diff --git a/hill.lisp b/hill.lisp
index 347b21a..10f0746 100644
--- a/hill.lisp
+++ b/hill.lisp
@@ -145,7 +145,10 @@ return a cons of (x . y) such char x * N1 + y * N2 = GCD."
   "Find the modular multiplicative inverse of N with respect to M. That is, some
 integer i such that (N * i) mod M = 1."
   (destructuring-bind (gcd (x . y))
-      (multiple-value-list (extended-gcd n m))
+      (multiple-value-list (extended-gcd (if (minusp n)
+                                             (+ 26 n)
+                                             n)
+                                         m))
     (declare (ignorable y))
     (unless (= 1 gcd)
       (error "N and M must be coprime. N: ~d, M: ~d" n m))
@@ -428,5 +431,5 @@ be the same value originally used to encrypt the text."
           'string))
 
 ;; Local Variables:
-;; jinx-local-words: "adjugate cofactor cofactors det plaintext prandom unnessesary xorshift"
+;; jinx-local-words: "adjugate cofactor cofactors coprime det plaintext prandom unnessesary xorshift"
 ;; End:
diff --git a/shift-affine.lisp b/shift-affine.lisp
index 13549e8..fde6706 100644
--- a/shift-affine.lisp
+++ b/shift-affine.lisp
@@ -61,7 +61,10 @@ return a cons of (x . y) such char x * N1 + y * N2 = GCD."
   "Find the modular multiplicative inverse of N with respect to M. That is, some
 integer i such that (N * i) mod M = 1."
   (destructuring-bind (gcd (x . y))
-      (multiple-value-list (extended-gcd n m))
+      (multiple-value-list (extended-gcd (if (minusp n)
+                                             (+ 26 n)
+                                             n)
+                                         m))
     (declare (ignorable y))
     (unless (= 1 gcd)
       (error "N and M must be coprime. N: ~d, M: ~d" n m))