Refactor node ID handling, use check digits (fixes #269)

New node ID:s contain four Luhn check digits and are grouped
differently. Code uses NodeID type instead of string, so it's formatted
homogenously everywhere.

luhn/luhn.go

@@ -0,0 +1,37 @@
+package luhn
+
+import "strings"
+
+type Alphabet string
+
+var (
+	Base32        Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ234567="
+	Base32Trimmed Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ234567"
+)
+
+func (a Alphabet) Generate(s string) rune {
+	factor := 1
+	sum := 0
+	n := len(a)
+
+	for i := range s {
+		codepoint := strings.IndexByte(string(a), s[i])
+		addend := factor * codepoint
+		if factor == 2 {
+			factor = 1
+		} else {
+			factor = 2
+		}
+		addend = (addend / n) + (addend % n)
+		sum += addend
+	}
+	remainder := sum % n
+	checkCodepoint := (n - remainder) % n
+	return rune(a[checkCodepoint])
+}
+
+func (a Alphabet) Validate(s string) bool {
+	t := s[:len(s)-1]
+	c := a.Generate(t)
+	return rune(s[len(s)-1]) == c
+}

luhn/luhn_test.go

@@ -0,0 +1,25 @@
+package luhn_test
+
+import (
+	"testing"
+
+	"github.com/calmh/syncthing/luhn"
+)
+
+func TestGenerate(t *testing.T) {
+	a := luhn.Alphabet("abcdef")
+	c := a.Generate("abcdef")
+	if c != 'e' {
+		t.Errorf("Incorrect check digit %c != e", c)
+	}
+}
+
+func TestValidate(t *testing.T) {
+	a := luhn.Alphabet("abcdef")
+	if !a.Validate("abcdefe") {
+		t.Errorf("Incorrect validation response for abcdefe")
+	}
+	if a.Validate("abcdefd") {
+		t.Errorf("Incorrect validation response for abcdefd")
+	}
+}