		Search-engine friendly clone of the ACL2 documentation.

Bip32-key-derivation

Bip32-ckd

Child key derivation from parent key.

Signature
(bip32-ckd parent i) → (mv error? child)
Arguments: parent — Guard (bip32-ext-key-p parent).; i — Guard (ubyte32p i).
Returns: error? — Type (booleanp error?).; child — Type (bip32-ext-key-p child).

This is the sum of bip32-ckd-priv and bip32-ckd-pub. It maps (extended) parent private keys to (extended) child private keys and (extended) parent public keys to (extended) child public keys. This function does not appear in [BIP32].

Definitions and Theorems

Function: bip32-ckd

(defun bip32-ckd (parent i)
  (declare (xargs :guard (and (bip32-ext-key-p parent)
                              (ubyte32p i))))
  (bip32-ext-key-case parent :priv
                      (b* (((mv error? child)
                            (bip32-ckd-priv parent.get i)))
                        (mv error? (bip32-ext-key-priv child)))
                      :pub
                      (b* (((mv error? child)
                            (bip32-ckd-pub parent.get i)))
                        (mv error? (bip32-ext-key-pub child)))))

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

(defthm booleanp-of-bip32-ckd.error?
  (b* (((mv ?error? ?child)
        (bip32-ckd parent i)))
    (booleanp error?))
  :rule-classes :rewrite)

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

(defthm bip32-ext-key-p-of-bip32-ckd.child
  (b* (((mv ?error? ?child)
        (bip32-ckd parent i)))
    (bip32-ext-key-p child))
  :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 parent i)))
         (bip32-ext-key-kind parent)))

Theorem: bip32-ckd-of-bip32-ext-key-fix-parent

(defthm bip32-ckd-of-bip32-ext-key-fix-parent
  (equal (bip32-ckd (bip32-ext-key-fix parent) i)
         (bip32-ckd parent i)))

Theorem: bip32-ckd-bip32-ext-key-equiv-congruence-on-parent

(defthm bip32-ckd-bip32-ext-key-equiv-congruence-on-parent
  (implies (bip32-ext-key-equiv parent parent-equiv)
           (equal (bip32-ckd parent i)
                  (bip32-ckd parent-equiv i)))
  :rule-classes :congruence)

Theorem: bip32-ckd-of-ubyte32-fix-i

(defthm bip32-ckd-of-ubyte32-fix-i
  (equal (bip32-ckd parent (ubyte32-fix i))
         (bip32-ckd parent i)))

Theorem: bip32-ckd-ubyte32-equiv-congruence-on-i

(defthm bip32-ckd-ubyte32-equiv-congruence-on-i
  (implies (acl2::ubyte32-equiv i i-equiv)
           (equal (bip32-ckd parent i)
                  (bip32-ckd parent i-equiv)))
  :rule-classes :congruence)