A Layman's Guide to a Subset of ASN.1, BER, and DER

Supersedes June 3, 1991 version, which was also published as NIST/OSI Implementors' Workshop document SEC-SIG-91-17. PKCS documents are available by electronic mail to .

Copyright (C) 1991-1993 RSA Laboratories, a division of RSA Data Security, Inc. License to copy this document is granted provided that it is identified as "RSA Data Security, Inc. Public-Key Cryptography Standards (PKCS)" in all material mentioning or referencing this document.
003-903015-110-000-000

Abstract. This note gives a layman's introduction to a subset of OSI's Abstract Syntax Notation One (ASN.1), Basic Encoding Rules (BER), and Distinguished Encoding Rules (DER). The particular purpose of this note is to provide background material sufficient for understanding and implementing the PKCS family of standards.

1. Introduction

One of the most complex systems today, and one that also involves a great deal of abstraction, is Open Systems Interconnection (OSI, described in X.200). OSI is an internationally standardized architecture that governs the interconnection of computers from the physical layer up to the user application layer. Objects at higher layers are defined abstractly and intended to be implemented with objects at lower layers. For instance, a service at one layer may require transfer of certain abstract objects between computers; a lower layer may provide transfer services for strings of ones and zeroes, using encoding rules to transform the abstract objects into such strings. OSI is called an open system because it supports many different implementations of the services at each layer.

OSI's method of specifying abstract objects is called ASN.1 (Abstract Syntax Notation One, defined in X.208), and one set of rules for representing such objects as strings of ones and zeros is called the BER (Basic Encoding Rules, defined in X.209). ASN.1 is a flexible notation that allows one to define a variety data types, from simple types such as integers and bit strings to structured types such as sets and sequences, as well as complex types defined in terms of others. BER describes how to represent or encode values of each ASN.1 type as a string of eight-bit octets. There is generally more than one way to BER-encode a given value. Another set of rules, called the Distinguished Encoding Rules (DER), which is a subset of BER, gives a unique encoding to each ASN.1 value.

The purpose of this note is to describe a subset of ASN.1, BER and DER sufficient to understand and implement one OSI- based application, RSA Data Security, Inc.'s Public-Key Cryptography Standards. The features described include an overview of ASN.1, BER, and DER and an abridged list of ASN.1 types and their BER and DER encodings. Sections 2-4 give an overview of ASN.1, BER, and DER, in that order. Section 5 lists some ASN.1 types, giving their notation, specific encoding rules, examples, and comments about their application to PKCS. Section 6 concludes with an example, X.500 distinguished names.

Advanced features of ASN.1, such as macros, are not described in this note, as they are not needed to implement PKCS. For information on the other features, and for more detail generally, the reader is referred to CCITT Recommendations X.208 and X.209, which define ASN.1 and BER. Terminology and notation. In this note, an octet is an eight- bit unsigned integer. Bit 8 of the octet is the most significant and bit 1 is the least significant.

The following meta-syntax is used for in describing ASN.1 notation:

BIT

2. Abstract Syntax Notation One

In ASN.1, a type is a set of values. For some types, there are a finite number of values, and for other types there are an infinite number. A value of a given ASN.1 type is an element of the type's set. ASN.1 has four kinds of type: simple types, which are "atomic" and have no components; structured types, which have components; tagged types, which are derived from other types; and other types, which include the CHOICE type and the ANY type. Types and values can be given names with the ASN.1 assignment operator (::=) , and those names can be used in defining other types and values.

Every ASN.1 type other than CHOICE and ANY has a tag, which consists of a class and a nonnegative tag number. ASN.1 types are abstractly the same if and only if their tag numbers are the same. In other words, the name of an ASN.1 type does not affect its abstract meaning, only the tag does. There are four classes of tag:

Universal, for types whose meaning is the same in all applications; these types are only defined in X.208.

Application, for types whose meaning is specific to an application, such as X.500 directory services; types in two different applications may have the same application-specific tag and different meanings.

Private, for types whose meaning is specific to a given enterprise.

Context-specific, for types whose meaning is specific to a given structured type; context-specific tags are used to distinguish between component types with the same underlying tag within the context of a given structured type, and component types in two different structured types may have the same tag and different meanings.

The types with universal tags are defined in X.208, which also gives the types' universal tag numbers. Types with other tags are defined in many places, and are always obtained by implicit or explicit tagging (see Section 2.3). Table 1 lists some ASN.1 types and their universal-class tags.

Type	Tag number (decimal)	Tag number (hexadecimal)
INTEGER	2	02
BIT STRING	3	03
OCTET STRING	4	04
NULL	5	05
OBJECT IDENTIFIER	6	06
SEQUENCE and SEQUENCE OF	16	10
SET and SET OF	17	11
PrintableString	19	13
T61String	20	14
IA5String	22	16
UTCTime	23	17

Table 1. Some types and their universal-class tags.

ASN.1 types and values are expressed in a flexible, programming-language-like notation, with the following special rules:

• Layout is not significant; multiple spaces and line breaks can be considered as a single space.

   

• Comments are delimited by pairs of hyphens (--), or a pair of hyphens and a line break.

   

• Identifiers (names of values and fields) and type references (names of types) consist of upper- and lower-case letters, digits, hyphens, and spaces; identifiers begin with lower-case letters; type references begin with upper-case letters.

 

2.1 Simple types

BIT STRING, an arbitrary string of bits (ones and zeroes).

IA5String, an arbitrary string of IA5 (ASCII) characters.

INTEGER, an arbitrary integer.

NULL, a null value.

OBJECT IDENTIFIER, an object identifier, which is a sequence of integer components that identify an object such as an algorithm or attribute type.

