Time-based one-time password algorithm
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A Time-based One-time Password Algorithm (TOTP) is an algorithm that computes a one-time password from a shared secret key and the current time. It is the cornerstone of Initiative For Open Authentication (OATH) and is used in a number of two factor authentication systems. Essentially, both the server and the client compute the time-limited token, then the server checks if the token supplied by the client matches the locally generated token.
The task here is to implement this algorithm using 'HMAC-SHA1' and an optional step is to generate the random Base-32 string used as the secret key, but this is not a requirement. A reference implementation, based on JavaScript, can be found at the following location:
http://blog.tinisles.com/2011/10/google-authenticator-one-time-password-algorithm-in-javascript
According to RFC 6238, the reference implementation is as follows:
- Generate a key, K, which is an arbitrary bytestring, and share it securely with the client.
- Agree upon an epoch, T0, and an interval, TI, which will be used to calculate the value of the counter C (defaults are the Unix epoch as T0 and 30 seconds as TI)
- Agree upon a cryptographic hash method (default is SHA-1)
- Agree upon a token length, N (default is 6)
Although RFC 6238 allows different parameters to be used, the Google implementation of the authenticator app does not support T0, TI values, hash methods and token lengths different from the default. It also expects the K secret key to be entered (or supplied in a QR code) in base-32 encoding according to RFC 3548.
- Google Authenticator App (Apple iOS)
- Google Authenticator App (Google Android)
- Microsoft Authenticator App (Windows Phone)
Caché ObjectScript
<lang cos> Class Utils.Security [ Abstract ] {
ClassMethod GetOTP(b32secret As %String) As %String { // convert base32 secret into string Set key=..B32ToStr(b32secret)
// get the unix time, divide by 30 and convert into eight-byte string Set epoch=..GetUnixTime() Set val=$Reverse($ZQChar(epoch\30))
// compute the HMAC SHA-1 hash and get the last nibble... Set hmac=$System.Encryption.HMACSHA1(val, key) Set last=$ASCII($Extract(hmac, *))
// calculate the offset and get one-time password string Set offset=$ZBoolean(last, $Char(15), 1) // logical 'AND' operation Set otpstr=$ZBoolean($Extract(hmac, offset+1, offset+4), $Char(127,255,255,255), 1)
// convert string into decimal and return last six digits Set otpdec=$ZLASCII($Reverse(otpstr)) Quit ..LeftPad(otpdec, 6) }
ClassMethod GetUnixTime() As %Integer [ Private ] { // current date and time in UTC time format Set now=$ZTimeStamp Set daydiff=(now - $ZDateH("1970-01-01", 3)) Set secs=$Piece(now, ",", 2)\1 Quit (daydiff*60*60*24)+secs }
ClassMethod LeftPad(str As %String, len As %Integer, pad As %String = 0) As %String [ Private ] { Quit $Extract($Translate($Justify(str, len), " ", pad), *-(len-1), *) }
ClassMethod ConvertBase10ToN(pNum As %Integer = "", pBase As %Integer = "", pBaseStr As %String = "", pPos As %Integer = 0) As %String [ Private ] { If pNum=0 Quit "" Set str=..ConvertBase10ToN(pNum\pBase, pBase, pBaseStr, pPos+1) Quit str_$Extract(pBaseStr, pNum#pBase+1) }
ClassMethod ConvertBaseNTo10(pStr As %String = "", pBase As %Integer = "", pBaseStr As %String = "", pPos As %Integer = 0) As %Integer [ Private ] { If pStr="" Quit 0 Set num=..ConvertBaseNTo10($Extract(pStr, 1, *-1), pBase, pBaseStr, pPos+1) Set dec=$Find(pBaseStr, $Extract(pStr, *))-2 Quit num+(dec*(pBase**pPos)) }
ClassMethod B32ToStr(b32str As %String) As %String [ Private ] { Set b32str=$ZConvert(b32str,"U") Set b32alp="ABCDEFGHIJKLMNOPQRSTUVWXYZ234567" Set (bits,str)="" For i=1:1:$Length(b32str) { Set val=$Find(b32alp, $Extract(b32str, i))-2 Set bits=bits_..LeftPad(..ConvertBase10ToN(val, 2, "01"), 5) } For i=1:8:$Length(bits) { Set chunk=$Extract(bits, i, i+7) Set str=str_$Char(..ConvertBaseNTo10(chunk, 2, "01")) } Quit str }
