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PyASN1 data model and scalar types
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<h3>
1. Data model for ASN.1 types
</h3>

<p>
All ASN.1 types could be categorized into two groups: scalar (also called
simple or primitive) and constructed. The first group is populated by
well-known types like Integer or String. Members of constructed group
hold other types (simple or constructed) as their inner components, thus
they are semantically close to a programming language records or lists.
</p>

<p>
In pyasn1, all ASN.1 types and values are implemented as Python objects.
The same pyasn1 object can represent either ASN.1 type and/or value
depending of the presense of value initializer on object instantiation.
We will further refer to these as <i>pyasn1 type object</i> versus <i>pyasn1
value object</i>.
</p>

<p>
Primitive ASN.1 types are implemented as immutable scalar objects. There values
could be used just like corresponding native Python values (integers,
strings/bytes etc) and freely mixed with them in expressions.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> asn1IntegerValue = univ.Integer(12)
>>> asn1IntegerValue - 2
10
>>> univ.OctetString('abc') == 'abc'
True   # Python 2
>>> univ.OctetString(b'abc') == b'abc'
True   # Python 3
</pre>
</td></tr></table>

<p>
It would be an error to perform an operation on a pyasn1 type object
as it holds no value to deal with:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> asn1IntegerType = univ.Integer()
>>> asn1IntegerType - 2
...
pyasn1.error.PyAsn1Error: No value for __coerce__()
</pre>
</td></tr></table>

<a name="1.1"></a>
<h4>
1.1 Scalar types
</h4>

<p>
In the sub-sections that follow we will explain pyasn1 mapping to those
primitive ASN.1 types. Both, ASN.1 notation and corresponding pyasn1
syntax will be given in each case.
</p>

<a name="1.1.1"></a>
<h4>
1.1.1 Boolean type
</h4>

<p>
This is the simplest type those values could be either True or False.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
;; type specification
FunFactorPresent ::= BOOLEAN

;; values declaration and assignment
pythonFunFactor FunFactorPresent ::= TRUE
cobolFunFactor FunFactorPresent :: FALSE
</pre>
</td></tr></table>

<p>
And here's pyasn1 version of it:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> class FunFactorPresent(univ.Boolean): pass
... 
>>> pythonFunFactor = FunFactorPresent(True)
>>> cobolFunFactor = FunFactorPresent(False)
>>> pythonFunFactor
FunFactorPresent('True(1)')
>>> cobolFunFactor
FunFactorPresent('False(0)')
>>> pythonFunFactor == cobolFunFactor
False
>>>
</pre>
</td></tr></table>

<p>
The NULL type is sometimes used to express the absense of any information.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
;; type specification
Vote ::= CHOICE {
  agreed BOOLEAN,
  skip NULL
}
</td></tr></table>

;; value declaration and assignment
myVote Vote ::= skip:NULL
</pre>

<p>
We will explain the CHOICE type later in this paper, meanwhile the NULL
type:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> skip = univ.Null()
>>> skip
Null('')
>>>
</pre>
</td></tr></table>

<a name="1.1.3"></a>
<h4>
1.1.3 Integer type
</h4>

<p>
ASN.1 defines the values of Integer type as negative or positive of whatever
length. This definition plays nicely with Python as the latter places no
limit on Integers. However, some ASN.1 implementations may impose certain
limits of integer value ranges. Keep that in mind when designing new
data structures.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
;; values specification
age-of-universe INTEGER ::= 13750000000
mean-martian-surface-temperature INTEGER ::= -63
</pre>
</td></tr></table>

<p>
A rather strigntforward mapping into pyasn1:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> ageOfUniverse = univ.Integer(13750000000)
>>> ageOfUniverse
Integer(13750000000)
>>>
>>> meanMartianSurfaceTemperature = univ.Integer(-63)
>>> meanMartianSurfaceTemperature
Integer(-63)
>>>
</pre>
</td></tr></table>

<p>
ASN.1 allows to assign human-friendly names to particular values of
an INTEGER type.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
Temperature ::= INTEGER {
  freezing(0),
  boiling(100) 
}
</pre>
</td></tr></table>

<p>
The Temperature type expressed in pyasn1:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ, namedval
>>> class Temperature(univ.Integer):
...   namedValues = namedval.NamedValues(('freezing', 0), ('boiling', 100))
...
>>> t = Temperature(0)
>>> t
Temperature('freezing(0)')
>>> t + 1
Temperature(1)
>>> t + 100
Temperature('boiling(100)')
>>> t = Temperature('boiling')
>>> t
Temperature('boiling(100)')
>>> Temperature('boiling') / 2
Temperature(50)
>>> -1 < Temperature('freezing')
True
>>> 47 > Temperature('boiling')
False
>>>
</pre>
</td></tr></table>

