NIST Special Publication 800-133

Recommendation for Cryptographic 

Key Generation

Elaine Barker

Allen Roginsky 

http://dx.doi.org/10.6028/NIST.SP.800-133

C O M P U T E R S E C U R I T Y
NIST Special Publication 800-133 

Recommendation for Cryptographic 

Key Generation

Elaine Barker

Allen Roginsky

Computer Security Division

Information Technology Laboratory

http://dx.doi.org/10.6028/NIST.SP.800-133

December 2012

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
iii

National Institute of Standards and Technology Special Publication 800-133

Natl. Inst. Stand. Technol. Spec. Publ. 800-133, 26 pages (December 2012)

http://dx.doi.org/10.6028/NIST.SP.800-133

CODEN: NSPUE2

 

 

Comments on this publication may be submitted to:

National Institute of Standards and Technology

Attn: Computer Security Division, Information Technology Laboratory

100 Bureau Drive (Mail Stop 8930) Gaithersburg, MD 20899-8930

Email: SP-800-133_Comments@nist.gov

Certain commercial entities, equipment, or materials may be identified in this document in order to 

describe an experimental procedure or concept adequately. Such identification is not intended to imply 

recommendation or endorsement by NIST, nor is it intended to imply that the entities, materials, or 

equipment are necessarily the best available for the purpose. 

There may be references in this publication to other publications currently under development by NIST 

in accordance with its assigned statutory responsibilities. The information in this publication, including 

concepts and methodologies, may be used by Federal agencies even before the completion of such 

companion publications. Thus, until each publication is completed, current requirements, guidelines, 

and procedures, where they exist, remain operative. For planning and transition purposes, Federal 

agencies may wish to closely follow the development of these new publications by NIST. 

Organizations are encouraged to review all draft publications during public comment periods and 

provide feedback to NIST. All NIST Computer Security Division publications, other than the ones 

noted above, are available at http://csrc.nist.gov/publications.
iv

Reports on Computer Systems Technology

The Information Technology Laboratory (ITL) at the National Institute of Standards and 

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Abstract

Cryptography is often used in an information technology security environment to protect data that 

is sensitive, has a high value, or is vulnerable to unauthorized disclosure or undetected 

modification during transmission or while in storage. Cryptography relies upon two basic 

components: an algorithm (or cryptographic methodology) and a cryptographic key. This 

Recommendation discusses the generation of the keys to be managed and used by the approved

cryptographic algorithms.

Keywords

asymmetric key; key agreement; key derivation; key generation; key wrapping; key replacement; 

key transport; key update; private key; public key; symmetric key

Acknowledgements

The National Institute of Standards and Technology (NIST) gratefully acknowledges and 

appreciates contributions by Rich Davis of the National Security Agency and the public and 

private sectors whose thoughtful and constructive comments improved the quality and usefulness 

of this publication.
v

Table of Contents

1 Introduction ............................................................................................... 1

2 Authority.................................................................................................... 1

3 Definitions, Acronyms and Symbols ........................................................ 2

3.1 Definitions............................................................................................................ 2

3.2 Acronyms............................................................................................................. 9

3.3 Symbols................................................................................................................ 9

4 General Discussion.................................................................................. 10

4.1 Keys to Be Generated ........................................................................................ 10

4.2 Where Keys are Generated ................................................................................ 10

4.3 Supporting a Security Strength .......................................................................... 10

5 Using the Output of a Random Bit Generator......................................... 11

6 Generation of Key Pairs for Asymmetric-Key Algorithms.................... 13

6.1 Key Pairs for Digital Signature Schemes........................................................... 13

6.2 Key Pairs for Key Establishment....................................................................... 13

6.3 Distributing the Key Pairs.................................................................................. 14

7 Generation of Keys for Symmetric-Key Algorithms.............................. 15

7.1 The “Direct Generation” of Symmetric Keys.................................................... 15

7.2 Distributing the Generated Symmetric Key.............................................. 15

7.3 Symmetric Keys Generated Using Key-Agreement Schemes........................... 16

7.4 Symmetric Keys Derived From a Pre-shared Key............................................. 17

7.5 Symmetric Keys Derived From Passwords ....................................................... 17

7.6 Symmetric Keys Produced by Combining Multiple Keys and Other Data ....... 18

7.7 Replacement of Symmetric Keys....................................................................... 19

Appendix A: References............................................................................... 20
1

Recommendation for Cryptographic Key Generation

1 Introduction

Cryptography is often used in an information technology security environment to protect 

data that is sensitive, has a high value, or is vulnerable to unauthorized disclosure or 

undetected modification during transmission or while in storage. Cryptography relies 

upon two basic components: an algorithm (or cryptographic methodology) and a 

cryptographic key. The algorithm is a mathematical function, and the key is a parameter 

used by that function. 