OCTET STRING, an arbitrary string of octets (eight-bit values).

PrintableString, an arbitrary string of printable characters.

T61String, an arbitrary string of T.61 (eight-bit) characters.

UTCTime, a "coordinated universal time" or Greenwich Mean Time (GMT) value.

Simple types fall into two categories: string types and non- string types. BIT STRING, IA5String, OCTET STRING, PrintableString, T61String, and UTCTime are string types.

String types can be viewed, for the purposes of encoding, as consisting of components, where the components are substrings. This view allows one to encode a value whose length is not known in advance (e.g., an octet string value input from a file stream) with a constructed, indefinite- length encoding (see Section 3).

The string types can be given size constraints limiting the length of values.

2.2 Structured types

SEQUENCE, an ordered collection of one or more types.

SEQUENCE OF, an ordered collection of zero or more occurrences of a given type.

SET, an unordered collection of one or more types.

SET OF, an unordered collection of zero or more occurrences of a given type.

The structured types can have optional components, possibly with default values.

2.3 Implicitly and explicitly tagged types

There are two ways to tag a type: implicitly and explicitly.

Implicitly tagged types are derived from other types by changing the tag of the underlying type. Implicit tagging is denoted by the ASN.1 keywords [class number] IMPLICIT (see Section 5.1).

Explicitly tagged types are derived from other types by adding an outer tag to the underlying type. In effect, explicitly tagged types are structured types consisting of one component, the underlying type. Explicit tagging is denoted by the ASN.1 keywords [class number] EXPLICIT (see Section 5.2).

The keyword [class number] alone is the same as explicit tagging, except when the "module" in which the ASN.1 type is defined has implicit tagging by default. ("Modules" are among the advanced features not described in this note.)

For purposes of encoding, an implicitly tagged type is considered the same as the underlying type, except that the tag is different. An explicitly tagged type is considered like a structured type with one component, the underlying type. Implicit tags result in shorter encodings, but explicit tags may be necessary to avoid ambiguity if the tag of the underlying type is indeterminate (e.g., the underlying type is CHOICE or ANY).

2.4 Other types

3. Basic Encoding Rules

There are three methods to encode an ASN.1 value under BER, the choice of which depends on the type of value and whether the length of the value is known. The three methods are primitive, definite-length encoding; constructed, definite- length encoding; and constructed, indefinite-length encoding. Simple non-string types employ the primitive, definite-length method; structured types employ either of the constructed methods; and simple string types employ any of the methods, depending on whether the length of the value is known. Types derived by implicit tagging employ the method of the underlying type and types derived by explicit tagging employ the constructed methods.

In each method, the BER encoding has three or four parts:

Identifier octets. These identify the class and tag number of the ASN.1 value, and indicate whether the method is primitive or constructed.

Length octets. For the definite-length methods, these give the number of contents octets. For the constructed, indefinite-length method, these indicate that the length is indefinite.

Contents octets. For the primitive, definite-length method, these give a concrete representation of the value. For the constructed methods, these give the concatenation of the BER encodings of the components of the value.

End-of-contents octets. For the constructed, indefinite- length method, these denote the end of the contents. For the other methods, these are absent.

The three methods of encoding are described in the following sections.

3.1 Primitive, definite-length method

Identifier octets. There are two forms: low tag number (for tag numbers between 0 and 30) and high tag number (for tag numbers 31 and greater).

Low-tag-number form. One octet. Bits 8 and 7 specify the class (see Table 2), bit 6 has value "0," indicating that the encoding is primitive, and bits 5-1 give the tag number.

Class	Bit 8	Bit 7
universal	0	0
application	0	1
context-specific	1	0
private	1	1

Table 2. Class encoding in identifier octets.

High-tag-number form. Two or more octets. First octet is as in low-tag-number form, except that bits 5-1 all have value "1." Second and following octets give the tag number, base 128, most significant digit first, with as few digits as possible, and with the bit 8 of each octet except the last set to "1."

 

Short form. One octet. Bit 8 has value "0" and bits 7-1 give the length.

Long form. Two to 127 octets. Bit 8 of first octet has value "1" and bits 7-1 give the number of additional length octets. Second and following octets give the length, base 256, most significant digit first.

 

Contents octets. These give a concrete representation of the value (or the value of the underlying type, if the type is derived by implicit tagging). Details for particular types are given in Section 5.

3.2 Constructed, definite-length method

Identifier octets. As described in Section 3.1, except that bit 6 has value "1," indicating that the encoding is constructed.

Length octets. As described in Section 3.1.

Contents octets. The concatenation of the BER encodings of the components of the value:

• For simple string types and types derived from them by implicit tagging, the concatenation of the BER encodings of consecutive substrings of the value (underlying value for implicit tagging).

   

• For structured types and types derived from them by implicit tagging, the concatenation of the BER encodings of components of the value (underlying value for implicit tagging).

   

• For types derived from anything by explicit tagging, the BER encoding of the underlying value.

 

3.3 Constructed, indefinite-length method

Identifier octets. As described in Section 3.2.

Length octets. One octet, 80.

Contents octets. As described in Section 3.2.

End-of-contents octets. Two octets, 00 00.

Since the end-of-contents octets appear where an ordinary BER encoding might be expected (e.g., in the contents octets of a sequence value), the 00 and 00 appear as identifier and length octets, respectively. Thus the end-of-contents octets is really the primitive, definite-length encoding of a value with universal class, tag number 0, and length 0.

4. Distinguished Encoding Rules

DER adds the following restrictions to the rules given in Section 3:

1. When the length is between 0 and 127, the short form of length must be used

    

2. When the length is 128 or greater, the long form of length must be used, and the length must be encoded in the minimum number of octets.

