cpsa-3.3.0: tst/station_to_station.tst

(herald "Station-to-station protocol" (algebra diffie-hellman))

(comment "CPSA 3.2.2")
(comment "All input read from station_to_station.scm")

(defprotocol station-to-station diffie-hellman
  (defrole init
    (vars (x expn) (h base) (a b name))
    (trace (send (exp (gen) x))
      (recv (cat h (enc (enc h (exp (gen) x) (privk b)) (exp h x))))
      (send (enc (enc (exp (gen) x) h (privk a)) (exp h x))))
    (uniq-gen x))
  (defrole resp
    (vars (y expn) (h base) (a b name))
    (trace (recv h)
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) h (privk b)) (exp h y))))
      (recv (enc (enc h (exp (gen) y) (privk a)) (exp h y))))
    (uniq-gen y)
    (ind-zero-in (y h))))

(defskeleton station-to-station
  (vars (a b name) (h base) (x expn))
  (defstrand init 3 (a a) (b b) (h h) (x x))
  (non-orig (privk a) (privk b))
  (uniq-gen x)
  (traces
    ((send (exp (gen) x))
      (recv (cat h (enc (enc h (exp (gen) x) (privk b)) (exp h x))))
      (send (enc (enc (exp (gen) x) h (privk a)) (exp h x)))))
  (label 0)
  (unrealized (0 1))
  (origs)
  (comment "3 in cohort - 3 not yet seen"))

(defskeleton station-to-station
  (vars (a b b-0 name) (x x-0 expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) x-0)) (x x))
  (defstrand init 3 (a b) (b b-0) (h (exp (gen) x)) (x x-0))
  (precedes ((0 0) (1 1)) ((1 2) (0 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x x-0)
  (operation encryption-test (added-strand init 3)
    (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
      (exp (gen) (mul x x-0))) (0 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) x-0)
          (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) x-0) (privk a))
          (exp (gen) (mul x x-0)))))
    ((send (exp (gen) x-0))
      (recv
        (cat (exp (gen) x)
          (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
          (exp (gen) (mul x x-0))))))
  (label 1)
  (parent 0)
  (unrealized (1 1))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton station-to-station
  (vars (a b name) (x y expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) y)) (x x))
  (defstrand resp 2 (b b) (h (exp (gen) x)) (y y))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen x y)
  (operation encryption-test (added-strand resp 2)
    (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
      (exp (gen) (mul x y))) (0 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y)))))
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))))
  (label 2)
  (parent 0)
  (unrealized)
  (shape)
  (maps ((0) ((a a) (b b) (x x) (h (exp (gen) y)))))
  (origs))

(defskeleton station-to-station
  (vars (a b name) (h base) (x expn))
  (defstrand init 3 (a a) (b b) (h h) (x x))
  (deflistener (exp h x))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x)
  (operation encryption-test (added-listener (exp h x))
    (enc (enc h (exp (gen) x) (privk b)) (exp h x)) (0 1))
  (traces
    ((send (exp (gen) x))
      (recv (cat h (enc (enc h (exp (gen) x) (privk b)) (exp h x))))
      (send (enc (enc (exp (gen) x) h (privk a)) (exp h x))))
    ((recv (exp h x)) (send (exp h x))))
  (label 3)
  (parent 0)
  (unrealized (0 1) (1 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton station-to-station
  (vars (a b b-0 name) (x x-0 expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) x-0)) (x x))
  (defstrand init 3 (a b) (b b-0) (h (exp (gen) x)) (x x-0))
  (deflistener (exp (gen) (mul x x-0)))
  (precedes ((0 0) (2 0)) ((1 0) (2 0)) ((1 2) (0 1)) ((2 1) (1 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x x-0)
  (operation encryption-test (added-listener (exp (gen) (mul x x-0)))
    (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
      (exp (gen) (mul x x-0))) (1 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) x-0)
          (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) x-0) (privk a))
          (exp (gen) (mul x x-0)))))
    ((send (exp (gen) x-0))
      (recv
        (cat (exp (gen) x)
          (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
          (exp (gen) (mul x x-0)))))
    ((recv (exp (gen) (mul x x-0))) (send (exp (gen) (mul x x-0)))))
  (label 4)
  (parent 1)
  (unrealized (2 0))
  (comment "empty cohort"))

