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![Scott Aaronson, “The Limits of
Quantum Computers,” Scientific
American, 2008
“… [quantum computers] would provide
dramatic speedups for a few specific
problems… For other problems, however—
such as playing chess, scheduling airline
flights and proving theorems—evidence now
strongly suggests that quantum computers
would suffer from many of the same
algorithmic limitations as today’s classical
computers.”](https://image.slidesharecdn.com/slidesfromatul-191210193313/85/Quantum-Computing-Cryptography-A-Brief-Introduction-5-320.jpg)
Uploaded byHedera Hashgraph
Quantum Computing & Cryptography: A Brief Introduction
The document discusses the implications of quantum computing on cryptography, emphasizing the weaknesses of public-key cryptography against quantum attacks, while secret-key cryptography may remain secure with larger key sizes. It outlines the current capabilities and limitations of quantum computers, highlighting the need for post-quantum cryptographic solutions and the importance of remaining agile in cryptographic practices. The presentation stresses the urgency of addressing vulnerabilities while awaiting standardization of new algorithms.
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Quantum Computing & Cryptography: A Brief Introduction
- 1. THE TRUST LAYEROF THE INTERNET
- 2. Quantum computing and cryptography HeadofCryptography AtulLuykx Warning:Inthis presentation, Crypto = Cryptography
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- 5. Scott Aaronson, “TheLimits of Quantum Computers,” Scientific American, 2008 “… [quantum computers] would provide dramatic speedups for a few specific problems… For other problems, however— such as playing chess, scheduling airline flights and proving theorems—evidence now strongly suggests that quantum computers would suffer from many of the same algorithmic limitations as today’s classical computers.”
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- 8. Introduction • Head ofCryptography at Hedera • Research Scientist at Visa Research • Post-doc at KU Leuven and UC Davis • PhD at KU Leuven
- 9. Case Study: Bitcointransaction Unlock Phone1. 2. Prepare Transaction 3. Send to blockchain
- 10. Case Study: Bitcointransaction Unlock Phone1. 2. Prepare Transaction 3. Send to blockchain
- 11. Secret-Key Cryptography Aka symmetric-keycrypto • Example: AES (Advanced Encryption Standard) • Impact of quantum computing: negligible, assuming you switch to a larger key size = 1011 Attempt Success? 0000 0001 0010 0011 0100 0101 … N N N N N N … Classical Quantum Grover’s algorithm 2k 2(k/2) AES128 k-bit key 2128 264 AES256 2256 2128
- 12. Step 3: Sendingto the blockchain Unlock Phone1. 2. Prepare Transaction 3. Send to blockchain nonce • Proof-of-work puzzle constructed with hash functions • Example: SHA-256
- 13. Cryptographic Hash functions •Best known method of solving proof-of-work puzzle: brute-force • Grover’s algorithm • Impact: negligible, increase hash function output, increase difficulty
- 14. Preparing a BitcoinTransaction Unlock Phone1. 2. Prepare Transaction 3. Send to blockchain From: you To: friend Amount: 1 BTC … Digital Signature Purpose: ensures transaction is authorized by sender
- 15. Digital signature • Typeof public-key cryptography • Example: RSA 3084, ECDSA • Vulnerable to quantum computers --- ability to recover keys using Shor’s algorithm From: you To: friend Amount: 1 BTC … Valid/Invalid Public Key (ID)
- 16. Flame Malware • Discoveredin 2012 • Used for espionage • Forged a Microsoft certificate to gain access to systems • Found a new cryptographic attack against an algorithm which was widely known by academics to be broken (MD5) • Estimated that the malware was active for as many as 5 years before its discovery • Powerful attack: undetected, widely applicable
- 17. Summary of Impact• Secretkey cryptography: increase the key length • Hash functions: increase output size • Digital signatures, public key cryptography --- need entirely different algorithms
- 18. Next steps • Howmuch time do we have? • What can we do about the attacks against public key crypto?
- 19. How much timedo we have • Current quantum computers < 100 qubits • Qubits are noisy --- require error correction to operate reliably • Best attacks need 1000’s of logical qubits • With error correction, up to 100 000’s • Estimates range from 200 qubits to 0.5 million qubits in 10 years
- 20. What solutions arethere? • Significant amount of research on post-quantum crypto • Lattices • Hash functions • Code-based • Multivariate • NIST competition Image source: Nick Matthewson’s talk at the Second PQC Standardization Conference
- 21. Conclusions • Wait andsee • Await standardization • Vetting of security of algorithms • But pay attention! Can’t just ignore crypto • Need to remain crypto-agile: ability to switch algorithms quickly if necessary
- 22. Further reading Scott Aaron,“The Limits of Quantum Computers”, Scientific American, 2008 http://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Computers.pdf Ronald de Wolf, “The Potential Impact of Quantum Computers on Society”, https://arxiv.org/pdf/1712.05380.pdf NIST Post-Quantum Cryptography, https://csrc.nist.gov/Projects/Post- Quantum-Cryptography Cloudflare Blog on Post-Quantum crypto, https://blog.cloudflare.com/towards-post-quantum-cryptography-in-tls/ How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits, https://arxiv.org/abs/1905.09749 Quantum attacks on Bitcoin, and how to protect against them, https://arxiv.org/pdf/1710.10377.pdf