    

3. For simple string types and implicitly tagged types derived from simple string types, the primitive, definite-length method must be employed.

    

4. For structured types, implicitly tagged types derived from structured types, and explicitly tagged types derived from anything, the constructed, definite-length method must be employed.

Other restrictions are defined for particular types (such as BIT STRING, SEQUENCE, SET, and SET OF), and can be found in Section 5.

5. Notation and encodings for some types

The types described are those presented in Section 2. They are listed alphabetically here.

Each description includes ASN.1 notation, BER encoding, and DER encoding. The focus of the encodings is primarily on the contents octets; the tag and length octets follow Sections 3 and 4. The descriptions also explain where each type is used in PKCS and related standards. ASN.1 notation is generally only for types, although for the type OBJECT IDENTIFIER, value notation is given as well.

5.1 Implicitly tagged types

Implicit tagging is used for optional SEQUENCE components with underlying type other than ANY throughout PKCS, and for the extendedCertificate alternative of PKCS #7's ExtendedCertificateOrCertificate type.

ASN.1 notation:

[[class] number] IMPLICIT Type

class = UNIVERSAL | APPLICATION | PRIVATE

where Type is a type, class is an optional class name, and number is the tag number within the class, a nonnegative integer.

In ASN.1 "modules" whose default tagging method is implicit tagging, the notation [[class] number] Type is also acceptable, and the keyword IMPLICIT is implied. (See Section 2.3.) For definitions stated outside a module, the explicit inclusion of the keyword IMPLICIT is preferable to prevent ambiguity.

If the class name is absent, then the tag is context- specific. Context-specific tags can only appear in a component of a structured or CHOICE type.

Example: PKCS #8's PrivateKeyInfo type has an optional attributes component with an implicit, context-specific tag:

PrivateKeyInfo ::= SEQUENCE {
  version Version,
  privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
  privateKey PrivateKey,
  attributes [0] IMPLICIT Attributes OPTIONAL }

Here the underlying type is Attributes, the class is absent (i.e., context-specific), and the tag number within the class is 0.

BER encoding. Primitive or constructed, depending on the underlying type. Contents octets are as for the BER encoding of the underlying value.

Example: The BER encoding of the attributes component of a PrivateKeyInfo value is as follows:

• the identifier octets are 80 if the underlying Attributes value has a primitive BER encoding and a0 if the underlying Attributes value has a constructed BER encoding

   

• the length and contents octets are the same as the length and contents octets of the BER encoding of the underlying Attributes value

DER encoding. Primitive or constructed, depending on the underlying type. Contents octets are as for the DER encoding of the underlying value.

5.2 Explicitly tagged types

Explicit tagging is used for optional SEQUENCE components with underlying type ANY throughout PKCS, and for the version component of X.509's Certificate type.

ASN.1 notation:

[[class] number] EXPLICIT Type

class = UNIVERSAL | APPLICATION | PRIVATE

where Type is a type, class is an optional class name, and number is the tag number within the class, a nonnegative integer.

If the class name is absent, then the tag is context- specific. Context-specific tags can only appear in a component of a SEQUENCE, SET or CHOICE type.

In ASN.1 "modules" whose default tagging method is explicit tagging, the notation [[class] number] Type is also acceptable, and the keyword EXPLICIT is implied. (See Section 2.3.) For definitions stated outside a module, the explicit inclusion of the keyword EXPLICIT is preferable to prevent ambiguity.

Example 1: PKCS #7's ContentInfo type has an optional content component with an explicit, context-specific tag:

ContentInfo ::= SEQUENCE {
  contentType ContentType,
  content
    [0] EXPLICIT ANY DEFINED BY contentType OPTIONAL }

Here the underlying type is ANY DEFINED BY contentType, the class is absent (i.e., context-specific), and the tag number within the class is 0.

Example 2: X.509's Certificate type has a version component with an explicit, context-specific tag, where the EXPLICIT keyword is omitted:

Certificate ::= ...
  version [0] Version DEFAULT v1988,
...

The tag is explicit because the default tagging method for the ASN.1 "module" in X.509 that defines the Certificate type is explicit tagging.

BER encoding. Constructed. Contents octets are the BER encoding of the underlying value.

Example: the BER encoding of the content component of a ContentInfo value is as follows:

• identifier octets are a0

   

• length octets represent the length of the BER encoding of the underlying ANY DEFINED BY contentType value

   

• contents octets are the BER encoding of the underlying ANY DEFINED BY contentType value

DER encoding. Constructed. Contents octets are the DER encoding of the underlying value.

5.3 ANY

The ANY type is used for content of a particular content type in PKCS #7's ContentInfo type, for parameters of a particular algorithm in X.509's AlgorithmIdentifier type, and for attribute values in X.501's Attribute and AttributeValueAssertion types. The Attribute type is used by PKCS #6, #7, #8, #9 and #10, and the AttributeValueAssertion type is used in X.501 distinguished names.

ASN.1 notation:

ANY [DEFINED BY identifier]

where identifier is an optional identifier.

In the ANY form, the actual type is indeterminate.

The ANY DEFINED BY identifier form can only appear in a component of a SEQUENCE or SET type for which identifier identifies some other component, and that other component has type INTEGER or OBJECT IDENTIFIER (or a type derived from either of those by tagging). In that form, the actual type is determined by the value of the other component, either in the registration of the object identifier value, or in a table of integer values.

Example: X.509's AlgorithmIdentifier type has a component of type ANY:

AlgorithmIdentifier ::= SEQUENCE {
  algorithm OBJECT IDENTIFIER,
  parameters ANY DEFINED BY algorithm OPTIONAL }

Here the actual type of the parameter component depends on the value of the algorithm component. The actual type would be defined in the registration of object identifier values for the algorithm component.

