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Bip43

Bip43-export-key

BIP 43 key export.

Signature
(bip43-export-key tree path public?) → exported
Arguments: tree — Guard (bip32-key-treep tree).; path — Guard (ubyte32-listp path).; public? — Guard (booleanp public?).
Returns: exported — Type (byte-listp exported).

[BIP43] prescribes that BIP 32 key serialization be always done with the version numbers of the mainnet, i.e. *bip32-version-priv-main* and *bip32-version-pub-main*.

This function specializes bip32-export-key by eliminating the boolean argument that selects mainnet or testnet, and by passing t as its value to bip32-export-key.

Definitions and Theorems

Function: bip43-export-key

(defun bip43-export-key (tree path public?)
 (declare (xargs :guard (and (bip32-key-treep tree)
                             (ubyte32-listp path)
                             (booleanp public?))))
 (declare
     (xargs :guard (and (bip32-path-in-tree-p path tree)
                        (or public? (bip32-key-tree-priv-p tree)))))
 (bip32-export-key tree path t public?))

Theorem: byte-listp-of-bip43-export-key

(defthm byte-listp-of-bip43-export-key
  (b* ((exported (bip43-export-key tree path public?)))
    (byte-listp exported))
  :rule-classes :rewrite)

Theorem: bip43-export-key-of-bip32-key-tree-fix-tree

(defthm bip43-export-key-of-bip32-key-tree-fix-tree
  (equal (bip43-export-key (bip32-key-tree-fix tree)
                           path public?)
         (bip43-export-key tree path public?)))

Theorem: bip43-export-key-bip32-key-tree-equiv-congruence-on-tree

(defthm bip43-export-key-bip32-key-tree-equiv-congruence-on-tree
  (implies (bip32-key-tree-equiv tree tree-equiv)
           (equal (bip43-export-key tree path public?)
                  (bip43-export-key tree-equiv path public?)))
  :rule-classes :congruence)

Theorem: bip43-export-key-of-ubyte32-list-fix-path

(defthm bip43-export-key-of-ubyte32-list-fix-path
  (equal (bip43-export-key tree (ubyte32-list-fix path)
                           public?)
         (bip43-export-key tree path public?)))

Theorem: bip43-export-key-ubyte32-list-equiv-congruence-on-path

(defthm bip43-export-key-ubyte32-list-equiv-congruence-on-path
  (implies (acl2::ubyte32-list-equiv path path-equiv)
           (equal (bip43-export-key tree path public?)
                  (bip43-export-key tree path-equiv public?)))
  :rule-classes :congruence)

Theorem: bip43-export-key-of-bool-fix-public?

(defthm bip43-export-key-of-bool-fix-public?
  (equal (bip43-export-key tree path (acl2::bool-fix public?))
         (bip43-export-key tree path public?)))

Theorem: bip43-export-key-iff-congruence-on-public?

(defthm bip43-export-key-iff-congruence-on-public?
  (implies (iff public? public?-equiv)
           (equal (bip43-export-key tree path public?)
                  (bip43-export-key tree path public?-equiv)))
  :rule-classes :congruence)