Applied Cryptography December 2017 ECDLP is the problem of finding - - PowerPoint PPT Presentation

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Applied Cryptography December 2017 ECDLP is the problem of finding - - PowerPoint PPT Presentation

Mar 03, 2023 328 likes •529 views

Applied Cryptography December 2017 ECDLP is the problem of finding an ECC user's secret key, given the user's public key. Unfortunately, there is a gap between ECDLP difficulty and ECC security.There are many attacks that break

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Applied Cryptography

December 2017

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…ECDLP is the problem of finding an ECC user's secret key, given the user's public key. Unfortunately, there is a gap between ECDLP difficulty and ECC security….There are many attacks that break real-world ECC without solving ECDLP. The core problem is that if you implement the standard curves, chances are you're doing it wrong.

https://safecurves.cr.yp.to/

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The Basics

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Use the right primitives

  • Encryption != Integrity
  • Encryption != Authentication
  • Hashing != Encryption
  • Hashing != Irreversible (in general)

Garbled != Senseless

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Understand your cryptographic libraries

  • Understand their purpose
  • Understand their assumptions
  • Validate input to the libraries
  • Check return values
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Side Channels

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Crypto black box

  • Perform complex mathematics
  • Fast enough to be suitable
  • On general purpose hardware
  • Correctly for all inputs

Without any measurable side effect

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Side effects?

  • Data and error conditions
  • Processing time
  • Data access time
  • Power fluctuations
  • Electromagnetic emissions

Acoustic emissions

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Password Storage

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What could be simpler?

  • Take password
  • Store in database
  • ….?
  • Profit!
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Step 1 – Hash it!

  • Get password
  • Store SHA256(password)
  • Preimage resistance for the win!

Precomputed dictionary attack Everything* falls

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Step 2 – Hash it with salt!

  • Get password
  • Store random || SHA256(random|| password)
  • No precomputation!

Active dictionary attack Pretty much everything falls

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Step 3 – Expensive hash it with salt!

  • Get password
  • Store random || PBKDF2(random|| password)
  • Slow computation!

Active dictionary attack with acceleration Normal passwords fail

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Step 4 – Argon2d with salt!

  • Get password
  • Store random || argon2d(random|| password)
  • No acceleration!

Active dictionary attack Bad passwords fail

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Step 2 – Argon2d with salt!

  • Get password
  • Store random || argon2d(random|| password)
  • *whew*

Denial of Service? Data independence?

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Conclusions

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Think big

  • Crypto without math is wrong
  • Crypto without system context also

wrong

  • Understand your users, your systems,

and your libraries

  • Secure accordingly
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Thank you!

scott.stender@nccgroup.trust @scottstender