diff --git a/lib/resty/nettle/mpz.lua b/lib/resty/nettle/mpz.lua
index 4fab628..8664c2d 100644
--- a/lib/resty/nettle/mpz.lua
+++ b/lib/resty/nettle/mpz.lua
@@ -16,6 +16,9 @@ size_t __gmpz_sizeinbase(const mpz_t op, int base);
 char * __gmpz_get_str(char *str, int base, const mpz_t op);
 int    __gmpz_set_str(mpz_t rop, const char *str, int base);
 void   __gmpz_set_ui(mpz_t, unsigned long int iv);
+int    __gmpz_invert(mpz_ptr, mpz_srcptr, mpz_srcptr);
+void   __gmpz_sub_ui(mpz_ptr, mpz_srcptr, unsigned long int);
+void   __gmpz_fdiv_r(mpz_ptr, mpz_srcptr, mpz_srcptr);
 ]]
 
 local ctx = ffi_typeof "mpz_t"
@@ -60,4 +63,16 @@ function mpz.set(op, value, base)
     return true
 end
 
+function mpz.invert(rop, op1, op2)
+    return gmp.__gmpz_invert(rop, op1, op2)
+end
+
+function mpz.sub(rop, op1, op2)
+    gmp.__gmpz_sub_ui(rop, op1, op2)
+end
+
+function mpz.div(rop, op1, op2)
+    gmp.__gmpz_fdiv_r(rop, op1, op2)
+end
+
 return mpz
diff --git a/lib/resty/nettle/rsa.lua b/lib/resty/nettle/rsa.lua
index 1f5f636..25203b5 100644
--- a/lib/resty/nettle/rsa.lua
+++ b/lib/resty/nettle/rsa.lua
@@ -106,35 +106,55 @@ function private.new(d, p, q, a, b, c, base)
             return nil, err
         end
     end
+    local p1
     if p then
         local ok, err = mpz.set(context[0].p, p, base)
         if not ok then
             return nil, err
         end
+        if d and not a then
+            p1 = mpz.new()
+            mpz.sub(p1, context[0].p, 1)
+        end
     end
+    local q1
     if q then
         local ok, err = mpz.set(context[0].q, q, base)
         if not ok then
             return nil, err
         end
+        if d and not b then
+            q1 = mpz.new()
+            mpz.sub(q1, context[0].q, 1)
+        end
     end
     if a then
         local ok, err = mpz.set(context[0].a, a, base)
         if not ok then
             return nil, err
         end
+    elseif p1 then
+        mpz.div(context[0].a, context[0].d, p1)
     end
     if b then
         local ok, err = mpz.set(context[0].b, b, base)
         if not ok then
             return nil, err
         end
+    elseif q1 then
+        mpz.div(context[0].b, context[0].d, q1)
     end
+
     if c then
         local ok, err = mpz.set(context[0].c, c, base)
         if not ok then
             return nil, err
         end
+    elseif q and p then
+        local ret = mpz.invert(context[0].c, context[0].q, context[0].p)
+        if ret == 0 then
+            ret = mpz.invert(context[0].c, context[0].q, context[0].p)
+        end
     end
     if d or p or q or a or b or c then
         if hogweed.nettle_rsa_private_key_prepare(context) ~= 1 then
diff --git a/lib/resty/nettle/types/mpz.lua b/lib/resty/nettle/types/mpz.lua
index 64f6c20..b2e50e5 100644
--- a/lib/resty/nettle/types/mpz.lua
+++ b/lib/resty/nettle/types/mpz.lua
@@ -8,6 +8,7 @@ typedef struct {
   int _mp_size;
   mp_limb_t *_mp_d;
 } __mpz_struct;
+typedef const __mpz_struct *mpz_srcptr;
 typedef __mpz_struct mpz_t[1];
 typedef __mpz_struct *mpz_ptr;
 ]]