Initial CommitHEADmain

3 files changed, 83 insertions, 0 deletions

diff --git a/.gitignore b/.gitignore
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--- /dev/null
+++ b/.gitignore
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+compiled
diff --git a/main.rkt b/main.rkt
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+++ b/main.rkt
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+#lang racket
+
+(require "modulo-arithmetic.rkt")
+
+;; 4a^3 + 27b^2 != 0
+(define a 2)
+(define b 3)
+
+(define (point-in-curve lst)
+  (define x (car lst))
+  (define y (cadr lst))
+  (= (* y y) (+ (* x x x) (* x a) b)))
+
+(define (add p q)
+  (cond ((not (point-in-curve p))
+         q)
+        ((not (point-in-curve q))
+         p)
+        (else
+         (define xp (first p))
+         (define xq (first q))
+         (define yp (second p))
+         (define yq (second q))
+         (let* ((m (if (equal? p q)
+                       (/ (+ (* 3 xp xp) a)
+                          (* 2 yp))
+                       (/ (- yp yq)
+                          (- xp xq))))
+                (xr (- (* m m) xp xq))
+                (yr (+ yp (* m (- xr xp)))))
+           (list xr (- yr))))))
+
+(define (mul n p)
+  (cond ((= n 0)
+         (list 0 0))
+        ((= n 1)
+         p)
+        (else
+         (add p (mul (sub1 n) p)))))
+
+(define curve-points (filter point-in-curve
+                             (cartesian-product (range cardinality)
+                                                (range cardinality))))
+
diff --git a/modulo-arithmetic.rkt b/modulo-arithmetic.rkt
new file mode 100644
index 0000000..5d80e6c
--- /dev/null
+++ b/modulo-arithmetic.rkt
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+#lang racket
+
+(define cardinality 487) ; must be prime
+
+(define (extended-euclid a b)
+  (define (euloop r s t)
+    (if (= 0 (second r))
+        (list r s t)
+        (let ((q (quotient (first r) (second r))))
+          (euloop (list (second r) (- (first r) (* q (second r))))
+                  (list (second s) (- (first s) (* q (second s))))
+                  (list (second t) (- (first t) (* q (second t))))))))
+  (match (euloop (list a b) (list 1 0) (list 0 1))
+         ((list r s t)
+          (list (first r) (first s) (first t)))))
+
+(define (inverse n)
+  (match (extended-euclid n cardinality)
+         ((list gdc x y)
+          (modulo x cardinality))))
+
+(define (add . args)
+  (modulo (apply + args) cardinality))
+
+(define (sub . args)
+  (modulo (apply - args) cardinality))
+
+(define (mul . args)
+  (modulo (apply * args) cardinality))
+
+(define (div a b)
+  (mul a (inverse b)))
+
+(provide cardinality
+         (rename-out (add +)
+                     (sub -)
+                     (mul *)
+                     (div /)))
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