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Post-quantum cryptography Daniel J. Bernstein & Tanja Lange University of Illinois at Chicago; Ruhr University Bochum & Technische Universiteit Eindhoven 12 September 2020 Cryptography Sender Receiver Alice Bob Tsai

  1. Post-quantum cryptography Daniel J. Bernstein & Tanja Lange University of Illinois at Chicago; Ruhr University Bochum & Technische Universiteit Eindhoven 12 September 2020

  2. � Cryptography Sender Receiver “Alice” “Bob” Tsai Ing-Wen picture credit: By 總 統 府 , Attribution, Wikimedia. Donald Trump picture credit: By Shealah Craighead - White House, Public Domain, Wikimedia. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 2

  3. � Cryptography Sender Untrustworthy network Receiver “Alice” “Eve” “Bob” ◮ Motivation #1: Communication channels are spying on our data. ◮ Motivation #2: Communication channels are modifying our data. Tsai Ing-Wen picture credit: By 總 統 府 , Attribution, Wikimedia. Donald Trump picture credit: By Shealah Craighead - White House, Public Domain, Wikimedia. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 2

  4. � Cryptography Sender Untrustworthy network Receiver “Alice” “Eve” “Bob” ◮ Motivation #1: Communication channels are spying on our data. ◮ Motivation #2: Communication channels are modifying our data. ◮ Literal meaning of cryptography: “secret writing”. ◮ Achieves various security goals by secretly transforming messages. ◮ Confidentiality: Eve cannot infer information about the content ◮ Integrity: Eve cannot modify the message without this being noticed ◮ Authenticity: Bob is convinced that the message originated from Alice Tsai Ing-Wen picture credit: By 總 統 府 , Attribution, Wikimedia. Donald Trump picture credit: By Shealah Craighead - White House, Public Domain, Wikimedia. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 2

  5. � Commonly used systems Sender Untrustworthy network Receiver “Alice” “Eve” “Bob” Cryptography with symmetric keys AES-128 . AES-192 . AES-256 . AES-GCM . ChaCha20 . HMAC-SHA-256 . Poly1305 . SHA-2 . SHA-3 . Salsa20 . Cryptography with public keys BN-254 . Curve25519 . DH . DSA . ECDH . ECDSA . EdDSA . NIST P-256 . NIST P-384 . NIST P-521 . RSA encrypt . RSA sign . secp256k1 . Tsai Ing-Wen picture credit: By 總 統 府 , Attribution, Wikimedia. Donald Trump picture credit: By Shealah Craighead - White House, Public Domain, Wikimedia. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 2

  12. � Commonly used systems Sender Untrustworthy network Receiver “Alice” “Eve” “Bob” Cryptography with symmetric keys AES-128 . AES-192 . AES-256 . AES-GCM . ChaCha20 . HMAC-SHA-256 . Poly1305 . SHA-2 . SHA-3 . Salsa20 . Cryptography with public keys BN-254 . Curve25519 . DH . DSA . ECDH . ECDSA . EdDSA . NIST P-256 . NIST P-384 . NIST P-521 . RSA encrypt . RSA sign . secp256k1 . Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 9

  13. � Commonly used systems Sender Untrustworthy network Receiver “Alice” “Eve” with quantum computer “Bob” Cryptography with symmetric keys AES-128 . AES-192 . AES-256 . AES-GCM . ChaCha20 . HMAC-SHA-256 . Poly1305 . SHA-2 . SHA-3 . Salsa20 . Cryptography with public keys BN-254 . Curve25519 . DH . DSA . ECDH . ECDSA . EdDSA . NIST P-256 . NIST P-384 . NIST P-521 . RSA encrypt . RSA sign . secp256k1 . Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 9

  14. � Symmetric-key authenticated encryption Sender Untrustworthy network Receiver “Alice” “Eve” with quantum computer “Bob” ◮ Very easy solutions if Alice and Bob already share long secret key k : ◮ “One-time pad” for confidentiality. ◮ “Wegman–Carter MAC” for integrity and authenticity. ◮ AES-256: Standardized method to expand short secret key (256-bit k ) into string indistinguishable from long secret key. ◮ AES introduced in 1998 by Daemen and Rijmen. Security analyzed in papers by dozens of cryptanalysts. ◮ No credible threat from quantum algorithms. Grover costs 2 128 . ◮ Some results assume attacker has quantum access to computation, then some systems are weaker . . . but I’d know if my laptop had turned into a quantum computer. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 9

  15. Post-quantum cryptography Cryptography under the assumption that the attacker has a quantum computer. ◮ 1994: Shor’s quantum algorithm. 1996: Grover’s quantum algorithm. Many subsequent papers on quantum algorithms: see quantumalgorithmzoo.org . ◮ 2003: Daniel J. Bernstein introduces term Post-quantum cryptography. ◮ 2006: First International Workshop on Post-Quantum Cryptography. PQCrypto 2006, 2008, 2010, 2011, 2013, 2014, 2016, 2017, 2018, 2019, (soon) 2020. ◮ 2015: NIST hosts its first workshop on post-quantum cryptography. ◮ 2016: NIST announces a standardization project for post-quantum systems. ◮ 2017: Deadline for submissions to the NIST competition. ◮ 2019: Second round of NIST competition begins. ◮ 2020: Third round of NIST competition begins. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 10