ClassMethod GenerateSecret() As %String { // initialise base 32 string and alphabet Set b32str="", b32alp="ABCDEFGHIJKLMNOPQRSTUVWXYZ234567"
// build a large base 32 string For pass=1:1:4 { Set b32str=b32str_..ConvertBase10ToN($System.Encryption.GenCryptToken(), 32, b32alp) }
// return randomly generated password Quit ..LeftPad(b32str, 16) }
} </lang>
- Example:
DEMO>for i=1:1:5 write ##class(Utils.Security).GetOTP("JBSWY3DPEHPK3PXP"),! hang 15 // wait fifteen seconds
992374
992374
169898
169898
487462
DEMO>write ##class(User.View.Security).GenerateSecret()
5FWQZLQVXIBCKKMJ
DEMO>write ##class(User.View.Security).GenerateSecret()
M4AKQBFI252H4BWO
Go
A slightly fixed version of a package by Zitao Zhang (released under a simplified BSD license). <lang go>// Package onetime provides a library for one-time password generation, // implementing the HOTP and TOTP algorithms as specified by IETF RFC-4226 // and RFC-6238. package onetime
import ( "crypto/hmac" "crypto/sha1" "encoding/binary" "errors" "hash" "math" "time" )
// OneTimePassword stores the configuration values relevant to HOTP/TOTP calculations. type OneTimePassword struct { Digit int // Length of code generated TimeStep time.Duration // Length of each time step for TOTP BaseTime time.Time // The start time for TOTP step calculation Hash func() hash.Hash // Hash algorithm used with HMAC }
// HOTP returns a HOTP code with the given secret and counter. func (otp *OneTimePassword) HOTP(secret []byte, count uint64) uint { hs := otp.hmacSum(secret, count) return otp.truncate(hs) }
func (otp *OneTimePassword) hmacSum(secret []byte, count uint64) []byte { mac := hmac.New(otp.Hash, secret) binary.Write(mac, binary.BigEndian, count) return mac.Sum(nil) }
func (otp *OneTimePassword) truncate(hs []byte) uint { sbits := dt(hs) snum := uint(sbits[3]) | uint(sbits[2])<<8 snum |= uint(sbits[1])<<16 | uint(sbits[0])<<24 return snum % uint(math.Pow(10, float64(otp.Digit))) }
// Simple returns a new OneTimePassword with the specified HTOP code length, // SHA-1 as the HMAC hash algorithm, the Unix epoch as the base time, and // 30 seconds as the step length. func Simple(digit int) (otp OneTimePassword, err error) { if digit < 6 { err = errors.New("minimum of 6 digits is required for a valid HTOP code") return } else if digit > 9 { err = errors.New("HTOP code cannot be longer than 9 digits") return } const step = 30 * time.Second otp = OneTimePassword{digit, step, time.Unix(0, 0), sha1.New} return }
// TOTP returns a TOTP code calculated with the current time and the given secret. func (otp *OneTimePassword) TOTP(secret []byte) uint { return otp.HOTP(secret, otp.steps(time.Now())) }
func (otp *OneTimePassword) steps(now time.Time) uint64 { elapsed := now.Unix() - otp.BaseTime.Unix() return uint64(float64(elapsed) / otp.TimeStep.Seconds()) }
func dt(hs []byte) []byte { offset := int(hs[len(hs)-1] & 0xf) p := hs[offset : offset+4] p[0] &= 0x7f return p }</lang>
- Example use:
(in a format that gets put into the generated documentation) <lang go>package onetime
import ( "crypto/sha256" "fmt" "time"
"github.com/gwwfps/onetime" )
func Example_simple() { // Simple 6-digit HOTP code: var secret = []byte("SOME_SECRET") var counter uint64 = 123456 var otp, _ = onetime.Simple(6) var code = otp.HOTP(secret, counter) fmt.Println(code) // Output: // 260040 }
func Example_authenticator() { // Google authenticator style 8-digit TOTP code: var secret = []byte("SOME_SECRET") var otp, _ = onetime.Simple(8) var code = otp.TOTP(secret) fmt.Println(code) }
func Example_custom() { // 9-digit 5-second-step TOTP starting on midnight 2000-01-01 UTC, using SHA-256: var secret = []byte("SOME_SECRET") const ts = 5 * time.Second var t = time.Date(2000, time.January, 1, 0, 0, 0, 0, time.UTC) var otp = onetime.OneTimePassword{ Digit: 9, TimeStep: ts, BaseTime: t, Hash: sha256.New} var code = otp.TOTP(secret) fmt.Println(code) }</lang>
Racket
This includes BASE32 encoding, token based authentication and other such stuff.
