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Cited by 81Cryptography and Data SecurityAdvanced Authentication Protocols SecurityCryptography and Residue Arithmetic

Recommendation for pair-wise key establishment using integer factorization cryptography

Open access
Barker, Elaine, Chen, Lily, Roginsky, Allen, Vassilev, Apostol, Davis, Richard, Simon, Scott·2019
DOI 10.6028/nist.sp.800-56br2
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Abstract

This publication has been developed by NIST in accordance with its statutory responsibilities under the Federal Information Security Modernization Act (FISMA) of 2014, 44 U.S.C. § 3551 et seq., Public Law (P.L.) 113-283.NIST is responsible for developing information security standards and guidelines, including minimum requirements for federal information systems, but such standards and guidelines shall not apply to national security systems without the express approval of appropriate federal officials exercising policy authority over such systems.This guideline is consistent with the requirements of the

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  • An n bit prime order elliptic curve group provides approximately n/2 bits of classical security, whilst RSA-1024, RSA-2048 and RSA-3072 provide approximately 80, 112 and 128 bits of classical security, respectively, according to the model used by NIST.

    “Note that an n bit prime order elliptic curve group provides approximately n/ 2 bits of classical security (see Appendix D to [4]), since the best classical attacks are cycle-finding attacks, whilst RSA-1024, RSA-2048 and RSA-3072 provide approximately 80 , 112 and 128 bits of classical security, respectively, according to the model used by NIST (see Appendix D to [5]).”

    From How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2021) · cites this paper as [5]

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  1. ISO/IEC 8825] International Organization for Standardization/International Electrotechnical Commission (2015) ISO/IEC 8825-1:2015 -Information Technology -ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.800-56Br2 Rules (CER) and Distinguished Encoding Rules (DER) (International Organization for Standardization, Geneva, Switzerland), 5th Ed. · DOI
  2. Output (p, q) as the prime factors. Any local copies of d, p, q , m, t, r, x, y, g and any intermediate values used during the execution of the RecoverPrimeFactors function shall be destroyed prior to or during steps 4 and 6. Note that this includes the values for p and q that are output in step 6. This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.800-56Br2 5. Section 4.2, para. 1: A sentence was inserted as sentence 3 (for clarification). 6. Section 4.3: Discussion about the the RSA-KEM-KWS scheme has been removed. A reference to the hybrid method for key transport has been inserted. Figure 3 was modified. · DOI

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Authors
Barker, E., Chen, L., Roginsky, A., Vassilev, A., Davis, R., & Simon, S.
Affiliations
National Institute of Standards and Technology (US)
ORCID
Publisher
National Institute of Standards and Technology
Published
2019-03
DOI
10.6028/nist.sp.800-56br2
OpenAlex
W4246562921
Cited by
81
References
26
Citations by year
2026: 8 · 2025: 3 · 2024: 5 · 2023: 18 · 2022: 14 · 2021: 8 · 2020: 14 · 2019: 11
Type
report
Language
en
Open access
Funders
Information Technology Laboratory
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Cryptography and Data Security
  • Physical Sciences › Computer Science › Computer Networks and Communications › Advanced Authentication Protocols Security
  • Physical Sciences › Computer Science › Information Systems › Cryptography and Residue Arithmetic
Keywords
pairwise key establishment, public-key cryptography, key exchange, NIST guidelines

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