High performance Short Id

ShortId.cs

/// <summary>
/// ShortId in string format, preferred when a GUID is overkill.
/// </summary>
public static class ShortId
{
    /// <summary>
    /// 32 chars (2^5). removed some chars for better readablity (i,l,o,u)
    /// </summary>
    private const string _chars = "0123456789abcdefghjkmnpqrstvwxyz";

    // If the probability of success is 50%, the probability of success in five attempts is 97%.
    private const byte _maxTrialTimes = 5; 

    /// <summary>
    /// Generates a short id. May be duplicated.
    /// </summary>
    /// <remarks>
    /// Based on long type (64-1=63 bit due to sign), so max length is 12 (13*5=65), not recommanded for fewer than 6 chars.
    /// </remarks>
    /// <param name="size">
    /// Length of the result string. Range 6-12, 10 as default. <br/>
    /// Default value 10 will contain 32^10 (around 10^15) possibilities <br/>
    /// When generating 10^6 times, it will have about 1.4% chance to have duplicate elements.
    /// </param>
    public static string New([Range(6, 12)] byte size = 10)
    {
        // max: 3FFF FFFF (62 bit), half of the long.MaxValue, but still enough for size 12
        long value = (long)Random.Shared.Next(int.MaxValue) * Random.Shared.Next(int.MaxValue); 

        var output = new char[size];
        for (int i = size - 1; i >= 0; i--)
        {
            output[i] = _chars[(int)(value % 32)];
            value >>= 5;
        }
        return new string(output);
    }

    /// <summary>
    /// Generates a unique short id that is different from the existing items.
    /// </summary>
    public static string New(IQueryable<string> existingIds, [Range(6, 12)] byte size = 10)
    {
        existingIds = existingIds.Where(x => x.Length == size);

        byte count = 0;
        string newId = New(size);
        while(existingIds.Contains(newId))
        {
            newId = New(size);
            count++;
            if (count > _maxTrialTimes)
                throw new Exception("Too many elements in the collection to find an unique id.");
        }
        return newId;
    }

    /// <summary>
    /// Generates a unique short id that is different from the existing items.
    /// </summary>
    public static string New(IEnumerable<string> existingIds, [Range(6, 12)] byte size = 10)
    {
        existingIds = existingIds.Where(x => x.Length == size);

        byte count = 0;
        string newId = New(size);
        while (existingIds.Contains(newId))
        {
            newId = New(size);
            count++;
            if (count > _maxTrialTimes)
                throw new Exception("Too many elements in the collection to find an unique id.");
        }
        return newId;
    }
}