;; Done in class

;; recursive version
(define mod-expt
  (lambda (b e m)
    (define mod*
      (lambda (x y)
        (modulo (* x y) m)))
    (cond ((= e 0) 1)
          ((odd? e) (mod* b (mod-expt (mod* b b) (quotient e 2) m)))
          (else (mod-expt (mod* b b) (/ e 2) m)))))

;; iterative version
(define mod-expt
  (lambda (b e m)
    (define mod*
      (lambda (x y)
        (modulo (* x y) m)))
    (define me
      (lambda (b e result)
        (cond ((= e 0) result)
              ((odd? e) (me (mod* b b) (quotient e 2) (mod* b result)))
              (else (me (mod* b b) (/ e 2) result)))))
    (me b e 1)))