• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
      • Soft
      • C
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Riscv
      • Bitcoin
        • Bip32
          • Bip32-wallet-structure
          • Bip32-key-trees
          • Bip32-key-serialization
          • Bip32-key-derivation
          • Bip32-executable-attachments
          • Bip32-extended-keys
          • Bip32-master-key-generation
            • Bip32-master-key
            • Bip32-master-tree
        • Bech32
        • Bip39
        • Bip44
        • Base58
        • Bip43
        • Bytes
        • Base58check
        • Cryptography
        • Bip-350
        • Bip-173
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Bip32-master-key-generation

Bip32-master-tree

Generate a key tree with (just) a master key from a seed.

Signature

(bip32-master-tree seed) → (mv error? tree)

Arguments

seed — Guard (byte-listp seed).

Returns

error? — Type (booleanp error?).

tree — Type (bip32-key-treep tree).

This lifts bip32-master-key from a single key to a singleton tree containing the key at the root, as a master key.

Definitions and Theorems

Function: bip32-master-tree

(defun bip32-master-tree (seed)
  (declare (xargs :guard (byte-listp seed)))
  (declare (xargs :guard (and (<= 16 (len seed))
                              (<= (len seed) 64))))
  (b* (((mv error? key)
        (bip32-master-key seed))
       (tree (bip32-key-tree (bip32-ext-key-priv key)
                             0 0 (list 0 0 0 0)
                             '(nil))))
    (mv error? tree)))

Theorem: booleanp-of-bip32-master-tree.error?

(defthm booleanp-of-bip32-master-tree.error?
  (b* (((mv ?error? ?tree)
        (bip32-master-tree seed)))
    (booleanp error?))
  :rule-classes :rewrite)

Theorem: bip32-key-treep-of-bip32-master-tree.tree

(defthm bip32-key-treep-of-bip32-master-tree.tree
  (b* (((mv ?error? ?tree)
        (bip32-master-tree seed)))
    (bip32-key-treep tree))
  :rule-classes :rewrite)

Theorem: bip32-key-tree->root-key-of-bip32-master-tree

(defthm bip32-key-tree->root-key-of-bip32-master-tree
 (equal
      (bip32-key-tree->root-key (mv-nth 1 (bip32-master-tree seed)))
      (bip32-ext-key-priv (mv-nth 1 (bip32-master-key seed)))))

Theorem: bip32-key-tree->root-depth-of-bip32-master-tree

(defthm bip32-key-tree->root-depth-of-bip32-master-tree
 (equal
    (bip32-key-tree->root-depth (mv-nth 1 (bip32-master-tree seed)))
    0))

Theorem: bip32-key-tree->root-index-of-bip32-master-tree

(defthm bip32-key-tree->root-index-of-bip32-master-tree
 (equal
    (bip32-key-tree->root-index (mv-nth 1 (bip32-master-tree seed)))
    0))

Theorem: bip32-key-tree->root-parent-of-bip32-master-tree

(defthm bip32-key-tree->root-parent-of-bip32-master-tree
 (equal
   (bip32-key-tree->root-parent (mv-nth 1 (bip32-master-tree seed)))
   (list 0 0 0 0)))

Theorem: bip32-key-tree->index-tree-of-bip32-master-tree

(defthm bip32-key-tree->index-tree-of-bip32-master-tree
 (equal
    (bip32-key-tree->index-tree (mv-nth 1 (bip32-master-tree seed)))
    (list nil)))

Theorem: bip32-key-tree-priv-p-of-bip32-master-tree

(defthm bip32-key-tree-priv-p-of-bip32-master-tree
  (bip32-key-tree-priv-p (mv-nth 1 (bip32-master-tree seed))))

Theorem: bip32-master-tree-of-byte-list-fix-seed

(defthm bip32-master-tree-of-byte-list-fix-seed
  (equal (bip32-master-tree (byte-list-fix seed))
         (bip32-master-tree seed)))

Theorem: bip32-master-tree-byte-list-equiv-congruence-on-seed

(defthm bip32-master-tree-byte-list-equiv-congruence-on-seed
  (implies (byte-list-equiv seed seed-equiv)
           (equal (bip32-master-tree seed)
                  (bip32-master-tree seed-equiv)))
  :rule-classes :congruence)