<p>
These values labels have no effect on Integer type operations, any value
still could be assigned to a type (information on value constraints will
follow further in this paper).
</p>

<a name="1.1.4"></a>
<h4>
1.1.4 Enumerated type
</h4>

<p>
ASN.1 Enumerated type differs from an Integer type in a number of ways.
Most important is that its instance can only hold a value that belongs
to a set of values specified on type declaration.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
error-status ::= ENUMERATED {
  no-error(0),
  authentication-error(10),
  authorization-error(20),
  general-failure(51)
}
</pre>
</td></tr></table>

<p>
When constructing Enumerated type we will use two pyasn1 features: values
labels (as mentioned above) and value constraint (will be described in
more details later on).
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ, namedval, constraint
>>> class ErrorStatus(univ.Enumerated):
...   namedValues = namedval.NamedValues(
...        ('no-error', 0),
...        ('authentication-error', 10),
...        ('authorization-error', 20),
...        ('general-failure', 51)
...   )
...   subtypeSpec = univ.Enumerated.subtypeSpec + \
...                    constraint.SingleValueConstraint(0, 10, 20, 51)
...
>>> errorStatus = univ.ErrorStatus('no-error')
>>> errorStatus
ErrorStatus('no-error(0)')
>>> errorStatus == univ.ErrorStatus('general-failure')
False
>>> univ.ErrorStatus('non-existing-state')
Traceback (most recent call last):
...
pyasn1.error.PyAsn1Error: Can't coerce non-existing-state into integer
>>>
</pre>
</td></tr></table>

<p>
Particular integer values associated with Enumerated value states
have no meaning. They should not be used as such or in any kind of
math operation. Those integer values are only used by codecs to
transfer state from one entity to another.
</p>

<p>
Values of the Real type are a three-component tuple of mantissa, base and 
exponent. All three are integers.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
pi ::= REAL { mantissa 314159, base 10, exponent -5 }
</pre>
</td></tr></table>

<p>
Corresponding pyasn1 objects can be initialized with either a three-component
tuple or a Python float. Infinite values could be expressed in a way, 
compatible with Python float type.

</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> pi = univ.Real((314159, 10, -5))
>>> pi
Real((314159, 10,-5))
>>> float(pi)
3.14159
>>> pi == univ.Real(3.14159)
True
>>> univ.Real('inf')
Real('inf')
>>> univ.Real('-inf') == float('-inf')
True
>>>
</pre>
</td></tr></table>

<p>
If a Real object is initialized from a Python float or yielded by a math
operation, the base is set to decimal 10 (what affects encoding).
</p>

<a name="1.1.6"></a>
<h4>
1.1.6 Bit string type
</h4>

<p>
ASN.1 BIT STRING type holds opaque binary data of an arbitrarily length.
A BIT STRING value could be initialized by either a binary (base 2) or 
hex (base 16) value.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
public-key BIT STRING ::= '1010111011110001010110101101101
                           1011000101010000010110101100010
                           0110101010000111101010111111110'B

signature  BIT STRING ::= 'AF01330CD932093392100B39FF00DE0'H
</pre>
</td></tr></table>

<p>
The pyasn1 BitString objects can initialize from native ASN.1 notation
(base 2 or base 16 strings) or from a Python tuple of binary components.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> publicKey = univ.BitString(
...          "'1010111011110001010110101101101"
...          "1011000101010000010110101100010"
...          "0110101010000111101010111111110'B"
)
>>> publicKey
BitString("'10101110111100010101101011011011011000101010000010110101100010\
0110101010000111101010111111110'B")
>>> signature = univ.BitString(
...          "'AF01330CD932093392100B39FF00DE0'H"
... )
>>> signature
BitString("'101011110000000100110011000011001101100100110010000010010011001\
1100100100001000000001011001110011111111100000000110111100000'B")
>>> fingerprint = univ.BitString(
...          (1, 0, 1, 1 ,0, 1, 1, 1, 0, 1, 0, 1)
... )
>>> fingerprint
BitString("'101101110101'B")
>>>
</pre>
</td></tr></table>

<p>
Another BIT STRING initialization method supported by ASN.1 notation
is to specify only 1-th bits along with their human-friendly label
and bit offset relative to the beginning of the bit string. With this 
method, all not explicitly mentioned bits are doomed to be zeros.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
bit-mask  BIT STRING ::= {
  read-flag(0),
  write-flag(2),
  run-flag(4)
}
</pre>
</td></tr></table>