The National Institute of Standards and Technology (NIST) has developed a wide variety 

of Federal Information Processing Standards (FIPS) and NIST Special Publications (SPs) 

to specify and approve cryptographic algorithms for Federal government use. In addition, 

guidance has been provided on the management of the cryptographic keys to be used with 

these approved cryptographic algorithms.

This Recommendation discusses the generation of the keys to be used with the approved

cryptographic algorithms. The keys are either generated using mathematical processing 

on the output of approved Random Bit Generators and possibly other parameters, or 

generated based upon keys that are generated in this fashion. 

2 Authority

This publication has been developed by the National Institute of Standards and 

Technology (NIST) in furtherance of its statutory responsibilities under the Federal 

Information Security Management Act (FISMA) of 2002, Public Law 107-347. 

NIST is responsible for developing standards and guidelines, including minimum 

requirements, for providing adequate information security for all agency operations and 

assets, but such standards and guidelines shall not apply to national security systems. 

This Recommendation has been prepared for use by federal agencies. It may be used by 

non-governmental organizations on a voluntary basis and is not subject to copyright. 

(Attribution would be appreciated by NIST.)

Nothing in this document should be taken to contradict standards and guidelines made 

mandatory and binding on federal agencies by the Secretary of Commerce under statutory 

authority. Nor should these guidelines be interpreted as altering or superseding the 

existing authorities of the Secretary of Commerce, Director of the OMB, or any other 

federal official. 

Conformance to the requirements in this Recommendation are the responsibility of 

entities installing, configuring or using applications or protocols that incorporate this 

Recommendation.
2

3 Definitions, Acronyms and Symbols

3.1 Definitions

Approved FIPS-approved and/or NIST-recommended. 

Asymmetric key A cryptographic key used with an asymmetric-key (public-key) 

algorithm. The key may be a private key or a public key.

Asymmetric-key 

algorithm

A cryptographic algorithm that uses two related keys, a public 

key and a private key. The two keys have the property that 

determining the private key from the public key is 

computationally infeasible. Also known as a public-key 

algorithm.

Bit string An ordered sequence of 0 and 1 bits.

Ciphertext Data in its encrypted form.

Compromise The unauthorized disclosure, modification or use of sensitive 

data (e.g., keying material and other security-related 

information).

Cryptographic 

algorithm

A well-defined computational procedure that takes variable 

inputs, often including a cryptographic key, and produces an 

output.
3

Cryptographic key 

(key)

A parameter used in conjunction with a cryptographic algorithm 

that determines its operation in such a way that an entity with 

knowledge of the key can reproduce or reverse the operation, 

while an entity without knowledge of the key cannot. Examples 

of cryptographic operations requiring the use of cryptographic 

keys include:

1. The transformation of plaintext data into ciphertext data,

2. The transformation of ciphertext data into plaintext data,

3. The computation of a digital signature from data,

4. The verification of a digital signature,

5. The computation of an authentication code from data, 

6. The verification of an authentication code from data and a 

received authentication code,

7. The computation of a shared secret that is used to derive 

keying material.

8. The derivation of additional keying material from a keyderivation key (i.e., a pre-shared key).

Cryptographic module The set of hardware, software, and/or firmware that implements 

security functions (including cryptographic algorithms and key 

generation) and is contained within a cryptographic module 

boundary. See [FIPS 140].

Cryptographic module 

boundary

An explicitly defined perimeter (i.e., the set of hardware, 

software and/or firmware) that establishes the boundary of a 

cryptographic module. See [FIPS 140].

Cryptoperiod The time span during which a specific key is authorized for use 

or in which the keys for a given system or application may 

remain in effect.

Data integrity A property possessed by data items that have not been altered in 

an unauthorized manner since they were created, transmitted or 

stored. 

Decryption The process of changing ciphertext into plaintext using a 

cryptographic algorithm and key.
4

Digital signature The result of a cryptographic transformation of data that, when 

properly implemented, provides origin authentication, assurance 

of data integrity and signatory non-repudiation.

Encryption The process of changing plaintext into ciphertext using a 

cryptographic algorithm and key.

Entity An individual (person), organization, device or process. Used 

interchangeably with “party”.

Entropy The entropy of a random variable X is a mathematical measure 

of the expected amount of information provided by an 

observation of X. As such, entropy is always relative to an 

observer and his or her knowledge prior to an observation.

Full entropy For the purposes of this Recommendation, an n-bit string is said 

to provide full entropy if the string is obtained through a 

process that is estimated to have at least (1−ε)n bits of entropy, 

where 0 ≤ ε ≤ 2-64.

Key See cryptographic key.

Key agreement A (pair-wise) key-establishment procedure in which the 

resultant secret keying material is a function of information 

contributed by both participants, so that neither party can 

predetermine the value of the secret keying material 

independently from the contributions of the other party. 

Contrast with key transport.

Key-agreement 

primitive

A primitive algorithm used in a key-agreement scheme

specified in [SP 800-56A], or in [SP 800-56B].