BER encoding. Same as the BER encoding of the actual value.

Example: The BER encoding of the value of the parameter component is the BER encoding of the value of the actual type as defined in the registration of object identifier values for the algorithm component.

DER encoding. Same as the DER encoding of the actual value.

5.4 BIT STRING

The BIT STRING type is used for digital signatures on extended certificates in PKCS #6's ExtendedCertificate type, for digital signatures on certificates in X.509's Certificate type, and for public keys in certificates in X.509's SubjectPublicKeyInfo type.

ASN.1 notation:

BIT STRING

Example: X.509's SubjectPublicKeyInfo type has a component of type BIT STRING:

SubjectPublicKeyInfo ::= SEQUENCE {
  algorithm AlgorithmIdentifier,
  publicKey BIT STRING }

BER encoding. Primitive or constructed. In a primitive encoding, the first contents octet gives the number of bits by which the length of the bit string is less than the next multiple of eight (this is called the "number of unused bits"). The second and following contents octets give the value of the bit string, converted to an octet string. The conversion process is as follows:

1. The bit string is padded after the last bit with zero to seven bits of any value to make the length of the bit string a multiple of eight. If the length of the bit string is a multiple of eight already, no padding is done.

    

2. The padded bit string is divided into octets. The first eight bits of the padded bit string become the first octet, bit 8 to bit 1, and so on through the last eight bits of the padded bit string.

In a constructed encoding, the contents octets give the concatenation of the BER encodings of consecutive substrings of the bit string, where each substring except the last has a length that is a multiple of eight bits.

Example: The BER encoding of the BIT STRING value "011011100101110111" can be any of the following, among others, depending on the choice of padding bits, the form of length octets, and whether the encoding is primitive or constructed:

03 04 06 6e 5d c0

03 04 06 6e 5d e0

03 81 04 06 6e 5d c0

23 09        
   03 03 00 6e 5d
   03 02 06 c0

DER encoding. Primitive. The contents octects are as for a primitive BER encoding, except that the bit string is padded with zero-valued bits.

Example: The DER encoding of the BIT STRING value "011011100101110111" is

03 04 06 6e 5d c0

5.5 CHOICE

The CHOICE type is used to represent the union of an extended certificate and an X.509 certificate in PKCS #7's ExtendedCertificateOrCertificate type.

ASN.1 notation:

CHOICE {
[identifier1] Type1,
...,
[identifiern] Typen }

where identifier1 , ..., identifiern are optional, distinct identifiers for the alternatives, and Type1, ..., Typen are the types of the alternatives. The identifiers are primarily for documentation; they do not affect values of the type or their encodings in any way.

The types must have distinct tags. This requirement is typically satisfied with explicit or implicit tagging on some of the alternatives.

Example: PKCS #7's ExtendedCertificateOrCertificate type is a CHOICE type:

ExtendedCertificateOrCertificate ::= CHOICE {
  certificate Certificate, -- X.509
  extendedCertificate [0] IMPLICIT ExtendedCertificate
}

Here the identifiers for the alternatives are certificate and extendedCertificate, and the types of the alternatives are Certificate and [0] IMPLICIT ExtendedCertificate.

BER encoding. Same as the BER encoding of the chosen alternative. The fact that the alternatives have distinct tags makes it possible to distinguish between their BER encodings.

Example: The identifier octets for the BER encoding are 30 if the chosen alternative is certificate, and a0 if the chosen alternative is extendedCertificate.

DER encoding. Same as the DER encoding of the chosen alternative.

5.6 IA5String

The IA5String type is used in PKCS #9's electronic-mail address, unstructured-name, and unstructured-address attributes.

ASN.1 notation:

IA5String

BER encoding. Primitive or constructed. In a primitive encoding, the contents octets give the characters in the IA5 string, encoded in ASCII. In a constructed encoding, the contents octets give the concatenation of the BER encodings of consecutive substrings of the IA5 string.

Example: The BER encoding of the IA5String value "test1@rsa.com" can be any of the following, among others, depending on the form of length octets and whether the encoding is primitive or constructed:

16 0d 74 65 73 74 31 40 72 73 61 2e 63 6f 6d

16 81 0d
   74 65 73 74 31 40 72 73 61 2e 63 6f 6d

36 13
   16 05 74 65 73 74 31
   16 01 40
   16 07 72 73 61 2e 63 6f 6d

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

Example: The DER encoding of the IA5String value "test1@rsa.com" is

16 0d 74 65 73 74 31 40 72 73 61 2e 63 6f 6d

5.7 INTEGER

The INTEGER type is used for version numbers throughout PKCS, cryptographic values such as modulus, exponent, and primes in PKCS #1's RSAPublicKey and RSAPrivateKey types and PKCS #3's DHParameter type, a message-digest iteration count in PKCS #5's PBEParameter type, and version numbers and serial numbers in X.509's Certificate type.

ASN.1 notation:

INTEGER [{ identifier1(value1) ... identifiern(valuen) }]

where identifier1, ..., identifiern are optional distinct identifiers and value1, ..., valuen are optional integer values. The identifiers, when present, are associated with values of the type.

Example: X.509's Version type is an INTEGER type with identified values:

Version ::= INTEGER { v1988(0) }

Certificate ::= ...
  version Version DEFAULT v1988,
...

BER encoding. Primitive. Contents octets give the value of the integer, base 256, in two's complement form, most significant digit first, with the minimum number of octets. The value 0 is encoded as a single 00 octet.

