• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Riscv
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
      • Poseidon-main-definition
        • Param
        • Hashp
        • Absorb1
        • Sponge
        • Hash
        • All-rounds
        • Sponge-validp
        • Squeeze1
        • Sub-words-partial
        • Squeeze
        • Round
        • Partial-rounds
        • Mode
        • Full-rounds
        • Permute
        • Sub-words
        • Add-round-constants
        • Mix-layer
        • Dot-product
        • Absorb
        • Pow-by-alpha
        • Param->size
        • Sub-words-full
        • Param->capacity-then-rate-p
        • Param->partial-last-p
        • Param-additional-theorems
        • Param->rounds
        • Param->descending-p
        • Init-sponge
      • Poseidon-instantiations
    • Where-do-i-place-my-book
    • Axe
    • Bigmems
    • Builtins
    • Execloader
    • Aleo
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• 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)))))