SOLAREUM
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  • 👋Solareum - Layer 1 Whitepaper
  • Solareum (SRM)
    • 📃Executive Summary
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    • 💫Final Thoughts
  • About Solareum
    • 👩‍🏫What is SolareumChain?
    • ➗Mathematical Analysis of Validators
  • Solareum Proof of Generation
    • 🧊Solareum Proof of Generation
    • 🛡️The BLS12-381 Elliptic Curve for zk-SNARK Proofs
      • FPGA Hardware
  • BLS Key Generation Signature Scheme Security
    • ♻️BLS Key Generation
      • Extract
      • Expand
      • IKM to lamport SK
      • parent SK to lamport PK
      • HKDF mod r
      • derive child SK
      • derive master SK
    • 💱Post-quantum security backup upgrade
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    • 🔏SolareumChain Algorithmic Security
    • 🔮BLS signature aggregation and Multisig security
      • BLS Signature Aggregation
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      • BLS signature aggregation definitions
    • 🍫Proving security definition references
      • Gedankenexperiment Setup
      • Gedankenexperiment Signature queries
      • Gedankenexperiment Forgery
      • Security and co-CDH Assumption
    • ✳️Adversaries and message query theorems
    • 💠Multi-Input Transactions and Transaction Validation Caching
      • SolareumChain Multi-Input Transactions
      • SolareumChain Transaction Validation Caching
  • SolareumChain ReFi Implementation
    • 💥Proof of Hold (PoH)
    • 🧇SolareumChain Inherited NFT Multipliers
  • SolareumChain Architecture and PoG Math
    • ⛓️SolareumChain Architecture and PoG Math
    • 💣Societal Impact of Blockchain Technology
    • 💡Energy Generation Analysis and Correlation
    • 🔋Energy Correlation Assurance Functions
    • 🧩zk-SNARK Validation
      • Case Study I: Proof of Hold and no Proof of Generation
      • Case Study II: No Proof of Hold and Proof of Generation
      • Case Study III: Proof of Hold and Proof of Generation
    • 🎴SolareumChain Address Generation
    • 🎱SolareumChain Genesis Architecture
    • 🍱Distributed Ledger Technology Energy Sustainability
    • 🌉SolareumChain Bridge
    • ⚡Sufficiency of Sub 128-bit Security for Pairing-Friendly Curves on SolareumChain
  • Other iNfo
    • 📝Conclusion
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  1. SolareumChain Architecture and PoG Math

Sufficiency of Sub 128-bit Security for Pairing-Friendly Curves on SolareumChain

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Last updated 1 year ago

Assurance of the discrete logarithm problem being hard relative to the prime group order r being at least 2*128 bits long as there are algorithms such as Pollard’s rho algorithm that have a runtime cost of O( √ 128) in big-Oh notation. Furthermore, the number field sieve method must not introduce vulnerabilities by ensuring that the extended field Fq k is sufficiently large. Due to finite field extensions of size 3072, there exist actualized security levels of maximum 117-120 bits, which is deemed to be a perfectly adequate security level as per the NCC Group. That is, there exist within the prime group of order r faster than Pollard’s rho algorithm for which there is a security threshold window of

∣∣O(√120)−O(√117)∣∣=0||O( √ 120) − O( √ 117)|| = 0∣∣O(√120)−O(√117)∣∣=0

wherein there are equivalent Big-oh notation runtime results at the bit security boundary.

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