Some example BER encodings (which also happen to be DER encodings) are given in Table 3.

Integer value	BER encoding
0	02 01 00
127	02 01 7F
128	02 02 00 80
256	02 02 01 00
-128	02 01 80
-129	02 02 FF 7F

Table 3. Example BER encodings of INTEGER values.

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

5.8 NULL

The NULL type is used for algorithm parameters in several places in PKCS.

ASN.1 notation:

NULL

BER encoding. Primitive. Contents octets are empty.

Example: The BER encoding of a NULL value can be either of the following, as well as others, depending on the form of the length octets:

05 00

05 81 00

DER encoding. Primitive. Contents octets are empty; the DER encoding of a NULL value is always 05 00.

5.9 OBJECT IDENTIFIER

OBJECT IDENTIFIER values are given meanings by registration authorities. Each registration authority is responsible for all sequences of components beginning with a given sequence. A registration authority typically delegates responsibility for subsets of the sequences in its domain to other registration authorities, or for particular types of object. There are always at least two components.

The OBJECT IDENTIFIER type is used to identify content in PKCS #7's ContentInfo type, to identify algorithms in X.509's AlgorithmIdentifier type, and to identify attributes in X.501's Attribute and AttributeValueAssertion types. The Attribute type is used by PKCS #6, #7, #8, #9, and #10, and the AttributeValueAssertion type is used in X.501 distinguished names. OBJECT IDENTIFIER values are defined throughout PKCS.

ASN.1 notation:

OBJECT IDENTIFIER

The ASN.1 notation for values of the OBJECT IDENTIFIER type is

{ [identifier] component1 ... componentn }

componenti = identifieri | identifieri (valuei) | valuei

where identifier, identifier1, ..., identifiern are identifiers, and value1, ..., valuen are optional integer values.

The form without identifier is the "complete" value with all its components; the form with identifier abbreviates the beginning components with another object identifier value. The identifiers identifier1, ..., identifiern are intended primarily for documentation, but they must correspond to the integer value when both are present. These identifiers can appear without integer values only if they are among a small set of identifiers defined in X.208.

Example: The following values both refer to the object identifier assigned to RSA Data Security, Inc.:

{ iso(1) member-body(2) 840 113549 }
{ 1 2 840 113549 }

(In this example, which gives ASN.1 value notation, the object identifier values are decimal, not hexadecimal.) Table 4 gives some other object identifier values and their meanings.

{ 1 2 }

{ 1 2 840 }

{ 1 2 840 113549 }

{ 1 2 840 113549 1 }

{ 2 5 }

{ 2 5 8 }

Table 4. Some object identifier values and their meanings.

BER encoding. Primitive. Contents octets are as follows, where value1, ..., valuen denote the integer values of the components in the complete object identifier:

1. The first octet has value 40 * value1 + value2. (This is unambiguous, since value1 is limited to values 0, 1, and 2; value2 is limited to the range 0 to 39 when value1 is 0 or 1; and, according to X.208, n is always at least 2.)

    

2. The following octets, if any, encode value3, ..., valuen. Each value is encoded base 128, most significant digit first, with as few digits as possible, and the most significant bit of each octet except the last in the value's encoding set to "1."

Example: The first octet of the BER encoding of RSA Data Security, Inc.'s object identifier is 40 * 1 + 2 = 42 = 2a16. The encoding of 840 = 6 * 128 + 4816 is 86 48 and the encoding of 113549 = 6 * 1282 + 7716 * 128 + d16 is 86 f7 0d. This leads to the following BER encoding:

06 06 2a 86 48 86 f7 0d

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

5.10 OCTET STRING

The OCTET STRING type is used for salt values in PKCS #5's PBEParameter type, for message digests, encrypted message digests, and encrypted content in PKCS #7, and for private keys and encrypted private keys in PKCS #8.

ASN.1 notation:

OCTET STRING [SIZE ({size | size1..size2})]

where size, size1, and size2 are optional size constraints. In the OCTET STRING SIZE (size) form, the octet string must have size octets. In the OCTET STRING SIZE (size1..size2) form, the octet string must have between size1 and size2 octets. In the OCTET STRING form, the octet string can have any size.

Example: PKCS #5's PBEParameter type has a component of type OCTET STRING:

PBEParameter ::= SEQUENCE {
  salt OCTET STRING SIZE(8),
  iterationCount INTEGER }

Here the size of the salt component is always eight octets.

BER encoding. Primitive or constructed. In a primitive encoding, the contents octets give the value of the octet string, first octet to last octet. In a constructed encoding, the contents octets give the concatenation of the BER encodings of substrings of the OCTET STRING value.

Example: The BER encoding of the OCTET STRING value 01 23 45 67 89 ab cd ef can be any of the following, among others, depending on the form of length octets and whether the encoding is primitive or constructed:

04 08 01 23 45 67 89 ab cd ef

04 81 08 01 23 45 67 89 ab cd ef

24 0c
   04 04 01 23 45 67
   04 04 89 ab cd ef

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

Example: The BER encoding of the OCTET STRING value 01 23 45 67 89 ab cd ef is

04 08 01 23 45 67 89 ab cd ef

5.11 PrintableString

This type is a string type.

The PrintableString type is used in PKCS #9's challenge- password and unstructured-address attributes, and in several X.521 distinguished names attributes.

ASN.1 notation:

PrintableString

BER encoding. Primitive or constructed. In a primitive encoding, the contents octets give the characters in the printable string, encoded in ASCII. In a constructed encoding, the contents octets give the concatenation of the BER encodings of consecutive substrings of the string.

