How to validate a International Securities Identification Number (ISIN) number

Question

If I am not wrong, ISIN numbers last position is a verification digit. What is the mathematical function that determines its value in function of the first 11 digits?

Answer 1

Building on the examples of others, here is a C# implementation which will validate both ISINs and CUSIPs (and maybe some other Luhn variations).

Usage:

foreach (var isin in ValidIsins)
{
    var calculatedChecksum = SecuritiesValidation.CalculateChecksum(isin.Substring(0, 11));
    var actualChecksum = (isin.Last() - '0');
    Assert.AreEqual(calculatedChecksum, actualChecksum);
}
foreach (var cusip in ValidCusips)
{
    var calculatedChecksum = SecuritiesValidation.CalculateChecksum(cusip.Substring(0, 8), true, true);
    var actualChecksum = (cusip.Last() - '0');
    Assert.AreEqual(calculatedChecksum, actualChecksum);
}

Implementation:

public static class SecuritiesValidation
{
    public static int CalculateChecksum(IEnumerable<char> codeWithoutChecksum, bool reverseLuhn = false, bool allowSymbols = false)
    {
        return reverseLuhn
            ? codeWithoutChecksum
                .Select((c, i) => c.OrdinalPosition(allowSymbols).ConditionalMultiplyByTwo(i.IsOdd()).SumDigits())
                .Sum()
                .TensComplement()
            : codeWithoutChecksum
                .ToArray()
                .ToDigits(allowSymbols)
                .Select((d, i) => d.ConditionalMultiplyByTwo(i.IsEven()).SumDigits())
                .Sum()
                .TensComplement();
    }

    public static bool IsChecksumCorrect(string code, bool reverseLuhn = false, bool allowSymbols = false)
    {
        try
        {
            var checksum = code.Last().ToInt();
            return checksum == CalculateChecksum(code.Take(code.Length - 1), reverseLuhn, allowSymbols);
        }
        catch
        {
            return false;
        }
    }

    /* Be careful here. This method is probably inapropriate for anything other than its designed purpose of Luhn-algorithm based validation.
     * Specifically:
     * - numbers are assigned a value equal to the number ('0' == 0, '1' == 1).
     * - letters are assigned a value indicating the number 9 plus the letters ordinal position in the English alphabet ('A' == 10, 'B' == 11).
     * - if symbols are allowed (eg: for CUSIP validation), they are assigned values beginning from 36 ('*' == 36, '@' == 37).
     */
    private static int OrdinalPosition(this char c, bool allowSymbols = false)
    {
        if (char.IsLower(c))
            return char.ToUpper(c) - 'A' + 10;

        if (char.IsUpper(c))
            return c - 'A' + 10;

        if (char.IsDigit(c))
            return c.ToInt();

        if (allowSymbols)
            switch (c)
            {
                case '*':
                    return 36;
                case '@':
                    return 37;
                case '#':
                    return 38;
            }
        throw new ArgumentOutOfRangeException("Specified character is not a letter, digit or allowed symbol.");
    }

    private static bool IsEven(this int x)
    {
        return (x % 2 == 0);
    }

    private static bool IsOdd(this int x)
    {
        return !IsEven(x);
    }

    private static int ToInt(this char digit)
    {
        if (char.IsDigit(digit))
            return digit - '0';
        throw new ArgumentOutOfRangeException("Specified character is not a digit.");
    }

    private static IEnumerable<int> ToDigits(this char[] s, bool allowSymbols = false)
    {
        var digits = new List<int>();
        for (var i = s.Length - 1; i >= 0; i--)
        {
            var ordinalPosition = s[i].OrdinalPosition(allowSymbols);
            digits.Add(ordinalPosition % 10);
            if (ordinalPosition > 9)
                digits.Add(ordinalPosition / 10);
        }
        return digits;
    }

    private static int SumDigits(this int value)
    {
        //return value > 9 ? ((value / 10) + (value % 10)) : value;
        return ((value / 10) + (value % 10));
    }

    private static int ConditionalMultiplyByTwo(this int value, bool condition)
    {
        return condition ? value * 2 : value;
    }

    private static int TensComplement(this int value)
    {
        return (10 - (value % 10)) % 10;
    }
}

It will likely make sense to use checksum validation in conjunction with a regular expression pattern match. These are the regex I use:

ISIN: ^(XS|AD|AE|AF|AG|AI|AL|AM|AO|AQ|AR|AS|AT|AU|AW|AX|AZ|BA|BB|BD|BE|BF|BG|BH|BI|BJ|BL|BM|BN|BO|BQ|BR|BS|BT|BV|BW|BY|BZ|CA|CC|CD|CF|CG|CH|CI|CK|CL|CM|CN|CO|CR|CU|CV|CW|CX|CY|CZ|DE|DJ|DK|DM|DO|DZ|EC|EE|EG|EH|ER|ES|ET|FI|FJ|FK|FM|FO|FR|GA|GB|GD|GE|GF|GG|GH|GI|GL|GM|GN|GP|GQ|GR|GS|GT|GU|GW|GY|HK|HM|HN|HR|HT|HU|ID|IE|IL|IM|IN|IO|IQ|IR|IS|IT|JE|JM|JO|JP|KE|KG|KH|KI|KM|KN|KP|KR|KW|KY|KZ|LA|LB|LC|LI|LK|LR|LS|LT|LU|LV|LY|MA|MC|MD|ME|MF|MG|MH|MK|ML|MM|MN|MO|MP|MQ|MR|MS|MT|MU|MV|MW|MX|MY|MZ|NA|NC|NE|NF|NG|NI|NL|NO|NP|NR|NU|NZ|OM|PA|PE|PF|PG|PH|PK|PL|PM|PN|PR|PS|PT|PW|PY|QA|RE|RO|RS|RU|RW|SA|SB|SC|SD|SE|SG|SH|SI|SJ|SK|SL|SM|SN|SO|SR|SS|ST|SV|SX|SY|SZ|TC|TD|TF|TG|TH|TJ|TK|TL|TM|TN|TO|TR|TT|TV|TW|TZ|UA|UG|UM|US|UY|UZ|VA|VC|VE|VG|VI|VN|VU|WF|WS|YE|YT|ZA|ZM|ZW)([0-9A-Z]{9})([0-9]{1})$

CUSIP: ^[A-Z0-9]{8}[0-9]$