SOLAREUM
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  • ๐Ÿ‘‹Solareum - Layer 1 Whitepaper
  • Solareum (SRM)
    • ๐Ÿ“ƒExecutive Summary
    • ๐Ÿ”ฅSolareumโ€™s Solution
    • โญSolareumโ€™s Value Proposition
    • ๐Ÿ’ซFinal Thoughts
  • About Solareum
    • ๐Ÿ‘ฉโ€๐ŸซWhat is SolareumChain?
    • โž—Mathematical Analysis of Validators
  • Solareum Proof of Generation
    • ๐ŸงŠSolareum Proof of Generation
    • ๐Ÿ›ก๏ธThe BLS12-381 Elliptic Curve for zk-SNARK Proofs
      • FPGA Hardware
  • BLS Key Generation Signature Scheme Security
    • โ™ป๏ธBLS Key Generation
      • Extract
      • Expand
      • IKM to lamport SK
      • parent SK to lamport PK
      • HKDF mod r
      • derive child SK
      • derive master SK
    • ๐Ÿ’ฑPost-quantum security backup upgrade
  • SolareumChain Algorithmic Security
    • ๐Ÿ”SolareumChain Algorithmic Security
    • ๐Ÿ”ฎBLS signature aggregation and Multisig security
      • BLS Signature Aggregation
      • Multisig Security
      • BLS signature aggregation definitions
    • ๐ŸซProving security definition references
      • Gedankenexperiment Setup
      • Gedankenexperiment Signature queries
      • Gedankenexperiment Forgery
      • Security and co-CDH Assumption
    • โœณ๏ธAdversaries and message query theorems
    • ๐Ÿ’ Multi-Input Transactions and Transaction Validation Caching
      • SolareumChain Multi-Input Transactions
      • SolareumChain Transaction Validation Caching
  • SolareumChain ReFi Implementation
    • ๐Ÿ’ฅProof of Hold (PoH)
    • ๐Ÿง‡SolareumChain Inherited NFT Multipliers
  • SolareumChain Architecture and PoG Math
    • โ›“๏ธSolareumChain Architecture and PoG Math
    • ๐Ÿ’ฃSocietal Impact of Blockchain Technology
    • ๐Ÿ’กEnergy Generation Analysis and Correlation
    • ๐Ÿ”‹Energy Correlation Assurance Functions
    • ๐Ÿงฉzk-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
    • ๐ŸŽดSolareumChain Address Generation
    • ๐ŸŽฑSolareumChain Genesis Architecture
    • ๐ŸฑDistributed Ledger Technology Energy Sustainability
    • ๐ŸŒ‰SolareumChain Bridge
    • โšกSufficiency of Sub 128-bit Security for Pairing-Friendly Curves on SolareumChain
  • Other iNfo
    • ๐Ÿ“Conclusion
  • Community
    • ๐ŸŒWebsite
    • ๐ŸŒ Telegram
    • โœ–๏ธTwitter
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  1. BLS Key Generation Signature Scheme Security
  2. BLS Key Generation

parent SK to lamport PK

parent_SK_to_lamport_PK

Inputs

parent_SK, the BLS Secret Key of the parent node index, the index of the desired child node, an integer 0 <= index < 2^32

Outputs

lamport_PK, the compressed lamport PK, a 32 octet string

Definitions

I2OSP is as defined in RFC3447 (Big endian decoding) flip_bits is a function that returns the bitwise negation of its input "" is the empty string a | b is the concatenation of a with b

Procedure

0. salt = I2OSP(index, 4) 1. IKM = I2OSP(parent_SK, 32) 2. lamport_0 = IKM_to_lamport_SK(IKM, salt) 3. not_IKM = flip_bits(IKM) 4. lamport_1 = IKM_to_lamport_SK(not_IKM, salt) 5. lamport_PK = "" 6. for i in 1, .., 255 lamport_PK = lamport_PK | SHA256(lamport_0[i]) 7. for i in 1, .., 255 lamport_PK = lamport_PK | SHA256(lamport_1[i]) 8. compressed_lamport_PK = SHA256(lamport_PK) 9. return compressed_lamport_PK

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Last updated 1 year ago

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