Cited by 19Coding theory and cryptographyError Correcting Code TechniquesCryptographic Implementations and Security

AES as Error Correction: Cryptosystems for Reliable Communication

Open access
Cohen, Alejandro, D’Oliveira, Rafael G. L., Duffy, Ken R., Woo, Jongchan, Medard, Muriel·2023·IEEE Communications Letters

Abstract

In this letter, we show that the Advanced Encryption Standard (AES) cryptosystem can be utilized as an error-correcting code to obtain reliability over noisy communication and data systems. Specifically, we show that by composing a simple padding followed by encrypting with AES, we can achieve error-correcting performance similar to random codes. We conduct an empirical comparison between our AES-based error correction approach, Random Linear Codes, and CA-Polar codes to assess their performance in practical scenarios. Our results show that the AES-based approach achieves nearly identical performance to the other well-established error-correcting codes.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper shows that cryptosystems with uniform or pseudouniform outputs, such as AES, can be used directly as error-correcting codes by padding the message and decoding with GRAND. Empirically, AES with zero padding performs almost the same as random linear codes and CA-Polar codes for a length-128, rate-0.91 setting.

Key findings

  • The deterministic CEC scheme can asymptotically transmit at rate \(k/n\) with arbitrarily low error probability if \(k/n < C\), where \(C\) is the BSC or AWGN capacity, when the cryptosystem is a random function.
  • The probabilistic CEC scheme can asymptotically transmit at rate \(k/(n+r)\) if \((k+r_0)/(n+r) < C\); the paper notes this bound “might not be tight.”
  • In simulations with \(n=128\), \(k=116\), zero padding \(n-k=12\), and rate \(R=0.91\), AES as an error-correcting code achieved BER and BLER “almost the same” as RLC and CA-Polar codes.
  • With hard-decision GRAND, RLC and AES achieved the same performance; CRC-based schemes using GRAND were slightly better at SNR higher than \(\sim 8\) dB.
  • The proposed input plaintext counter (IP-CTR) mode avoids CBC-style error propagation and the CTR issue that plaintext is not an AES input, while obtaining the same error-correcting performance as the ECB-based scheme in Section IV-A.

Methods

  • Theoretical: defines cryptosystems, random functions, and random codes, then proves that padding followed by a random-function cryptosystem yields a random code and thus approaches capacity under the noisy-channel coding theorem.
  • Empirical: simulates an AWGN channel with BPSK modulation, comparing AES-FIPS-197 with zero padding, random linear codes, and CRC-aided polar codes, all of length \(n=128\) and rate \(R=0.91\).
  • Decoding: uses a modified joint decryption-decoding scheme with GRAND and the soft-information variant ORBGRAND.

Limitations

  • The paper states that security guarantees of the padding approach require further analysis and leaves this direction for future work.
  • The paper states that the bound in Theorem 2 might not be tight, so higher rates than stated might be achievable.
  • Evident from the text: the empirical evaluation is limited to AWGN/BPSK, a single short block length \(n=128\), rate \(R=0.91\), and does not include a security analysis; the paper also notes ECB mode does not hide raw-data patterns.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1109/lcomm.2023.3285404

Cites

41 of 41 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 12 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    In practical scenarios, AES as error correction and Random Linear Codes and CA-Polar codes achieve almost the same performance.

    “We empirically contrast the performance of the proposed approach using AES as error correction with that of Random Linear Codes and CA-Polar codes and show that in practical scenarios, they achieve almost the same performance.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The AWGN/BPSK simulation setup represents practical scenarios.
  • Findingown data

    In IP-CTR mode, the same error correcting performance as shown in Section IV-A is obtained.

    “We note that, as shown in Figure 6, in IP-CTR mode we obtain the same error correcting performance as shown in Section IV-A.”
    Quote in the paperNot a substantial claim
  • Findingcitation

    Coding schemes with CRC and using GRAND decoder can obtain slightly better performance in SNR higher than about 8 dB.

    “However, we note that the coding schemes with CRC and using GRAND decoder can obtain slightly better performance in SNR higher than ∼ 8dB.”
    Quote in the paperNot a substantial claim
  • Findingown data

    The BER and BLER performance of AES as an error-correcting code is almost the same as those of an RLC and CA-Polar code.

    “Indeed, we show that the bit error rate (BER) and block error rate (BLER) performance of AES as an error-correcting code is almost the same as those of an RLC and CA-Polar code.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The AWGN/BPSK simulation setup represents practical scenarios.
  • Findingown data

    A simple padding followed by AES is an effective mechanism for error correction when combined with Guessing Additive Noise Decoding (GRAND).

