ETSI TR 103 823 V1.1.1 (2021-09)

CYBER; Quantum-Safe Public-Key Encryption and Key Encapsulation

DTR/CYBER-QSC-0017

General Information

• Status: Not Published
• Technical Committee: CYBER QSC - Quantum-Safe Cryptography
• Current Stage: 12 - Completion
• Due Date: 13-Oct-2021
• Completion Date: 20-Sep-2021

Standards Content (Sample)

TECHNICAL REPORT
CYBER;
Quantum-Safe Public-Key Encryption and Key Encapsulation

2 ETSI TR 103 823 V1.1.1 (2021-09)

Reference
DTR/CYBER-QSC-0017
Keywords
algorithm, cybersecurity
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ETSI
3 ETSI TR 103 823 V1.1.1 (2021-09)
Contents
Intellectual Property Rights . 7
Foreword . 7
Modal verbs terminology . 7
1 Scope . 8
2 References . 8
2.1 Normative references . 8
2.2 Informative references . 8
3 Definition of terms, symbols and abbreviations . 9
3.1 Terms . 9
3.2 Symbols . 10
3.3 Abbreviations . 10
4 Introduction . 11
5 Background . 12
5.1 Terminology . 12
5.2 Families of post-quantum algorithms . 12
5.3 Security categories . 13
5.4 Security properties . 13
5.5 Finalists and alternate candidates at a glance . 14
6 Finalists . 15
6.1 Classic McEliece . 15
6.1.1 Overview . 15
6.1.2 Parameters. 15
6.1.3 Auxiliary primitives . 15
6.1.4 Public-key encryption scheme . 16
6.1.4.1 McEliece.PKE.KeyGen . 16
6.1.4.2 McEliece.PKE.Enc . 16
6.1.4.3 McEliece.PKE.Dec . 16
6.1.5 Key encapsulation mechanism . 17
6.1.5.1 McEliece.KEM.KeyGen . 17
6.1.5.2 McEliece.KEM.Enc . 17
6.1.5.3 McEliece.KEM.Dec . 17
6.1.6 Parameter sets . 18
6.1.7 Security . 18
6.1.8 Performance . 18
6.2 KYBER . 19
6.2.1 Overview . 19
6.2.2 Parameters. 19
6.2.3 Auxiliary primitives . 20
6.2.4 Public-key encryption scheme . 20
6.2.4.1 KYBER.PKE.KeyGen . 20
6.2.4.2 KYBER.PKE.Enc . 21
6.2.4.3 KYBER.PKE.Dec . 21
6.2.5 Key encapsulation mechanism . 21
6.2.5.1 KYBER.KEM.KeyGen . 21
6.2.5.2 KYBER.KEM.Enc . 22
6.2.5.3 KYBER.KEM.Dec . 22
6.2.6 Parameter sets . 22
6.2.7 Security . 23
6.2.8 Performance . 23
6.3 NTRU . 23
6.3.1 Overview . 23
6.3.2 Parameters. 24
6.3.3 Auxiliary primitives . 24
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4 ETSI TR 103 823 V1.1.1 (2021-09)
6.3.4 Public-key encryption scheme . 24
6.3.4.1 NTRU.PKE.KeyGen . 24
6.3.4.2 NTRU.PKE.Enc . 25
6.3.4.3 NTRU.PKE.Dec . 25
6.3.5 Key encapsulation mechanism . 25
6.3.5.1 NTRU.KEM.KeyGen . 25
6.3.5.2 NTRU.KEM.Enc . 26
6.3.5.3 NTRU.KEM.Dec . 26
6.3.6 Parameter sets . 26
6.3.7 Security . 26
6.3.8 Performance . 27
6.4 SABER . 27
6.4.1 Overview . 27
6.4.2 Parameters. 27
6.4.3 Auxiliary primitives . 28
6.4.4 Public-key encryption scheme . 28
6.4.4.1 SABER.PKE.KeyGen . 28
6.4.4.2 SABER.PKE.Enc . 29
6.4.4.3 SABER.PKE.Dec . 29
6.4.5 Key encapsulation mechanism . 29
6.4.5.1 SABER.KEM.KeyGen . 29
6.4.5.2 SABER.KEM.Enc . 29
6.4.5.3 SABER.KEM.Dec . 30
6.4.6 Parameter sets . 30
6.4.7 Security . 30
6.4.8 Performance . 31
7 Alternate candidates . 31
7.1 BIKE . 31
7.1.1 Overview . 31
7.1.2 Parameters. 32
7.1.3 Decoding . 32
7.1.4 Auxiliary primitives . 32
7.1.5 Public-key encryption scheme . 32
7.1.5.1 BIKE.PKE.KeyGen. 32
7.1.5.2 BIKE.PKE.Enc . 33
7.1.5.3 BIKE.PKE.Dec . 33
