O(n) Luhn check

Luhn.cs

public class Luhn
{
    public static bool CheckLuhnDigit(string digits, int last = 1)
    {
        var checksum = CalculateLuhnDigit(digits, last);
        int checkDigit = checksum > -1 ? digits[^last] - '0' : 0;
        return checksum == checkDigit;
    }

    public static int CalculateLuhnDigit(string digits, int lastIndex = 0)
    {
        int luhnDigit = -1;
        lastIndex = Math.Abs(lastIndex);
        int minimumLength = 1 + lastIndex;

        if (!string.IsNullOrEmpty(digits) && digits.Length > minimumLength)
        {
            long sum = 0;
            for (int i = 0; i < digits.Length - lastIndex; i++)
            {
                int digit = digits[^(i + minimumLength)] - '0';
                if (digit < 0 || digit > 9)
                    return luhnDigit;
                sum += (i % 2 == 0) ? Luhn(digit) : digit;
            }
            luhnDigit = (int)(10 - (sum % 10)) % 10;
        }

        return luhnDigit;

        int Luhn(int digit) => (digit *= 2) > 9 ? digit - 9 : digit;
    }
}