<p>
To express this in pyasn1, we will employ the named values feature (as with
Enumeration type).
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ, namedval
>>> class BitMask(univ.BitString):
...   namedValues = namedval.NamedValues(
...        ('read-flag', 0),
...        ('write-flag', 2),
...        ('run-flag', 4)
... )
>>> bitMask = BitMask('read-flag,run-flag')
>>> bitMask
BitMask("'10001'B")
>>> tuple(bitMask)
(1, 0, 0, 0, 1)
>>> bitMask[4]
1
>>>
</pre>
</td></tr></table>

<p>
The BitString objects mimic the properties of Python tuple type in part
of immutable sequence object protocol support.
</p>

<a name="1.1.7"></a>
<h4>
1.1.7 OctetString type
</h4>

<p>
The OCTET STRING type is a confusing subject. According to ASN.1
specification, this type is similar to BIT STRING, the major difference
is that the former operates in 8-bit chunks of data. What is important
to note, is that OCTET STRING was NOT designed to handle text strings - the
standard provides many other types specialized for text content. For that
reason, ASN.1 forbids to initialize OCTET STRING values with "quoted text
strings", only binary or hex initializers, similar to BIT STRING ones,
are allowed.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
thumbnail OCTET STRING ::= '1000010111101110101111000000111011'B
thumbnail OCTET STRING ::= 'FA9823C43E43510DE3422'H
</pre>
</td></tr></table>

<p>
However, ASN.1 users (e.g. protocols designers) seem to ignore the original
purpose of the OCTET STRING type - they used it for handling all kinds of
data, including text strings.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
welcome-message OCTET STRING ::= "Welcome to ASN.1 wilderness!"
</pre>
</td></tr></table>

<p>
In pyasn1, we have taken a liberal approach and allowed both BIT STRING
style and quoted text initializers for the OctetString objects. To avoid
possible collisions, quoted text is the default initialization syntax.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> thumbnail = univ.OctetString(
...    binValue='1000010111101110101111000000111011'
... )
>>> thumbnail
OctetString(hexValue='85eebcec0')
>>> thumbnail = univ.OctetString(
...    hexValue='FA9823C43E43510DE3422'
... )
>>> thumbnail
OctetString(hexValue='fa9823c43e4351de34220')
>>>
</pre>
</td></tr></table>

<p>
Most frequent usage of the OctetString class is to instantiate it with
a text string.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> welcomeMessage = univ.OctetString('Welcome to ASN.1 wilderness!')
>>> welcomeMessage
OctetString(b'Welcome to ASN.1 wilderness!')
>>> print('%s' % welcomeMessage)
Welcome to ASN.1 wilderness!
>>> welcomeMessage[11:16]
OctetString(b'ASN.1')
>>> 
</pre>
</td></tr></table>

<p>
OctetString objects support the immutable sequence object protocol.
In other words, they behave like Python 3 bytes (or Python 2 strings).
</p>

<p>
When running pyasn1 on Python 3, it's better to use the bytes objects for
OctetString instantiation, as it's more reliable and efficient.
</p>

<p>
Additionally, OctetString's can also be instantiated with a sequence of
8-bit integers (ASCII codes).
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> univ.OctetString((77, 101, 101, 103, 111))
OctetString(b'Meego')
</pre>
</td></tr></table>

<p>
It is sometimes convenient to express OctetString instances as 8-bit
characters (Python 3 bytes or Python 2 strings) or 8-bit integers.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> octetString = univ.OctetString('ABCDEF')
>>> octetString.asNumbers()
(65, 66, 67, 68, 69, 70)
>>> octetString.asOctets()
b'ABCDEF'
</pre>
</td></tr></table>

<a name="1.1.8"></a>
<h4>
1.1.8 ObjectIdentifier type
</h4>

<p>
Values of the OBJECT IDENTIFIER type are sequences of integers that could
be used to identify virtually anything in the world. Various ASN.1-based
protocols employ OBJECT IDENTIFIERs for their own identification needs.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
internet-id OBJECT IDENTIFIER ::= {
  iso(1) identified-organization(3) dod(6) internet(1)
}
</pre>
</td></tr></table>

<p>
One of the natural ways to map OBJECT IDENTIFIER type into a Python
one is to use Python tuples of integers. So this approach is taken by
pyasn1.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> internetId = univ.ObjectIdentifier((1, 3, 6, 1))
>>> internetId
ObjectIdentifier('1.3.6.1')
>>> internetId[2]
6
>>> internetId[1:3]
ObjectIdentifier('3.6')
</pre>
</td></tr></table>

<p>
A more human-friendly "dotted" notation is also supported.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import univ
>>> univ.ObjectIdentifier('1.3.6.1')
ObjectIdentifier('1.3.6.1')
</pre>
</td></tr></table>