7.1.6 Key encapsulation mechanism . 33
7.1.6.1 BIKE.KEM.KeyGen . 33
7.1.6.2 BIKE.KEM.Enc . 34
7.1.6.3 BIKE.KEM.Dec . 34
7.1.7 Parameter sets . 34
7.1.8 Security . 35
7.1.9 Performance . 35
7.2 FrodoKEM . 35
7.2.1 Overview . 35
7.2.2 Parameters. 35
7.2.3 Auxiliary primitives . 36
7.2.4 Public-key encryption scheme . 36
7.2.4.1 Frodo.PKE.KeyGen . 36
7.2.4.2 Frodo.PKE.Enc . 36
7.2.4.3 Frodo.PKE.Dec . 37
7.2.5 Key encapsulation mechanism . 37
7.2.5.1 Frodo.KEM.KeyGen . 37
7.2.5.2 Frodo.KEM.Enc . 37
7.2.5.3 Frodo.KEM.Dec . 37
7.2.6 Parameter sets . 38
7.2.7 Security . 38
7.2.8 Performance . 39
7.3 HQC . 39
7.3.1 Overview . 39
7.3.2 Parameters. 39
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5 ETSI TR 103 823 V1.1.1 (2021-09)
7.3.3 Auxiliary error correction . 39
7.3.4 Auxiliary primitives . 40
7.3.5 Public-key encryption scheme . 40
7.3.5.1 HQC.PKE.KeyGen . 40
7.3.5.2 HQC.PKE.Enc . 40
7.3.5.3 HQC.PKE.Dec . 41
7.3.6 Key encapsulation mechanism . 41
7.3.6.1 HQC.KEM.KeyGen . 41
7.3.6.2 HQC.KEM.Enc . 41
7.3.6.3 HQC.KEM.Dec . 41
7.3.7 Parameter sets . 42
7.3.8 Security . 42
7.3.9 Performance . 43
7.4 NTRU Prime . 43
7.4.1 Overview . 43
7.4.2 Parameters. 43
7.4.3 Auxiliary primitives . 43
7.4.4 Streamlined NTRU Prime public-key encryption scheme . 44
7.4.4.1 SNTRUP.PKE.KeyGen . 44
7.4.4.2 SNTRUP.PKE.Enc . 44
7.4.4.3 SNTRUP.PKE.Dec . 45
7.4.5 Streamlined NTRU Prime key encapsulation mechanism . 45
7.4.5.1 SNTRUP.KEM.KeyGen . 45
7.4.5.2 SNTRUP.KEM.Enc . 45
7.4.5.3 SNTRUP.KEM.Dec . 45
7.4.6 NTRU LPRime public-key encryption scheme . 46
7.4.6.1 NTRULPR.PKE.KeyGen . 46
7.4.6.2 NTRULPR.PKE.Enc . 46
7.4.6.3 NTRULPR.PKE.Dec. 46
7.4.7 NTRU LPRime key encapsulation mechanism. 47
7.4.7.1 NTRULPR.KEM.KeyGen . 47
7.4.7.2 NTRULPR.KEM.Enc . 47
7.4.7.3 NTRULPR.KEM.Dec . 47
7.4.8 Parameter sets . 47
7.4.9 Security . 48
7.4.10 Performance . 49
7.5 SIKE . 49
7.5.1 Overview . 49
7.5.2 Parameters. 50
7.5.3 Auxiliary primitives . 50
7.5.4 Public-key encryption scheme . 50
7.5.4.1 SIKE.PKE.KeyGen . 50
7.5.4.2 SIKE.PKE.Enc . 50
7.5.4.3 SIKE.PKE.Dec . 51
7.5.5 Key encapsulation mechanism . 51
7.5.5.1 SIKE.KEM.KeyGen . 51
7.5.5.2 SIKE.KEM.Enc . 51
7.5.5.3 SIKE.KEM.Dec . 52
7.5.6 Parameter sets . 52
7.5.7 Security . 53
7.5.8 Performance . 53
Annex A: Proofs of security. 54
A.1 Introduction . 54
A.2 Security models . 54
A.3 Computational resources . 54
A.4 Tightness . 54
A.5 Worst-case to average-case reductions . 55
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6 ETSI TR 103 823 V1.1.1 (2021-09)
A.6 Random oracles . 55
Annex B: Security properties . 56
B.1 Introduction . 56
B.2 Public-key encryption. 56
B.3 Key encapsulation . 56
B.4 One-wayness . 57
B.5 CPA to CCA transforms . 57
Annex C: Code-based costing methodology . 58
C.1 Introduction . 58
C.2 Information set decoding . 58
C.3 Asymptotic complexity . 58
C.4 Quantum information set decoding . 59
C.5 Costing metrics . 59
Annex D: Lattice costing methodology . 60
D.1 Introduction . 60
D.2 Lattice reduction . 60
D.3 Enumeration and sieving . 60
D.4 Core-SVP . 60
D.5 Alternative metrics . 61
History . 62