<lang racket>#lang racket (require (only-in web-server/stuffers/hmac-sha1 HMAC-SHA1))
(define << arithmetic-shift) ; deep down, there lurks a C programmer in me (define && bitwise-and)
- These are the parameters available through RFC6238
(define T0 (make-parameter current-seconds)) ; produces unix epoch times. parameterised for testing (define X (make-parameter 30)) (define H (make-parameter (lambda (k d) (HMAC-SHA1 k d)))) (define N (make-parameter 6))
(define (HOTP sha1-bytes (Digit (N)))
(define (DT b)
(define offset (&& #b1111 (bytes-ref b 19)))
(define P/32 (subbytes b offset (+ offset 4)))
(+ (<< (bytes-ref P/32 3) 0) (<< (bytes-ref P/32 2) 8) (<< (bytes-ref P/32 1) 16)
(<< (&& #b01111111 (bytes-ref P/32 0)) 24)))
(define s-bits (DT sha1-bytes))
(modulo s-bits (expt 10 Digit)))
(define (Generate-HOTP K C (Digit (N)))
(HOTP ((H) K (integer->integer-bytes C 8 #t)) Digit))
(define (T #:previous-timeframe (T- 0))
(- (quotient ((T0)) (X)) T-))
(define (TOTP K #:previous-timeframe (T- 0)) (Generate-HOTP K (T #:previous-timeframe T-) (N)))
- RFC 3548
(define (pad-needed bits)
(modulo (- 5 bits) 5))
(define (5-bits->base32-char n)
(string-ref "ABCDEFGHIJKLMNOPQRSTUVWXYZ234567" n))
(define (base32-encode-block bs)
(define v (for/fold ((v 0)) ((b bs)) (+ (<< v 8) b))) (define v-bits (* 8 (bytes-length bs))) (define pad (pad-needed v-bits)) (define padded-bits (+ v-bits pad)) (define v-padded (<< v pad)) (for ((end-bit (in-range padded-bits 4 -5))) (write-char (5-bits->base32-char (bitwise-bit-field v-padded (- end-bit 5) end-bit)))) (write-string (make-string (- 8 (/ padded-bits 5)) #\=)))
(define A-char (char->integer #\A)) (define Z-char (char->integer #\Z)) (define 2-char (char->integer #\2)) (define 7-char (char->integer #\7)) (define =-char (char->integer #\=)) (define (byte->5bit b)
(cond [(<= A-char b Z-char) (- b A-char)] [(<= 2-char b 7-char) (+ 26 (- b 2-char))] [else #f]))
(define (base32-decode-block bs)
(for*/fold ((v 0) (b 0)) ((bt bs) (b5 (in-value (byte->5bit bt))) #:break (not b5))
(define v+ (+ (<< v 5) b5))
(define b+ (+ b 5))
(cond
[(< b+ 8) (values v+ b+)]
[else
(define start-bit (- b+ 8))
(write-byte (&& 255 (<< v+ (- start-bit))))
(values (bitwise-bit-field v+ 0 start-bit) start-bit)])))
(define (base32-encode) (for ((bs (in-port (curry read-bytes 5)))) (base32-encode-block bs))) (define (base32-decode) (for ((bs (in-port (curry read-bytes 8)))) (base32-decode-block bs)))
(define (base32-encode-bytes b) (with-input-from-bytes b (λ () (with-output-to-bytes base32-encode)))) (define (base32-decode-bytes b) (with-input-from-bytes b (λ () (with-output-to-bytes base32-decode))))
(module+ main
(require racket/date) ;; my secret, as stuck on a postit note on my monitor (define Tims-K #"Super Secret Password Key 88!") (define ((pseudo-time-now (offset 0))) (+ 1413976828 offset)) (define totp #f) (parameterize ((T0 (pseudo-time-now))) (printf "I want authentication at: ~a ~s~%" ((T0)) (date->string (seconds->date ((T0))) #t)) (set! totp (TOTP (base32-encode-bytes Tims-K))) (printf "My TOTP is: ~a~%" totp) (printf "sent to authentication service...~%")) ;; as stored on authenticator (define K/base32 (base32-encode-bytes Tims-K)) (printf "K/base32: ~a~%" K/base32) (parameterize ((T0 (pseudo-time-now 1))) (printf "1 second later... authentication service checks against: ~a~%" totp) (define auth-totp (TOTP K/base32)) (printf "~a is the same? ~a~%" auth-totp (= totp auth-totp))) (parameterize ((T0 (pseudo-time-now 3))) (printf "but 3 seconds later... authentication service checks against: ~a~%" totp) (define auth-totp (TOTP K/base32)) (printf "~a is the same? ~a~%" auth-totp (= totp auth-totp)) (printf "oh dear... fall back one time-frame...~%") (define auth-totp-1 (TOTP K/base32 #:previous-timeframe 1)) (printf "~a is *that* the same? ~a~%" auth-totp-1 (= totp auth-totp-1))))
