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• 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)