Example: The BER encoding of the PrintableString value "Test User 1" can be any of the following, among others, depending on the form of length octets and whether the encoding is primitive or constructed:

13 0b 54 65 73 74 20 55 73 65 72 20 31

13 81 0b
54 65 73 74 20 55 73 65 72 20 31

33 0f
   13 05 54 65 73 74 20
   13 06 55 73 65 72 20 31

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

Example: The DER encoding of the PrintableString value "Test User 1" is

13 0b 54 65 73 74 20 55 73 65 72 20 31

5.12 SEQUENCE

The SEQUENCE type is used throughout PKCS and related standards.

ASN.1 notation:

SEQUENCE {
[identifier1] Type1 [{ OPTIONAL | DEFAULT value1}],
...,
[identifiern] Typen [{ OPTIONAL | DEFAULT valuen}]}

where identifier1 , ..., identifiern are optional, distinct identifiers for the components, Type1, ..., Typen are the types of the components, and value1, ..., valuen are optional default values for the components. The identifiers are primarily for documentation; they do not affect values of the type or their encodings in any way.

The OPTIONAL qualifier indicates that the value of a component is optional and need not be present in the sequence. The DEFAULT qualifier also indicates that the value of a component is optional, and assigns a default value to the component when the component is absent.

The types of any consecutive series of components with the OPTIONAL or DEFAULT qualifier, as well as of any component immediately following that series, must have distinct tags. This requirement is typically satisfied with explicit or implicit tagging on some of the components.

Example: X.509's Validity type is a SEQUENCE type with two components:

Validity ::= SEQUENCE {
  start UTCTime,
  end UTCTime }

Here the identifiers for the components are start and end, and the types of the components are both UTCTime.

BER encoding. Constructed. Contents octets are the concatenation of the BER encodings of the values of the components of the sequence, in order of definition, with the following rules for components with the OPTIONAL and DEFAULT qualifiers:

• if the value of a component with the OPTIONAL or DEFAULT qualifier is absent from the sequence, then the encoding of that component is not included in the contents octets

   

• if the value of a component with the DEFAULT qualifier is the default value, then the encoding of that component may or may not be included in the contents octets

DER encoding. Constructed. Contents octets are the same as the BER encoding, except that if the value of a component with the DEFAULT qualifier is the default value, the encoding of that component is not included in the contents octets.

5.13 SEQUENCE OF

The SEQUENCE OF type is used in X.501 distinguished names.

ASN.1 notation:

SEQUENCE OF Type

where Type is a type.

Example: X.501's RDNSequence type consists of zero or more occurences of the RelativeDistinguishedName type, most significant occurrence first:

RDNSequence ::= SEQUENCE OF RelativeDistinguishedName

BER encoding. Constructed. Contents octets are the concatenation of the BER encodings of the values of the occurrences in the collection, in order of occurence.

DER encoding. Constructed. Contents octets are the concatenation of the DER encodings of the values of the occurrences in the collection, in order of occurence.

5.14 SET

The SET type is not used in PKCS.

ASN.1 notation:

SET {
[identifier1] Type1 [{ OPTIONAL | DEFAULT value1}],
...,
[identifiern] Typen [{ OPTIONAL | DEFAULT valuen}]}

where identifier1, ..., identifiern are optional, distinct identifiers for the components, Type1, ..., Typen are the types of the components, and value1, ..., valuen are optional default values for the components. The identifiers are primarily for documentation; they do not affect values of the type or their encodings in any way.

The OPTIONAL qualifier indicates that the value of a component is optional and need not be present in the set. The DEFAULT qualifier also indicates that the value of a component is optional, and assigns a default value to the component when the component is absent.

The types must have distinct tags. This requirement is typically satisfied with explicit or implicit tagging on some of the components.

BER encoding. Constructed. Contents octets are the concatenation of the BER encodings of the values of the components of the set, in any order, with the following rules for components with the OPTIONAL and DEFAULT qualifiers:

• if the value of a component with the OPTIONAL or DEFAULT qualifier is absent from the set, then the encoding of that component is not included in the contents octets

   

• if the value of a component with the DEFAULT qualifier is the default value, then the encoding of that component may or may not be included in the contents octets

DER encoding. Constructed. Contents octets are the same as for the BER encoding, except that:

1. If the value of a component with the DEFAULT qualifier is the default value, the encoding of that component is not included.

    

2. There is an order to the components, namely ascending order by tag.

5.15 SET OF

The SET OF type is used for sets of attributes in PKCS #6, #7, #8, #9 and #10, for sets of message-digest algorithm identifiers, signer information, and recipient information in PKCS #7, and in X.501 distinguished names.

ASN.1 notation:

SET OF Type

where Type is a type.

Example: X.501's RelativeDistinguishedName type consists of zero or more occurrences of the AttributeValueAssertion type, where the order is unimportant:

RelativeDistinguishedName ::=
  SET OF AttributeValueAssertion

BER encoding. Constructed. Contents octets are the concatenation of the BER encodings of the values of the occurrences in the collection, in any order.

DER encoding. Constructed. Contents octets are the same as for the BER encoding, except that there is an order, namely ascending lexicographic order of BER encoding. Lexicographic comparison of two different BER encodings is done as follows: Logically pad the shorter BER encoding after the last octet with dummy octets that are smaller in value than any normal octet. Scan the BER encodings from left to right until a difference is found. The smaller-valued BER encoding is the one with the smaller-valued octet at the point of difference.

5.16 T61String

The T61String type is used in PKCS #9's unstructured-address and challenge-password attributes, and in several X.521 attributes.

ASN.1 notation:

T61String

BER encoding. Primitive or constructed. In a primitive encoding, the contents octets give the characters in the T.61 string, encoded in ASCII. In a constructed encoding, the contents octets give the concatenation of the BER encodings of consecutive substrings of the T.61 string.

