, ALICE, AND THEIR FRENEMIE EVE .. PLUS PHOTONS http://searchsecurity.techtarget.com/definition/quantum-cryptography Pretty neat, right? See this paper from ETSI for more sweet applications of Quantum Cr ypto: http://w w w.etsi.org/ima ges/files/ETSI WhitePa per s/QuantumSa f eWhitepaper.pdf SECTION IV: CONCLUSION NSA suite b cryptography announcement Kaspersky 2015 security bulletin NIST call for quantum-resistant algorithms Research into PQCrypto Already making movements toward new standards & analyzing what we have Historically, though it can take decades to establish and implement new crypto-standards, we’ve got time. For references & current status: jessir yan2016.wordpress.com QUESTIONS?