Ruby implementation of the Time-Based One-Time Password (TOTP) Algorithm described at http://tools.ietf.org/html/rfc6238

totp

[jgalang@rashomon:~/Code/skunkworks/2fa]
∴ ruby totp_demo.rb

Time(sec)  	Time (UTC format)	Value of T(Hex) 	TOTP    	Mode  	OK
------------------------------------------------------------------------------------------
59         	1970-01-01 00:00:59	0000000000000001	94287082	SHA1  	 ✔
59         	1970-01-01 00:00:59	0000000000000001	46119246	SHA256	 ✔
59         	1970-01-01 00:00:59	0000000000000001	90693936	SHA512	 ✔
1111111109 	2005-03-18 01:58:29	00000000023523EC	07081804	SHA1  	 ✔
1111111109 	2005-03-18 01:58:29	00000000023523EC	68084774	SHA256	 ✔
1111111109 	2005-03-18 01:58:29	00000000023523EC	25091201	SHA512	 ✔
1111111111 	2005-03-18 01:58:31	00000000023523ED	14050471	SHA1  	 ✔
1111111111 	2005-03-18 01:58:31	00000000023523ED	67062674	SHA256	 ✔
1111111111 	2005-03-18 01:58:31	00000000023523ED	99943326	SHA512	 ✔
1234567890 	2009-02-13 23:31:30	000000000273EF07	89005924	SHA1  	 ✔
1234567890 	2009-02-13 23:31:30	000000000273EF07	91819424	SHA256	 ✔
1234567890 	2009-02-13 23:31:30	000000000273EF07	93441116	SHA512	 ✔
2000000000 	2033-05-18 03:33:20	0000000003F940AA	69279037	SHA1  	 ✔
2000000000 	2033-05-18 03:33:20	0000000003F940AA	90698825	SHA256	 ✔
2000000000 	2033-05-18 03:33:20	0000000003F940AA	38618901	SHA512	 ✔
20000000000	2603-10-11 11:33:20	0000000027BC86AA	65353130	SHA1  	 ✔
20000000000	2603-10-11 11:33:20	0000000027BC86AA	77737706	SHA256	 ✔
20000000000	2603-10-11 11:33:20	0000000027BC86AA	47863826	SHA512	 ✔

totp.rb

# Ruby implementation of the Time-Based One-Time Password (TOTP)
# Algorithm described at http://tools.ietf.org/html/rfc6238
#
# Copyright (c) 2013 Juris Galang
# MIT Licence: http://opensource.org/licenses/MIT
#
require 'base64'
require 'openssl'

class TOTP
  DEFAULT_INTERVAL = 30
  DEFAULT_LENGTH   = 8
  DEFAULT_CRYPTO   = 'sha1'
  
  def initialize secret, interval: DEFAULT_INTERVAL, length: DEFAULT_LENGTH, crypto: DEFAULT_CRYPTO
    @secret   = secret
    @interval = interval
    @length   = length
    @crypto   = crypto
  end

  def at time = Time.now
    "%0.#{@length}d" % otp(step time)
  end
  
  private
  
  def otp step
    msg    = [step].pack('H*') 
    key    = [@secret].pack('H*')
    hash   = OpenSSL::HMAC.digest(@crypto, key, msg)
    
    offset = hash[hash.length - 1].ord & 0xf
    hash   = hash[offset .. offset + 3].bytes
    value  = ((hash[0] & 0x7f) << 24) |
             ((hash[1] & 0xff) << 16) |
             ((hash[2] & 0xff) <<  8) |
             (hash[3] & 0xff)
             
    (value % (10 ** @length))             
  end
  
  def step time
    '%0.16x' % (time.to_i / @interval).to_s(16).hex
  end
end

totp_demo.rb

# Sample usage and verification against the reference implementation's
# output as described at http://tools.ietf.org/html/rfc6238#appendix-B
#
# Copyright (c) 2013 Juris Galang
# MIT Licence: http://opensource.org/licenses/MIT
#
require './totp.rb'

