; factoring rsa moduli

(define (expm b e m)
  (define (m* x y) (modulo (* x y) m))
  (cond ((zero? e) 1)
        ((even? e) (expm (m* b b) (/ e 2) m))
        (else (m* b (expm (m* b b) (/ (- e 1) 2) m)))))

(define primes
  (let ((sieve (make-vector 1001 #t)) (ps (list)))
    (do ((p 2 (+ p 1))) ((< 1000 p) (reverse ps))
      (when (vector-ref sieve p)
        (set! ps (cons p ps))
        (do ((i (* p p) (+ i p))) ((< 1000 i))
          (vector-set! sieve i #f))))))

(define (next-prime n) (cadr (member n primes)))

(define (rsa-factors n e d)
  (let ((k (- (* d e) 1)))
    (let loop ((g 2) (t k))
      (when verbose?
        (display g) (display " ")
        (display t) (newline))
      (if (positive? (modulo t 2))
          (loop (next-prime g) k)
          (let* ((t (/ t 2))
                 (x (expm g t n))
                 (y (gcd (- x 1) n)))
            (if (and (< 1 x) (< 1 y))
                (values y (/ n y))
                (loop g t)))))))

(define verbose? #t)

(call-with-values
  (lambda () (rsa-factors 25777 3 16971))
  (lambda (p q) (display p) (newline)
                (display q) (newline)))
(newline)

(define n #xa66791dc6988168de7ab77419bb7fb0c001c62710270075142942e19a8d8c51d053b3e3782a1de5dc5af4ebe99468170114a1dfe67cdc9a9af55d655620bbab)
(define e #x10001)
(define d #x123c5b61ba36edb1d3679904199a89ea80c09b9122e1400c09adcf7784676d01d23356a7d44d6bd8bd50e94bfc723fa87d8862b75177691c11d757692df8881)

(call-with-values
  (lambda () (rsa-factors n e d))
  (lambda (p q) (display p) (newline)
                (display q) (newline)))

2 50912
2 25456
2 12728
2 6364
2 3182
2 1591
3 50912
3 25456
3 12728
3 6364
3 3182
3 1591
5 50912
5 25456
5 12728
5 6364
149
173

2 3912086784511471289561151952301925086168946454709316095960618800742799369173365724802767882894790378640224771497700744632822349777243736269522672978216650880
2 1956043392255735644780575976150962543084473227354658047980309400371399684586682862401383941447395189320112385748850372316411174888621868134761336489108325440
2 978021696127867822390287988075481271542236613677329023990154700185699842293341431200691970723697594660056192874425186158205587444310934067380668244554162720
2 489010848063933911195143994037740635771118306838664511995077350092849921146670715600345985361848797330028096437212593079102793722155467033690334122277081360
23234950162188993388155927630085331316851060055334470382368804331834850828939
23443439767333138692938389505422341860387525814723848738690073331642118819681