(defskeleton station-to-station
  (vars (a b name) (x expn) (x-0 expr))
  (defstrand init 3 (a a) (b b) (h (exp (gen) x-0)) (x x))
  (deflistener (exp (gen) (mul x x-0)))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x)
  (operation nonce-test (algebra-contracted (h (exp (gen) x-0)))
    (exp (gen) (mul x x-0)) (1 0) (exp (gen) x))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) x-0)
          (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) x-0) (privk a))
          (exp (gen) (mul x x-0)))))
    ((recv (exp (gen) (mul x x-0))) (send (exp (gen) (mul x x-0)))))
  (label 5)
  (parent 3)
  (unrealized (0 1))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton station-to-station
  (vars (a b b-0 name) (x x-0 expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) x-0)) (x x))
  (deflistener (exp (gen) (mul x x-0)))
  (defstrand init 3 (a b) (b b-0) (h (exp (gen) x)) (x x-0))
  (precedes ((0 0) (1 0)) ((0 0) (2 1)) ((1 1) (0 1)) ((2 0) (1 0))
    ((2 2) (0 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x x-0)
  (operation encryption-test (added-strand init 3)
    (enc (exp (gen) x-0) (exp (gen) x) (privk b)) (0 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) x-0)
          (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) x-0) (privk a))
          (exp (gen) (mul x x-0)))))
    ((recv (exp (gen) (mul x x-0))) (send (exp (gen) (mul x x-0))))
    ((send (exp (gen) x-0))
      (recv
        (cat (exp (gen) x)
          (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
          (exp (gen) (mul x x-0))))))
  (label 6)
  (parent 5)
  (unrealized (1 0) (2 1))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton station-to-station
  (vars (a b name) (x y expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) y)) (x x))
  (deflistener (exp (gen) (mul x y)))
  (defstrand resp 2 (b b) (h (exp (gen) x)) (y y))
  (precedes ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (1 0)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen x y)
  (operation encryption-test (added-strand resp 2)
    (enc (exp (gen) y) (exp (gen) x) (privk b)) (0 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y)))))
    ((recv (exp (gen) (mul x y))) (send (exp (gen) (mul x y))))
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))))
  (label 7)
  (parent 5)
  (unrealized (1 0))
  (comment "empty cohort"))

(defskeleton station-to-station
  (vars (a b b-0 name) (x x-0 expn))
  (defstrand init 3 (a a) (b b) (h (exp (gen) x-0)) (x x))
  (deflistener (exp (gen) (mul x x-0)))
  (defstrand init 3 (a b) (b b-0) (h (exp (gen) x)) (x x-0))
  (deflistener (exp (gen) (mul x x-0)))
  (precedes ((0 0) (1 0)) ((0 0) (3 0)) ((1 1) (0 1)) ((2 0) (1 0))
    ((2 0) (3 0)) ((2 2) (0 1)) ((3 1) (2 1)))
  (non-orig (privk a) (privk b))
  (uniq-gen x x-0)
  (operation encryption-test (added-listener (exp (gen) (mul x x-0)))
    (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
      (exp (gen) (mul x x-0))) (2 1))
  (traces
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) x-0)
          (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) x-0) (privk a))
          (exp (gen) (mul x x-0)))))
    ((recv (exp (gen) (mul x x-0))) (send (exp (gen) (mul x x-0))))
    ((send (exp (gen) x-0))
      (recv
        (cat (exp (gen) x)
          (enc (enc (exp (gen) x) (exp (gen) x-0) (privk b-0))
            (exp (gen) (mul x x-0)))))
      (send
        (enc (enc (exp (gen) x-0) (exp (gen) x) (privk b))
          (exp (gen) (mul x x-0)))))
    ((recv (exp (gen) (mul x x-0))) (send (exp (gen) (mul x x-0)))))
  (label 8)
  (parent 6)
  (unrealized (1 0) (3 0))
  (comment "empty cohort"))

