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Pedersen-hash

Pedersen-segment-scalar

The function \langle\cdot\rangle in [ZPS:5.4.1.7].

Signature
(pedersen-segment-scalar segment) → i
Arguments: segment — Guard (bit-listp segment).
Returns: i — Type (integerp i).

This returns the scalar that is used in the Jubjub multiplication, i.e. \langle M_i \rangle for the segment M_i.

Definitions and Theorems

Function: pedersen-segment-scalar-loop

(defun pedersen-segment-scalar-loop (j segment)
  (declare (xargs :guard (and (posp j) (bit-listp segment))))
  (declare (xargs :guard (integerp (/ (len segment) 3))))
  (let ((__function__ 'pedersen-segment-scalar-loop))
    (declare (ignorable __function__))
    (if (consp segment)
        (+ (* (pedersen-enc (take 3 segment))
              (expt 2 (* 4 (1- j))))
           (pedersen-segment-scalar-loop (1+ j)
                                         (nthcdr 3 segment)))
      0)))

Theorem: integerp-of-pedersen-segment-scalar-loop

(defthm integerp-of-pedersen-segment-scalar-loop
  (implies (posp j)
           (b* ((i (pedersen-segment-scalar-loop j segment)))
             (integerp i)))
  :rule-classes (:type-prescription :rewrite))

Function: pedersen-segment-scalar

(defun pedersen-segment-scalar (segment)
  (declare (xargs :guard (bit-listp segment)))
  (declare (xargs :guard (integerp (/ (len segment) 3))))
  (let ((__function__ 'pedersen-segment-scalar))
    (declare (ignorable __function__))
    (pedersen-segment-scalar-loop 1 segment)))

Theorem: integerp-of-pedersen-segment-scalar

(defthm integerp-of-pedersen-segment-scalar
  (b* ((i (pedersen-segment-scalar segment)))
    (integerp i))
  :rule-classes (:type-prescription :rewrite))