ETSI
7 ETSI TR 103 823 V1.1.1 (2021-09)
Intellectual Property Rights
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Foreword
This Technical Report (TR) has been produced by ETSI Technical Committee Cyber Security (CYBER).
Modal verbs terminology
In the present document "should", "should not", "may", "need not", "will", "will not", "can" and "cannot" are to be
interpreted as described in clause 3.2 of the ETSI Drafting Rules (Verbal forms for the expression of provisions).
"must" and "must not" are NOT allowed in ETSI deliverables except when used in direct citation.
ETSI
8 ETSI TR 103 823 V1.1.1 (2021-09)
1 Scope
The present document provides technical descriptions of the Public-Key Encryption (PKE) and Key Encapsulation
Mechanisms (KEMs) submitted to the National Institute for Standards and Technology (NIST) for the third round of
their Post-Quantum Cryptography (PQC) standardization process.
2 References
2.1 Normative references
Normative references are not applicable in the present document.
2.2 Informative references
References are either specific (identified by date of publication and/or edition number or version number) or
non-specific. For specific references, only the cited version applies. For non-specific references, the latest version of the
referenced document (including any amendments) applies.
NOTE: While any hyperlinks included in this clause were valid at the time of publication, ETSI cannot guarantee
their long term validity.
The following referenced documents are not necessary for the application of the present document but they assist the
user with regard to a particular subject area.
[i.1] NIST FIPS 197: "Advanced Encryption Standard (AES)".
[i.2] NIST FIPS 180-4: "Secure Hash Standard".
[i.3] NIST FIPS 202: "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions".
[i.4] NIST IR 8105: "Report on Post-Quantum Cryptography".
[i.5] NIST FIPS 186-4: "Digital Signature Standard (DSS)".
[i.6] NIST SP-56A: "Recommendation for Pair-Wise Key Establishment Schemes Using Discrete
Logarithm Cryptography".
[i.7] NIST SP-56B: "Recommendation for Pair-Wise Key Establishment Schemes Using Integer
Factorization Cryptography".
[i.8] NIST: "Submission Requirements and Evaluation Criteria for the Post-Quantum Cryptography
Standardization Process", December 2016.
NOTE: Available at https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-
proposals-final-dec-2016.pdf.
[i.9] NIST Post-Quantum Cryptography Standardization: "Round 1 Submissions".
NOTE: Available at https://csrc.nist.gov/Projects/Post-Quantum-Cryptography/Round-1-Submissions.
[i.10] NIST IR 8240: "Status Report on the First Round of the NIST Post-Quantum Standardization
Process".
[i.11] NIST Post-Quantum Cryptography Standardization: "Round 2 Submissions".
NOTE: Available at https://csrc.nist.gov/Projects/post-quantum-cryptography/round-2-submissions.
[i.12] NIST IR 8309: "Status Report on the Second Round of the NIST Post-Quantum Standardization
Process".
ETSI
9 ETSI TR 103 823 V1.1.1 (2021-09)
[i.13] NIST Post-Quantum Cryptography Standardization: "Round 3 Submissions".
NOTE: Available at https://csrc.nist.gov/Projects/post-quantum-cryptography/round-3-submissions.
[i.14] ETSI TR 103 616: "CYBER; Quantum-Safe Signatures".
[i.15] E. Fujisaki and T. Okamoto: "Secure integration of asymmetric and symmetric encryption
schemes", CRYPTO, 1999.
[i.16] D. Hofheinz, K. Hövelmanns and E. Kiltz: "A modular analysis of the Fujisaki-Okamoto
transformation", TCC, 2017.
[i.17] N. Drucker, Shay Gueron and D. Kostic: "QC-MDPC decoders with several shades of gray",
PQCrypto, 2020.
[i.18] R. Canto Torres and N. Sendrier: "Analysis of information set decoding for a sub-linear error
weight", PQCrypto, 2016.
[i.19] N. Bindel, M. Hamburg, K. Hövelmanns, A. Hülsing, and E. Persichetti: "Tighter proofs of CCA
security in the quantum random oracle model", TCC, 2019.
[i.20] M.R. Albrecht, V. Gheorghiu, E.W. Postlethwaite and J.M. Schanck: "Estimating quantum
speedups for lattice sieves", Cryptology ePrint Archive, Report 2019/1161, 2019.
[i.21] E. Prange: "The use of information sets in decoding cyclic codes", IRE Transactions on