SECRETS = {
  'SHA1'   => '3132333435363738393031323334353637383930',
  'SHA256' => '3132333435363738393031323334353637383930313233343536373839303132',
  'SHA512' => '31323334353637383930313233343536373839303132333435363738393031323334353637383930313233343536373839303132333435363738393031323334'
}

lines  = DATA.read.split("\n")
header = lines[1].split('|').map!{ |n| n.strip }.delete_if{ |n| n.empty? }
input  = lines[3..-1].delete_if{ |l| l =~ /\+/ }

puts
puts sprintf("%-11s\t%-13s\t%-16s\t%-8s\t%-6s\t%-2s", *header, 'OK')
puts '-' * 90

input.each do |line|
  t_sec, t_utc, t_hex, expected, crypto = *line.split('|').map!{ |n| n.strip }.delete_if{ |n| n.empty? }
    
  time    = Time.utc(*t_utc.split(/ |:|-/))
  secret  = SECRETS[crypto]
  totp    = TOTP.new(secret, crypto: crypto)

  matched = expected == totp.at(time) ? '✔' : '✘'
  puts sprintf("%-11s\t%s\t%s\t%s\t%-6s\t%2s", t_sec, t_utc, t_hex, expected, crypto, matched)
end

__END__
+---------------+-----------------------+------------------+--------+--------+
|  Time(sec)    |   Time (UTC format)   | Value of T(Hex)  |  TOTP  | Mode   |
+---------------+-----------------------+------------------+--------+--------+
|  59           |  1970-01-01 00:00:59  | 0000000000000001 |94287082| SHA1   |
|  59           |  1970-01-01 00:00:59  | 0000000000000001 |46119246| SHA256 |
|  59           |  1970-01-01 00:00:59  | 0000000000000001 |90693936| SHA512 |
+---------------+-----------------------+------------------+--------+--------+
|  1111111109   |  2005-03-18 01:58:29  | 00000000023523EC |07081804| SHA1   |
|  1111111109   |  2005-03-18 01:58:29  | 00000000023523EC |68084774| SHA256 |
|  1111111109   |  2005-03-18 01:58:29  | 00000000023523EC |25091201| SHA512 |
+---------------+-----------------------+------------------+--------+--------+
|  1111111111   |  2005-03-18 01:58:31  | 00000000023523ED |14050471| SHA1   |
|  1111111111   |  2005-03-18 01:58:31  | 00000000023523ED |67062674| SHA256 |
|  1111111111   |  2005-03-18 01:58:31  | 00000000023523ED |99943326| SHA512 |
+---------------+-----------------------+------------------+--------+--------+
|  1234567890   |  2009-02-13 23:31:30  | 000000000273EF07 |89005924| SHA1   |
|  1234567890   |  2009-02-13 23:31:30  | 000000000273EF07 |91819424| SHA256 |
|  1234567890   |  2009-02-13 23:31:30  | 000000000273EF07 |93441116| SHA512 |
+---------------+-----------------------+------------------+--------+--------+
|  2000000000   |  2033-05-18 03:33:20  | 0000000003F940AA |69279037| SHA1   |
|  2000000000   |  2033-05-18 03:33:20  | 0000000003F940AA |90698825| SHA256 |
|  2000000000   |  2033-05-18 03:33:20  | 0000000003F940AA |38618901| SHA512 |
+---------------+-----------------------+------------------+--------+--------+
|  20000000000  |  2603-10-11 11:33:20  | 0000000027BC86AA |65353130| SHA1   |
|  20000000000  |  2603-10-11 11:33:20  | 0000000027BC86AA |77737706| SHA256 |
|  20000000000  |  2603-10-11 11:33:20  | 0000000027BC86AA |47863826| SHA512 |
+---------------+-----------------------+------------------+--------+--------+

Pretty sure
'%0.16x' % (time.to_i / @interval).to_s(16).hex
has redundant code. Why not just:
'%0.16x' % (time.to_i / @interval)