    “We empirically demonstrate our idea by showing that a simple padding followed by AES, is an effective mechanism for error correction when combined with Guessing Additive Noise Decoding (GRAND) [11]- [13], which can decode any code, including the nonlinear construct yielded by AES.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: AES's output is sufficiently random or pseudorandom to act as a random function for error correction.
  • May combine two claims. 2
  • Classified as probably not a substantial claim. 7
  • May combine two claims.

    Premisecitation

    In the asymptotic regime, random codes are capacity achieving for the BSC and AWGN channels.

    “In the asymptotic regime, i.e., when n goes to infinity, random codes are capacity achieving for the BSC and AWGN channels.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning

    IP-CTR mode avoids both error propagation and the plaintext being used as an input to AES.

    “Thus, IP-CTR mode avoids both issues mentioned above.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A pseudorandom function is computationally indistinguishable from a random function.

    “It is important to note that a pseudorandom function, as usually utilized in classical cryptosystems, is computationally indistinguishable from a random function [17].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Interpretationown data

    The empirical results validate the theoretical result given in Section III.

    “We empirically validate the theoretical result given in Section III.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Reversing the ordering to encoding then encrypting was proposed in a setting where reliability and security can be obtained by partial encryption after error correction encoding.

    “More recently, however, the reverse ordering of encoding and then encrypting was proposed in a setting where reliability and security can be obtained by partial encryption after error correction encoding [9].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    Any padding P of size n-k serves the purpose.

    “Any padding P of size n-k serves our purpose.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Structured codes can slightly outperform random codes in the tested rate and code-size regime when one utilizes a hard-decision decoder.

    “This is settled with the known results in the literature, which show that structured codes can slightly outperform the performance of random codes in the tested rate and code-size regime when one utilizes a hard-decision decoder.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim.

    Premisecitation

    The traditional encoding process consists of two separated stages: encryption followed by an error correcting code.

    “Thus, the traditional encoding process consists of two separated stages/systems: encryption followed by an error correcting code.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [7]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [8]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Premisenone given

    The output of ECB mode is the same whenever a message is repeated.

    “This is because the output of the ECB mode is the same whenever a message is repeated.”
    Quote in the paperSubstantial claim
9 of 9
  • The authors state this as an assumption.

    Crypt_pk is a random function.

    “suppose that Crypt p k is a random function”
  • The paper relies on this without support.

    AES's output is sufficiently random or pseudorandom to act as a random function for error correction.

    “whose outcome is considered pseudo-random”
  • The paper relies on this without support.

    The AWGN/BPSK simulation setup represents practical scenarios.

    “in practical scenarios”
    “Our simulations employ a Gaussian channel model with AWGN and Binary Phase Shift Keying (BPSK) modulation.”
3 of 3

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Number of codewords per message uses output expansion instead of random-bit count

    Minor

    The paper allows r 0 < r and defines r 0 as the number of random input bits. Those inputs can produce at most 2^r0 codewords for a fixed message, not the stated 2^r when r 0 < r.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 5

  1. 2023, GRAND-Code
  2. 2014, AES
  3. 2019, NR Multiplexing and Channel Coding
  4. 2022, Eb/N0&#x2014;Wikipedia the Free Encyclopedia
  5. stallings, 2006, Cryptography and Network Security 4/E

Cited by

Sorted by citations

Authors
Cohen, A., D’Oliveira, R. G. L., Duffy, K. R., Woo, J., & Medard, M.
Affiliations
  • Technion – Israel Institute of Technology (IL)
  • Clemson University (US)
  • Northeastern University (US)
  • Massachusetts Institute of Technology (US)
  • Research Laboratory of Electronics, MIT, Cambridge, MA, USA
Venue
IEEE Communications Letters
Published
2023-08
Volume
27
Issue
8
Pages
1964-1968
ISSN
  • 1089-7798 (ISSN-L)
  • 1558-2558
  • 2373-7891
OpenAlex
W4380303715
Cited by
19
References
31
Citations by year
2026: 4 · 2025: 6 · 2024: 7 · 2023: 2
FWCI
1.66
Type
journal article
Language
en
Open access
Locations
  • IEEE Communications Letters (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
Defense Advanced Research Projects Agency (number HR00112120008)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
  • Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
  • Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
Keywords
Advanced Encryption Standard, error correction, random linear codes, noisy communication, data reliability, padding, random codes

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