src/third_party/mozjs-45/python/pyasn1/doc/scalar.html - cobalt - Git at Google

 <html>
 <title>
 PyASN1 data model and scalar types
 </title>
 <head>
 </head>
 <body>
 <center>
 <table width=60%>
 <tr>
 <td>

 <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>

 <a name="1.1.2"></a>
 <h4>
 1.1.2 Null type
 </h4>

 <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>

 <a name="1.1.5"></a>
 <h4>
 1.1.5 Real type
 </h4>

 <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>

 </td>
 </tr>
 </table>
 </center>
 </body>
 </html>
	<html>
	<title>
	PyASN1 data model and scalar types
	</title>
	<head>
	</head>
	<body>
	<center>
	<table width=60%>
	<tr>
	<td>

	<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>

	<a name="1.1.2"></a>
	<h4>
	1.1.2 Null type
	</h4>

	<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>

	<a name="1.1.5"></a>
	<h4>
	1.1.5 Real type
	</h4>

	<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>

	</td>
	</tr>
	</table>
	</center>
	</body>
	</html>