• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • 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
      • Bitcoin
        • Bip32
          • Bip32-wallet-structure
          • Bip32-key-trees
            • Bip32-extend-tree
            • Bip32-valid-depths-p
            • Bip32-key-tree
            • Bip32-path-set-closedp
            • Bip32-valid-keys-p
            • Bip32-index-tree
            • Bip32-path-in-tree-p
            • Bip32-ckd*
            • Bip32-get-pub-key-at-path
            • Bip32-get-priv-key-at-path
            • Bip32-ckd-priv*
            • Bip32-ckd-pub*
            • Bip32-path
            • Bip32-key-tree-priv-p
            • Bip32-path-set
          • Bip32-key-serialization
          • Bip32-key-derivation
          • Bip32-executable-attachments
          • Bip32-extended-keys
          • Bip32-master-key-generation
        • 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-key-trees

Bip32-ckd*

Key designated by a specified path in the tree with the specified root key.

Signature

(bip32-ckd* root path) → (mv error? key)

Arguments

root — Guard (bip32-ext-key-p root).

path — Guard (ubyte32-listp path).

Returns

error? — Type (booleanp error?).

key — Type (bip32-ext-key-p key).

Definitions and Theorems

Function: bip32-ckd*

(defun bip32-ckd* (root path)
  (declare (xargs :guard (and (bip32-ext-key-p root)
                              (ubyte32-listp path))))
  (bip32-ext-key-case root :priv
                      (b* (((mv error? key)
                            (bip32-ckd-priv* root.get path)))
                        (mv error? (bip32-ext-key-priv key)))
                      :pub
                      (b* (((mv error? key)
                            (bip32-ckd-pub* root.get path)))
                        (mv error? (bip32-ext-key-pub key)))))

Theorem: booleanp-of-bip32-ckd*.error?

(defthm booleanp-of-bip32-ckd*.error?
  (b* (((mv ?error? ?key)
        (bip32-ckd* root path)))
    (booleanp error?))
  :rule-classes :rewrite)

Theorem: bip32-ext-key-p-of-bip32-ckd*.key

(defthm bip32-ext-key-p-of-bip32-ckd*.key
  (b* (((mv ?error? ?key)
        (bip32-ckd* root path)))
    (bip32-ext-key-p key))
  :rule-classes :rewrite)

Theorem: bip32-ext-key-kind-of-bip32-ckd*

(defthm bip32-ext-key-kind-of-bip32-ckd*
  (equal (bip32-ext-key-kind (mv-nth 1 (bip32-ckd* root path)))
         (bip32-ext-key-kind root)))

Theorem: bip32-ckd*-of-bip32-ext-key-fix-root

(defthm bip32-ckd*-of-bip32-ext-key-fix-root
  (equal (bip32-ckd* (bip32-ext-key-fix root)
                     path)
         (bip32-ckd* root path)))

Theorem: bip32-ckd*-bip32-ext-key-equiv-congruence-on-root

(defthm bip32-ckd*-bip32-ext-key-equiv-congruence-on-root
  (implies (bip32-ext-key-equiv root root-equiv)
           (equal (bip32-ckd* root path)
                  (bip32-ckd* root-equiv path)))
  :rule-classes :congruence)

Theorem: bip32-ckd*-of-ubyte32-list-fix-path

(defthm bip32-ckd*-of-ubyte32-list-fix-path
  (equal (bip32-ckd* root (ubyte32-list-fix path))
         (bip32-ckd* root path)))

Theorem: bip32-ckd*-ubyte32-list-equiv-congruence-on-path

(defthm bip32-ckd*-ubyte32-list-equiv-congruence-on-path
  (implies (acl2::ubyte32-list-equiv path path-equiv)
           (equal (bip32-ckd* root path)
                  (bip32-ckd* root path-equiv)))
  :rule-classes :congruence)