  16. 21 December 2017: NIST posts 69 submissions from 260 people. BIG QUAKE . BIKE . CFPKM . Classic McEliece . Compact LWE . CRYSTALS-DILITHIUM . CRYSTALS-KYBER . DAGS . Ding Key Exchange . DME . DRS . DualModeMS . Edon-K . EMBLEM and R.EMBLEM . FALCON . FrodoKEM . GeMSS . Giophantus . Gravity-SPHINCS . Guess Again . Gui . HILA5 . HiMQ-3 . HK17 . HQC . KINDI . LAC . LAKE . LEDAkem . LEDApkc . Lepton . LIMA . Lizard . LOCKER . LOTUS . LUOV . McNie . Mersenne-756839 . MQDSS . NewHope . NTRU Prime . NTRU-HRSS-KEM . NTRUEncrypt . NTS-KEM . Odd Manhattan . OKCN/AKCN/CNKE . Ouroboros-R . Picnic . pqNTRUSign . pqRSA encryption . pqRSA signature . pqsigRM . QC-MDPC KEM . qTESLA . RaCoSS . Rainbow . Ramstake . RankSign . RLCE-KEM . Round2 . RQC . RVB . SABER . SIKE . SPHINCS+ . SRTPI . Three Bears . Titanium . WalnutDSA . Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 11

  17. By end of 2017: 8 out of 69 submissions attacked. BIG QUAKE . BIKE . CFPKM . Classic McEliece . Compact LWE . CRYSTALS-DILITHIUM . CRYSTALS-KYBER . DAGS . Ding Key Exchange . DME . DRS . DualModeMS . Edon-K . EMBLEM and R.EMBLEM . FALCON . FrodoKEM . GeMSS . Giophantus . Gravity-SPHINCS . Guess Again . Gui . HILA5 . HiMQ-3 . HK17 . HQC . KINDI . LAC . LAKE . LEDAkem . LEDApkc . Lepton . LIMA . Lizard . LOCKER . LOTUS . LUOV . McNie . Mersenne-756839 . MQDSS . NewHope . NTRU Prime . NTRU-HRSS-KEM . NTRUEncrypt . NTS-KEM . Odd Manhattan . OKCN/AKCN/CNKE . Ouroboros-R . Picnic . pqNTRUSign . pqRSA encryption . pqRSA signature . pqsigRM . QC-MDPC KEM . qTESLA . RaCoSS . Rainbow . Ramstake . RankSign . RLCE-KEM . Round2 . RQC . RVB . SABER . SIKE . SPHINCS+ . SRTPI . Three Bears . Titanium . WalnutDSA . Some less security than claimed; some really broken; some attack scripts. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 11

  18. By end of 2018: 22 out of 69 submissions attacked. BIG QUAKE . BIKE . CFPKM . Classic McEliece . Compact LWE . CRYSTALS-DILITHIUM . CRYSTALS-KYBER . DAGS . Ding Key Exchange . DME . DRS . DualModeMS . Edon-K . EMBLEM and R.EMBLEM . FALCON . FrodoKEM . GeMSS . Giophantus . Gravity-SPHINCS . Guess Again . Gui . HILA5 . HiMQ-3 . HK17 . HQC . KINDI . LAC . LAKE . LEDAkem . LEDApkc . Lepton . LIMA . Lizard . LOCKER . LOTUS . LUOV . McNie . Mersenne-756839 . MQDSS . NewHope . NTRU Prime . NTRU-HRSS-KEM . NTRUEncrypt . NTS-KEM . Odd Manhattan . OKCN/AKCN/CNKE . Ouroboros-R . Picnic . pqNTRUSign . pqRSA encryption . pqRSA signature . pqsigRM . QC-MDPC KEM . qTESLA . RaCoSS . Rainbow . Ramstake . RankSign . RLCE-KEM . Round2 . RQC . RVB . SABER . SIKE . SPHINCS+ . SRTPI . Three Bears . Titanium . WalnutDSA . Some less security than claimed; some really broken; some attack scripts. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 11

  19. 30 January 2019: 26 candidates retained for second round. BIG QUAKE . BIKE . CFPKM . Classic McEliece . Compact LWE . CRYSTALS-DILITHIUM . CRYSTALS-KYBER . DAGS . Ding Key Exchange . DME . DRS . DualModeMS . Edon-K . EMBLEM and R.EMBLEM . FALCON . FrodoKEM . GeMSS . Giophantus . Gravity-SPHINCS . Guess Again . Gui . HILA5 . HiMQ-3 . HK17 . HQC . KINDI . LAC . LAKE . LEDAkem . LEDApkc . Lepton . LIMA . Lizard . LOCKER . LOTUS . LUOV . McNie . Mersenne-756839 . MQDSS . NewHope . NTRU Prime . NTRU-HRSS-KEM . NTRUEncrypt . NTS-KEM . Odd Manhattan . OKCN/AKCN/CNKE . Ouroboros-R . Picnic . pqNTRUSign . pqRSA encryption . pqRSA signature . pqsigRM . QC-MDPC KEM . qTESLA . RaCoSS . Rainbow . Ramstake . RankSign . RLCE-KEM . Round2 . RQC . RVB . SABER . SIKE . SPHINCS+ . SRTPI . Three Bears . Titanium . WalnutDSA . Some less security than claimed; some really broken; some attack scripts. Merges for second round: HILA5 & Round2; LAKE, LOCKER, & Ouroboros-R; LEDAkem & LEDApkc; NTRUEncrypt & NTRU-HRSS-KEM. Daniel J. Bernstein & Tanja Lange Post-quantum cryptography 11

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