Example: The BER encoding of the T61String value "cl'es publiques" (French for "public keys") can be any of the following, among others, depending on the form of length octets and whether the encoding is primitive or constructed:

14 0f
   63 6c c2 65 73 20 70 75 62 6c 69 71 75 65 73

14 81 0f
   63 6c c2 65 73 20 70 75 62 6c 69 71 75 65 73

34 15
   14 05 63 6c c2 65 73
   14 01 20
   14 09 70 75 62 6c 69 71 75 65 73

The eight-bit character c2 is a T.61 prefix that adds an acute accent (') to the next character.

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

Example: The DER encoding of the T61String value "cl'es publiques" is

14 0f 63 6c c2 65 73 20 70 75 62 6c 69 71 75 65 73

5.17 UTCTime

YYMMDDhhmmZ
YYMMDDhhmm+hh'mm'
YYMMDDhhmm-hh'mm'
YYMMDDhhmmssZ
YYMMDDhhmmss+hh'mm'
YYMMDDhhmmss-hh'mm'

where:

YY is the least significant two digits of the year

MM is the month (01 to 12)

DD is the day (01 to 31)

hh is the hour (00 to 23)

mm are the minutes (00 to 59)

ss are the seconds (00 to 59)

Z indicates that local time is GMT, + indicates that local time is later than GMT, and - indicates that local time is earlier than GMT

hh' is the absolute value of the offset from GMT in hours

mm' is the absolute value of the offset from GMT in minutes

This type is a string type.

The UTCTime type is used for signing times in PKCS #9's signing-time attribute and for certificate validity periods in X.509's Validity type.

ASN.1 notation:

UTCTime

BER encoding. Primitive or constructed. In a primitive encoding, the contents octets give the characters in the string, encoded in ASCII. In a constructed encoding, the contents octets give the concatenation of the BER encodings of consecutive substrings of the string. (The constructed encoding is not particularly interesting, since UTCTime values are so short, but the constructed encoding is permitted.)

Example: The time this sentence was originally written was 4:45:40 p.m. Pacific Daylight Time on May 6, 1991, which can be represented with either of the following UTCTime values, among others:

"910506164540-0700"

"910506234540Z"

These values have the following BER encodings, among others:

17 0d 39 31 30 35 30 36 32 33 34 35 34 30 5a

17 11 39 31 30 35 30 36 31 36 34 35 34 30 2D 30 37 30 30

DER encoding. Primitive. Contents octets are as for a primitive BER encoding.

6. An example

6.1 Abstract notation

Name ::= CHOICE {
  RDNSequence }

RDNSequence ::= SEQUENCE OF RelativeDistinguishedName

RelativeDistinguishedName ::=
  SET OF AttributeValueAssertion

AttributeValueAssertion ::= SEQUENCE {
   AttributeType,
   AttributeValue }

AttributeType ::= OBJECT IDENTIFIER

AttributeValue ::= ANY

The Name type identifies an object in an X.500 directory. Name is a CHOICE type consisting of one alternative: RDNSequence. (Future revisions of X.500 may have other alternatives.)

The RDNSequence type gives a path through an X.500 directory tree starting at the root. RDNSequence is a SEQUENCE OF type consisting of zero or more occurences of RelativeDistinguishedName.

The RelativeDistinguishedName type gives a unique name to an object relative to the object superior to it in the directory tree. RelativeDistinguishedNameSET OF type consisting of zero or more occurrences of AttributeValueAssertion.

The AttributeValueAssertion type assigns a value to some attribute of a relative distinguished name, such as country name or common name. AttributeValueAssertion is a SEQUENCE type consisting of two components, an AttributeType type and an AttributeValue type.

The AttributeType type identifies an attribute by object identifier. The AttributeValue type gives an arbitrary attribute value. The actual type of the attribute value is determined by the attribute type.

6.2 DER encoding

The name is that of the Test User 1 from the PKCS examples [Kal93]. The name is represented by the following path:

Each level corresponds to one RelativeDistinguishedName value, each of which happens for this name to consist of one AttributeValueAssertion value. The AttributeType value is before the equals sign, and the AttributeValue value (a printable string for the given attribute types) is after the equals sign.

The countryName, organizationName, and commonUnitName are attribute types defined in X.520 as:

attributeType OBJECT IDENTIFIER ::=
  { joint-iso-ccitt(2) ds(5) 4 }

countryName OBJECT IDENTIFIER ::= { attributeType 6 }

organizationName OBJECT IDENTIFIER ::=
  { attributeType 10 }

commonUnitName OBJECT IDENTIFIER ::=
  { attributeType 3 }

6.2.1 AttributeType

06 03 55 04 06

countryName

06 03 55 04 0a

organizationName

06 03 55 04 03

commonName

The identifier octets follow the low-tag form, since the tag is 6 for OBJECT IDENTIFIER. Bits 8 and 7 have value "0," indicating universal class, and bit 6 has value "0," indicating that the encoding is primitive. The length octets follow the short form. The contents octets are the concatenation of three octet strings derived from subidentifiers (in decimal): 40 * 2 + 5 = 85 = 5516; 4; and 6, 10, or 3.

6.2.2 AttributeValue

13 02 55 53

13 14
   45 78 61 6d 70 6c 65 20 4f 72 67 61 6e 69 7a 61
   74 69 6f 6e

13 0b
   54 65 73 74 20 55 73 65 72 20 31

The identifier octets follow the low-tag-number form, since the tag for PrintableString, 19 (decimal), is between 0 and 30. Bits 8 and 7 have value "0" since PrintableString is in the universal class. Bit 6 has value "0" since the encoding is primitive. The length octets follow the short form, and the contents octets are the ASCII representation of the attribute value.