(comment "Nothing left to do")

(defprotocol station-to-station diffie-hellman
  (defrole init
    (vars (x expn) (h base) (a b name))
    (trace (send (exp (gen) x))
      (recv (cat h (enc (enc h (exp (gen) x) (privk b)) (exp h x))))
      (send (enc (enc (exp (gen) x) h (privk a)) (exp h x))))
    (uniq-gen x))
  (defrole resp
    (vars (y expn) (h base) (a b name))
    (trace (recv h)
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) h (privk b)) (exp h y))))
      (recv (enc (enc h (exp (gen) y) (privk a)) (exp h y))))
    (uniq-gen y)
    (ind-zero-in (y h))))

(defskeleton station-to-station
  (vars (a b name) (h base) (y expn))
  (defstrand resp 3 (a a) (b b) (h h) (y y))
  (ind-zero-in (y h))
  (non-orig (privk a) (privk b))
  (uniq-gen y)
  (traces
    ((recv h)
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) h (privk b)) (exp h y))))
      (recv (enc (enc h (exp (gen) y) (privk a)) (exp h y)))))
  (label 9)
  (unrealized (0 2))
  (origs)
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton station-to-station
  (vars (a b b-0 name) (y x expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (defstrand init 3 (a a) (b b-0) (h (exp (gen) y)) (x x))
  (precedes ((0 1) (1 1)) ((1 0) (0 0)) ((1 2) (0 2)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen y x)
  (operation encryption-test (added-strand init 3)
    (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
      (exp (gen) (mul y x))) (0 2))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul y x)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
            (exp (gen) (mul y x)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x))))))
  (label 10)
  (parent 9)
  (unrealized (1 1))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton station-to-station
  (vars (a b name) (h base) (y expn))
  (defstrand resp 3 (a a) (b b) (h h) (y y))
  (deflistener (exp h y))
  (precedes ((0 1) (1 0)) ((1 1) (0 2)))
  (ind-zero-in (y h))
  (non-orig (privk a) (privk b))
  (uniq-gen y)
  (operation encryption-test (added-listener (exp h y))
    (enc (enc h (exp (gen) y) (privk a)) (exp h y)) (0 2))
  (traces
    ((recv h)
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) h (privk b)) (exp h y))))
      (recv (enc (enc h (exp (gen) y) (privk a)) (exp h y))))
    ((recv (exp h y)) (send (exp h y))))
  (label 11)
  (parent 9)
  (unrealized (0 2) (1 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton station-to-station
  (vars (a b name) (x y expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (defstrand init 3 (a a) (b b) (h (exp (gen) y)) (x x))
  (precedes ((0 1) (1 1)) ((1 0) (0 0)) ((1 2) (0 2)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen x y)
  (operation encryption-test (displaced 2 0 resp 2)
    (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
      (exp (gen) (mul x y))) (1 1))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y)))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y))))))
  (label 12)
  (parent 10)
  (unrealized)
  (shape)
  (maps ((0) ((a a) (b b) (y y) (h (exp (gen) x)))))
  (origs))

(defskeleton station-to-station
  (vars (a b b-0 name) (y x expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (defstrand init 3 (a a) (b b-0) (h (exp (gen) y)) (x x))
  (deflistener (exp (gen) (mul y x)))
  (precedes ((0 1) (2 0)) ((1 0) (0 0)) ((1 2) (0 2)) ((2 1) (1 1)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen y x)
  (operation encryption-test (added-listener (exp (gen) (mul y x)))
    (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
      (exp (gen) (mul y x))) (1 1))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul y x)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
            (exp (gen) (mul y x)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((recv (exp (gen) (mul y x))) (send (exp (gen) (mul y x)))))
  (label 13)
  (parent 10)
  (unrealized (2 0))
  (comment "empty cohort"))