Information Theory 8.5 (1962): 5-9.
[i.22] P.J. Lee and E.F. Brickell: "An observation on the security of McEliece's public-key
cryptosystem", EUROCRYPT, 1988.
[i.23] J. Stern: "A method for finding codewords of small weight", International Colloquium on Coding
Theory and Applications. Springer, Berlin, Heidelberg, 1988.
[i.24] A. May, A. Meurer and E. Thomae: "Decoding random linear codes in O ̃(2^0.054n)",
ASIACRYPT, 2011.
[i.25] A. Becker, A. Joux, A. May and A. Meurer: "Decoding random binary linear codes in 2^(n/20):
How 1 + 1 = 0 improves information set decoding", EUROCRYPT, 2012.
[i.26] N. Sendrier: "Decoding one out of many", PQCrypto, 2011.
[i.27] D.J. Bernstein: "Grover vs. McEliece", PQCrypto, 2010.
[i.28] G. Kachigar and J.-P. Tillich: "Quantum information set decoding algorithms", PQCrypto, 2017.
[i.29] M. Naehrig and J. Renes: "Dual isogenies and their application to public-key compression for
isogeny-based cryptography", ASIACRYPT, 2019.
[i.30] G. Pereira, J. Doliskani and D. Jao: "x-only point addition formula and faster torsion basis
generation in compressed SIKE", Cryptology ePrint Archive, Report 2020/431, 2020.
3 Definition of terms, symbols and abbreviations
3.1 Terms
For the purposes of the present document, the following terms apply:
weight: number of non-zero components of a vector or the number of non-zero coefficients of a polynomial
ETSI
10 ETSI TR 103 823 V1.1.1 (2021-09)
3.2 Symbols
For the purposes of the present document, the following symbols apply:
� Bold upper-case letters denote matrices (over some ring or field)
�
� The transpose of the matrix �
� The � � identity matrix
�
� Bold lower-case letters denote vectors (over some ring or field)
�
� The transpose of the vector �
⟨a,b⟩ The inner product of vectors � and � (defined over some common ring)
0 The all-zero vector consisting of � entries
�
� ≔� � is assigned the value of �
� =� The values of � and � are equal
� ≠� The values of � and � are not equal
� ∥� The concatenation of � and �
⊕ Bitwise exclusive or
⊥ Failure
⌈�⌋ The value of � when rounded to the nearest integer, with ties broken by rounding up
⌊ ⌉
� Modulus switching of � from modulus � to modulus �
�→�
� �
� � A cryptographic hash function
���� A cryptographic hash function
��(�) The weight of the polynomial �
� A finite field
� A finite field modulo �
�
ℤ The ring of integers
ℤ The ring of integers modulo �
�
� A ring of polynomials
� A ring of polynomials modulo �
�
��
� The set of � � matrices with coefficients in �
� �
�
� The set of 1� matrices with coefficients in �
� �
� Centered binomial distribution of width �
�
� Probability distribution over ℤ
3.3 Abbreviations
For the purposes of the present document, the following abbreviations apply:
AES Advanced Encryption Standard
BIKE Bit Flipping Key Exchange
BKZ Blockwise Korkine-Zolotarev
CCA Chosen-Ciphertext Attack
CPA Chosen-Plaintext Attack
DEM Data Encapsulation Mechanism
HQC Hamming Quasi-Cyclic
KEM Key Encapsulation Mechanism
KDF Key Derivation Function
LWE Learning With Errors
LWR Learning With Rounding
MLWE Module Learning With Errors
MLWR Module Learning With Rounding
NIST National Institute of Standards and Technology
NTT Number Theoretic Transform
OW-CPA One-Wayness against Chosen-Plaintext Attack
PKE Public-Key Encryption
PQC Post-Quantum Cryptography
PRF Pseudorandom Function
QROM Quantum Random Oracle Model
RLWR Ring Learning With Rounding
ROM Random Oracle Model
ETSI
11 ETSI TR 103 823 V1.1.1 (2021-09)
SHA Secure Hash Algorithm
SIDH Supersingular Isogeny Diffie-Hellman
SIKE Supersingular Isogeny Key Encapsulation
SVP Shortest Vector Problem
XOF Extendable Output Function
4 Introduction
The National Institute of Standards and Technology (NIST), an agency of the U.S. Department of Commerce, is
responsible for producing cryptographic standards for the protection of sensitive U.S. Federal Government information.
NIST standards, such as the Advanced Encryption Standard (AES) [i.1] and Secure Hash Algorithm (SHA) standards
[i.2] [i.3], are used globally in many different protocols and products.
In April 2016 NIST announced [i.4] their intention to a
...