6.2.3 AttributeValueAssertion

30 09
   06 03 55 04 06
   13 02 55 53

30 1b
   06 03 55 04 0a
   13 14 ... 6f 6e

30 12
   06 03 55 04 0b
   13 0b ... 20 31

The identifier octets follow the low-tag-number form, since the tag for SEQUENCE, 16 (decimal), is between 0 and 30. Bits 8 and 7 have value "0" since SEQUENCE is in the universal class. Bit 6 has value "1" since the encoding is constructed. The length octets follow the short form, and the contents octets are the concatenation of the DER encodings of the attributeType and attributeValue components.

6.2.4 RelativeDistinguishedName

31 0b
   30 09 ... 55 53

31 1d
   30 1b ... 6f 6e

31 14
   30 12 ... 20 31

The identifier octets follow the low-tag-number form, since the tag for SET OF, 17 (decimal), is between 0 and 30. Bits 8 and 7 have value "0" since SET OF is in the universal class Bit 6 has value "1" since the encoding is constructed. The lengths octets follow the short form, and the contents octets are the DER encodings of the respective AttributeValueAssertion values, since there is only one value in each set.

6.2.5 RDNSequence

30 42
   31 0b ... 55 53
   31 1d ... 6f 6e
   31 14 ... 20 31

The identifier octets follow the low-tag-number form, since the tag for SEQUENCE OF, 16 (decimal), is between 0 and 30. Bits 8 and 7 have value "0" since SEQUENCE OF is in the universal class. Bit 6 has value "1" since the encoding is constructed. The lengths octets follow the short form, and the contents octets are the concatenation of the DER encodings of the three RelativeDistinguishedName values, in order of occurrence.

6.2.6 Name

30 42
   31 0b
      30 09                                   
         06 03 55 04 06                       
         13 02 55 53    

   31 1d
      30 1b
         06 03 55 04 0a                       
         13 14                                
            45 78 61 6d 70 6c 65 20 4f 72 67
            67 61 6e 69 7a 61 74 69 6f 6e

   31 14
      30 12
         06 03 55 04 03                       
         13 0b                                
            54 65 73 74 20 55 73 65 72 20 31

References

PKCS #3 RSA Laboratories. PKCS #3: Diffie-Hellman Key- Agreement Standard. Version 1.4, November 1993.

PKCS #5 RSA Laboratories. PKCS #5: Password-Based Encryption Standard. Version 1.5, November 1993.

PKCS #6 RSA Laboratories. PKCS #6: Extended-Certificate Syntax Standard. Version 1.5, November 1993.

PKCS #7 RSA Laboratories. PKCS #7: Cryptographic Message Syntax Standard. Version 1.5, November 1993.

PKCS #8 RSA Laboratories. PKCS #8: Private-Key Information Syntax Standard. Version 1.2, November 1993.

PKCS #9 RSA Laboratories. PKCS #9: Selected Attribute Types. Version 1.1, November 1993.

PKCS #10 RSA Laboratories. PKCS #10: Certification Request Syntax Standard. Version 1.0, November 1993.

X.200 CCITT. Recommendation X.200: Reference Model of Open Systems Interconnection for CCITT Applications. 1984.

X.208 CCITT. Recommendation X.208: Specification of Abstract Syntax Notation One (ASN.1). 1988.

X.209 CCITT. Recommendation X.209: Specification of Basic Encoding Rules for Abstract Syntax Notation One (ASN.1). 1988.

X.500 CCITT. Recommendation X.500: The Directory--Overview of Concepts, Models and Services. 1988.

X.501 CCITT. Recommendation X.501: The Directory-- Models. 1988.

X.509 CCITT. Recommendation X.509: The Directory-- Authentication Framework. 1988.

X.520 CCITT. Recommendation X.520: The Directory-- Selected Attribute Types. 1988.

[Kal93] Burton S. Kaliski Jr. Some Examples of the PKCS Standards. RSA Laboratories, November 1993.

[NIST92] NIST. Special Publication 500-202: Stable Implementation Agreements for Open Systems Interconnection Protocols. Part 11 (Directory Services Protocols). December 1992.

Revision history

The June 3, 1991 version is part of the initial public release of PKCS. It was published as NIST/OSI Implementors' Workshop document SEC-SIG-91-17.

November 1, 1993 version

The November 1, 1993 version incorporates several editorial changes, including the addition of a revision history. It is updated to be consistent with the following versions of the PKCS documents:

PKCS #1: RSA Encryption Standard. Version 1.5, November 1993.

PKCS #3: Diffie-Hellman Key-Agreement Standard. Version 1.4, November 1993.

PKCS #5: Password-Based Encryption Standard. Version 1.5, November 1993.

PKCS #6: Extended-Certificate Syntax Standard. Version 1.5, November 1993.

PKCS #7: Cryptographic Message Syntax Standard. Version 1.5, November 1993.

PKCS #8: Private-Key Information Syntax Standard. Version 1.2, November 1993.

PKCS #9: Selected Attribute Types. Version 1.1, November 1993.

PKCS #10: Certification Request Syntax Standard. Version 1.0, November 1993.

The following substantive changes were made:

Section 5: Description of T61String type is added.

Section 6: Names are changed, consistent with other PKCS examples.

Author's address

Burton S. Kaliski Jr., Ph.D.
Chief Scientist
RSA Laboratories              (415) 595-7703
100 Marine Parkway            (415) 595-4126 (fax)
Redwood City, CA  94065  USA  burt@rsa.com