(defskeleton station-to-station
  (vars (a b name) (y expn) (y-0 expr))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) y-0)) (y y))
  (deflistener (exp (gen) (mul y y-0)))
  (precedes ((0 1) (1 0)) ((1 1) (0 2)))
  (ind-zero-in (y (exp (gen) y-0)))
  (non-orig (privk a) (privk b))
  (uniq-gen y)
  (operation nonce-test (algebra-contracted (h (exp (gen) y-0)))
    (exp (gen) (mul y y-0)) (1 0) (exp (gen) y)
    (enc (enc (exp (gen) y) (exp (gen) y-0) (privk b))
      (exp (gen) (mul y y-0))))
  (traces
    ((recv (exp (gen) y-0))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) y-0) (privk b))
            (exp (gen) (mul y y-0)))))
      (recv
        (enc (enc (exp (gen) y-0) (exp (gen) y) (privk a))
          (exp (gen) (mul y y-0)))))
    ((recv (exp (gen) (mul y y-0))) (send (exp (gen) (mul y y-0)))))
  (label 14)
  (parent 11)
  (unrealized (0 2))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton station-to-station
  (vars (a b b-0 name) (y x expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (deflistener (exp (gen) (mul y x)))
  (defstrand init 3 (a a) (b b-0) (h (exp (gen) y)) (x x))
  (precedes ((0 1) (1 0)) ((0 1) (2 1)) ((1 1) (0 2)) ((2 0) (0 0))
    ((2 2) (0 2)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen y x)
  (operation encryption-test (added-strand init 3)
    (enc (exp (gen) x) (exp (gen) y) (privk a)) (0 2))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul y x)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((recv (exp (gen) (mul y x))) (send (exp (gen) (mul y x))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
            (exp (gen) (mul y x)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x))))))
  (label 15)
  (parent 14)
  (unrealized (1 0) (2 1))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton station-to-station
  (vars (a b name) (x y expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (deflistener (exp (gen) (mul x y)))
  (defstrand init 3 (a a) (b b) (h (exp (gen) y)) (x x))
  (precedes ((0 1) (1 0)) ((0 1) (2 1)) ((1 1) (0 2)) ((2 0) (0 0))
    ((2 2) (0 2)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen x y)
  (operation encryption-test (displaced 3 0 resp 2)
    (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
      (exp (gen) (mul x y))) (2 1))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y)))))
    ((recv (exp (gen) (mul x y))) (send (exp (gen) (mul x y))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul x y)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul x y))))))
  (label 16)
  (parent 15)
  (unrealized (1 0))
  (comment "empty cohort"))

(defskeleton station-to-station
  (vars (a b b-0 name) (y x expn))
  (defstrand resp 3 (a a) (b b) (h (exp (gen) x)) (y y))
  (deflistener (exp (gen) (mul y x)))
  (defstrand init 3 (a a) (b b-0) (h (exp (gen) y)) (x x))
  (deflistener (exp (gen) (mul y x)))
  (precedes ((0 1) (1 0)) ((0 1) (3 0)) ((1 1) (0 2)) ((2 0) (0 0))
    ((2 2) (0 2)) ((3 1) (2 1)))
  (ind-zero-in (y (exp (gen) x)))
  (non-orig (privk a) (privk b))
  (uniq-gen y x)
  (operation encryption-test (added-listener (exp (gen) (mul y x)))
    (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
      (exp (gen) (mul y x))) (2 1))
  (traces
    ((recv (exp (gen) x))
      (send
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b))
            (exp (gen) (mul y x)))))
      (recv
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((recv (exp (gen) (mul y x))) (send (exp (gen) (mul y x))))
    ((send (exp (gen) x))
      (recv
        (cat (exp (gen) y)
          (enc (enc (exp (gen) y) (exp (gen) x) (privk b-0))
            (exp (gen) (mul y x)))))
      (send
        (enc (enc (exp (gen) x) (exp (gen) y) (privk a))
          (exp (gen) (mul y x)))))
    ((recv (exp (gen) (mul y x))) (send (exp (gen) (mul y x)))))
  (label 17)
  (parent 15)
  (unrealized (1 0) (3 0))
  (comment "empty cohort"))

(comment "Nothing left to do")