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• Poseidon-main-definition

Round

Perform a round.

Signature

(round stat constants alpha partial-first-p mds prime full-p) 
  → 
new-stat

Arguments

stat — Guard (fe-listp stat prime).

constants — Guard (fe-listp constants prime).

alpha — Guard (integerp alpha).

partial-first-p — Guard (booleanp partial-first-p).

mds — Guard (fe-list-listp mds prime).

prime — Guard (primep prime).

full-p — Guard (booleanp full-p).

Returns

new-stat — Type (fe-listp new-stat prime), given (primep prime).

We add the round constants, we apply the S-box substitution, and we multiply by the MDS matrix. The round may be full or partial, which affects only the S-box substitution.

Definitions and Theorems

Function: round

(defun round (stat constants
                   alpha partial-first-p mds prime full-p)
  (declare (xargs :guard (and (integerp alpha)
                              (booleanp partial-first-p)
                              (primep prime)
                              (booleanp full-p)
                              (fe-listp stat prime)
                              (fe-listp constants prime)
                              (fe-list-listp mds prime))))
  (declare (xargs :guard (and (equal (len constants) (len stat))
                              (all-len-equal-p mds (len stat)))))
  (let ((__function__ 'round))
    (declare (ignorable __function__))
    (b* ((stat (add-round-constants stat constants prime))
         (stat (sub-words stat
                          alpha partial-first-p prime full-p))
         (stat (mix-layer mds stat prime)))
      stat)))

Theorem: fe-listp-of-round

(defthm fe-listp-of-round
  (implies (primep prime)
           (b* ((new-stat (round stat constants alpha
                                 partial-first-p mds prime full-p)))
             (fe-listp new-stat prime)))
  :rule-classes :rewrite)

Theorem: len-of-round

(defthm len-of-round
 (implies (equal (len mds) (len stat))
          (b* ((?new-stat (round stat constants alpha
                                 partial-first-p mds prime full-p)))
            (equal (len new-stat) (len stat)))))