<p>
Symbolic names of the arcs of object identifier, sometimes present in
ASN.1 specifications, are not preserved and used in pyasn1 objects.
</p>

<p>
The ObjectIdentifier objects mimic the properties of Python tuple type in
part of immutable sequence object protocol support.
</p>

<a name="1.1.9"></a>
<h4>
1.1.9 Character string types
</h4>

<p>
ASN.1 standard introduces a diverse set of text-specific types. All of them
were designed to handle various types of characters. Some of these types seem
be obsolete nowdays, as their target technologies are gone. Another issue
to be aware of is that raw OCTET STRING type is sometimes used in practice
by ASN.1 users instead of specialized character string types, despite
explicit prohibition imposed by ASN.1 specification.
</p>

<p>
The two types are specific to ASN.1 are NumericString and PrintableString.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
welcome-message ::= PrintableString {
  "Welcome to ASN.1 text types"
}

dial-pad-numbers ::= NumericString {
  "0", "1", "2", "3", "4", "5", "6", "7", "8", "9"
}
</pre>
</td></tr></table>

<p>
Their pyasn1 implementations are:
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import char
>>> '%s' % char.PrintableString("Welcome to ASN.1 text types")
'Welcome to ASN.1 text types'
>>> dialPadNumbers = char.NumericString(
      "0" "1" "2" "3" "4" "5" "6" "7" "8" "9"
)
>>> dialPadNumbers
NumericString(b'0123456789')
>>>
</pre>
</td></tr></table>

<p>
The following types came to ASN.1 from ISO standards on character sets.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import char
>>> char.VisibleString("abc")
VisibleString(b'abc')
>>> char.IA5String('abc')
IA5String(b'abc')
>>> char.TeletexString('abc')
TeletexString(b'abc')
>>> char.VideotexString('abc')
VideotexString(b'abc')
>>> char.GraphicString('abc')
GraphicString(b'abc')
>>> char.GeneralString('abc')
GeneralString(b'abc')
>>>
</pre>
</td></tr></table>

<p>
The last three types are relatively recent addition to the family of
character string types: UniversalString, BMPString, UTF8String.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import char
>>> char.UniversalString("abc")
UniversalString(b'abc')
>>> char.BMPString('abc')
BMPString(b'abc')
>>> char.UTF8String('abc')
UTF8String(b'abc')
>>> utf8String = char.UTF8String('У попа была собака')
>>> utf8String
UTF8String(b'\xd0\xa3 \xd0\xbf\xd0\xbe\xd0\xbf\xd0\xb0 \xd0\xb1\xd1\x8b\xd0\xbb\xd0\xb0 \
\xd1\x81\xd0\xbe\xd0\xb1\xd0\xb0\xd0\xba\xd0\xb0')
>>> print(utf8String)
У попа была собака
>>>
</pre>
</td></tr></table>

<p>
In pyasn1, all character type objects behave like Python strings. None of
them is currently constrained in terms of valid alphabet so it's up to
the data source to keep an eye on data validation for these types.
</p>

<a name="1.1.10"></a>
<h4>
1.1.10 Useful types
</h4>

<p>
There are three so-called useful types defined in the standard:
ObjectDescriptor, GeneralizedTime, UTCTime. They all are subtypes
of GraphicString or VisibleString types therefore useful types are
character string types.
</p>

<p>
It's advised by the ASN.1 standard to have an instance of ObjectDescriptor
type holding a human-readable description of corresponding instance of
OBJECT IDENTIFIER type. There are no formal linkage between these instances
and provision for ObjectDescriptor uniqueness in the standard.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import useful
>>> descrBER = useful.ObjectDescriptor(
      "Basic encoding of a single ASN.1 type"
)
>>> 
</pre>
</td></tr></table>

<p>
GeneralizedTime and UTCTime types are designed to hold a human-readable
timestamp in a universal and unambiguous form. The former provides
more flexibility in notation while the latter is more strict but has
Y2K issues.
</p>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
;; Mar 8 2010 12:00:00 MSK
moscow-time GeneralizedTime ::= "20110308120000.0"
;; Mar 8 2010 12:00:00 UTC
utc-time GeneralizedTime ::= "201103081200Z"
;; Mar 8 1999 12:00:00 UTC
utc-time UTCTime ::= "9803081200Z"
</pre>
</td></tr></table>

<table bgcolor="lightgray" border=0 width=100%><TR><TD>
<pre>
>>> from pyasn1.type import useful
>>> moscowTime = useful.GeneralizedTime("20110308120000.0")
>>> utcTime = useful.UTCTime("9803081200Z")
>>> 
</pre>
</td></tr></table>

<p>
Despite their intended use, these types possess no special, time-related,
handling in pyasn1. They are just printable strings.
</p>

<hr>

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