(module+ test
(require tests/eli-tester)
(test
;; From RFC4226 Page 7
(HOTP (bytes
#x1f #x86 #x98 #x69 #x0e #x02 #xca #x16 #x61 #x85
#x50 #xef #x7f #x19 #xda #x8e #x94 #x5b #x55 #x5a)
6)
=> 872921
(pad-needed 0) => 0
(pad-needed 2) => 3
(pad-needed 4) => 1
(pad-needed 6) => 4
(pad-needed 8) => 2
(pad-needed 10) => 0
(pad-needed 12) => 3
;; http://commons.apache.org/proper/commons-codec/xref-test/org/apache/commons/codec/binary/Base32Test.html
(base32-encode-bytes #"") => #""
(base32-encode-bytes #"f") => #"MY======"
(base32-encode-bytes #"fo") => #"MZXQ===="
(base32-encode-bytes #"foo") => #"MZXW6==="
(base32-encode-bytes #"foob") => #"MZXW6YQ="
(base32-encode-bytes #"fooba") => #"MZXW6YTB"
(base32-encode-bytes #"foobar") => #"MZXW6YTBOI======"
(base32-decode-bytes #"") => #""
(base32-decode-bytes #"MY======") => #"f"
(base32-decode-bytes #"MZXQ====") => #"fo"
(base32-decode-bytes #"MZXW6===") => #"foo"
(base32-decode-bytes #"MZXW6YQ=") => #"foob"
(base32-decode-bytes #"MZXW6YTB") => #"fooba"
(base32-decode-bytes #"MZXW6YTBOI======") => #"foobar"
(base32-encode-bytes #"Super Secret Password Key 88!")
=> #"KN2XAZLSEBJWKY3SMV2CAUDBONZXO33SMQQEWZLZEA4DQII="
))</lang>
- Output:
23 tests passed I want authentication at: 1413976828 "Wednesday, October 22nd, 2014 12:20:28pm" My TOTP is: 742249 sent to authentication service... K/base32: KN2XAZLSEBJWKY3SMV2CAUDBONZXO33SMQQEWZLZEA4DQII= 1 second later... authentication service checks against: 742249 742249 is the same? #t but 3 seconds later... authentication service checks against: 742249 317129 is the same? #f oh dear... fall back one time-frame... 742249 is *that* the same? #t
Tcl
This TOTP/HOTP module clocks in small by taking advantage of tcllib's existing hashing and base32 modules.
<lang Tcl>
- rfc6238 contains examples of hotp with 8-digit modulus and sha1/sha256/sha512 hmac
- these require options handling, perhaps http://wiki.tcl.tk/38965
catch {namespace delete ::totp} namespace eval ::totp {
package require sha1
oo::class create totp {
variable Secret
variable Interval
variable Window
constructor {secret {interval 30} {window 300}} {
if {![string is digit $interval]} {
set interval [expr {[clock scan $interval] - [clock scan now]}]
}
if {![string is digit $window]} {
set window [expr {[clock scan $window] - [clock scan now]}]
}
if {$window % $interval} {
throw {TOTP BADARGS} "$window is not a multiple of $interval"
}
set window [expr {$window / $interval}]
set Secret $secret
set Interval $interval
set Window $window
}
method totp Template:When now {
if {![string is integer $when]} {
set when [clock scan $when]
}
set when [expr {$when / $Interval}]
set bytes [binary format W $when]
binary scan $bytes H* when
hotp $Secret $bytes
}
}
proc hotp {secret bytes} {
set hmac [sha1::hmac -bin $secret $bytes]
set ofs [string index $hmac end]
binary scan $ofs c ofs
set ofs [expr {$ofs & 0xf}]
set chunk [string range $hmac $ofs $ofs+4]
binary scan $chunk I code
return [expr {($code & 0x7fffffff) % 1000000}]
}
namespace export *
} namespace import ::totp::*
if 0 { ;# tests
if {[info commands assert] eq ""} {
proc assert {what} {
puts [uplevel 1 [list subst $what]]
}
}
totp::totp create t 12345678901234567890
assert {287082 eq [t totp 59]}
t destroy
package require base32
totp::totp create t [base32::decode AAAAAAAAAAAAAAAA]
proc google {when} {
list [t totp [expr {$when-30}]] [t totp $when] [t totp [expr {$when+30}]]
}
assert {{306281 553572 304383} eq [google 1400000000]}
}</lang>