Key derivation 1. A process by which one or more keys are derived from a 

shared secret and other information during a key agreement 

transaction. 

2. A process that derives new keying material from a key (i.e., 

a key-derivation key) that is currently available.

Key-derivation key A key used as an input to a key-derivation method to derive 

other keys. See [SP 800-108]. 

Key establishment A procedure that results in secret keying material that is shared 

among different parties.
5

Key-generating 

module

A cryptographic module in which a given key is generated.

Key generation The process of generating keys for cryptography.

Key pair A private key and its corresponding public key; a key pair is 

used with an asymmetric-key (public-key) algorithm.

Key-pair owner The entity that is authorized to use the private key associated 

with a public key, whether that entity generated the key pair 

itself or a trusted party generated the key pair for the entity.

Key transport A key-establishment procedure whereby one party (the sender) 

selects a value for the secret keying material and then securely 

distributes that value to another party (the receiver) using an 

asymmetric algorithm. 

Key update A procedure in which a new cryptographic key is computed as a 

function of the (old) cryptographic key that it will replace.

Key wrapping A method of encrypting and decrypting keys and (possibly) 

associated data using a symmetric key; both confidentiality and 

integrity protection are provided. 

Module See Cryptographic module.

Non-repudiation A service that may be afforded by the appropriate application of 

a digital signature. Non-repudiation refers to the assurance that 

the owner of a signature key pair that was capable of generating 

an existing signature corresponding to certain data cannot 

convincingly deny having signed the data.

Origin authentication A process that provides assurance of the origin of information 

(e.g., by providing assurance of the originator’s identity).
6

Owner 1. For an asymmetric key pair, consisting of a private key and 

a public key, the owner is the entity that is authorized to use 

the private key associated with a public key, whether that 

entity generated the key pair itself or a trusted party 

generated the key pair for the entity.

2. For a symmetric key (i.e., a secret key), the entity or entities 

that are authorized to share and use the key.

Party See Entity.

Password A string of characters (letters, numbers and other symbols) that 

are used to authenticate an identity or to verify access 

authorization. A passphrase is a special case of a password that 

is a sequence of words or other text. In this document, the use 

of the term “password' includes this special case.

Permutation An ordered (re)arrangement of the elements of a (finite) set; a 

function that is both a one-to-one and onto mapping of a set to 

itself.

Plaintext data In this Recommendation, data that will be encrypted by an 

encryption algorithm or obtained from ciphertext using a 

decryption algorithm. 

Pre-shared key A secret key that has been established between the parties who 

are authorized to use it by means of some secure method (e.g.,

using a secure manual-distribution process or automated keyestablishment scheme).
7

Private key A cryptographic key used with an asymmetric-key (public-key)

cryptographic algorithm that is not made public and is uniquely 

associated with an entity that is authorized to use it. In an 

asymmetric-key cryptosystem, the private key is associated 

with a public key. Depending on the algorithm that employs the 

private key, it may be used to:

1. Compute the corresponding public key,

2. Compute a digital signature that may be verified using 

the corresponding public key,

3. Decrypt data that was encrypted using the corresponding 

public key, or

4. Compute a key derivation key, which may then be used 

as an input to a key derivation process.

Public key A cryptographic key used with an asymmetric-key (public-key)

cryptographic algorithm that may be made public and is 

associated with a private key and an entity that is authorized to 

use that private key. Depending on the algorithm that employs 

the public key, it may be used to:

1. Verify a digital signature that is signed by the 

corresponding private key,

2. Encrypt data that can be decrypted by the corresponding 

private key, or

3. Compute a piece of shared data (i.e., data that is known 

only by two or more specific entities).

Public-key algorithm See Asymmetric-key algorithm.

Random Bit Generator 

(RBG)

A device or algorithm that outputs bits that are computationally 

indistinguishable from bits that are independent and unbiased.

Rekey A procedure in which a new cryptographic key is generated in a 

manner that is independent of the (old) cryptographic key that it 

will replace. Contrast with Key update.

Secret key A cryptographic key used by one or more (authorized) entities 

in a symmetric-key cryptographic algorithm; the key is not 

made public. 
8

Secure channel A path for transferring data between two entities or components 

that ensures confidentiality, integrity and replay protection, as 

well as mutual authentication between the entities or 

components. The secure channel may be provided using 

cryptographic, physical or procedural methods, or a 

combination thereof.

Security strength A number associated with the amount of work (that is, the 

number of basic operations of some sort) required to break a 

cryptographic algorithm or system. Security strength is often 

expressed in bits. If the security strength is S bits, then it is 

expected that (roughly) 2S basic operations are required to break 

the algorithm or system.

Shall This term is used to indicate a requirement of a Federal 

Information Processing Standard (FIPS) or a requirement that 

must be fulfilled to claim conformance to this 

Recommendation. Note that shall may be coupled with not to 

become shall not.

Shared secret A secret value that has been computed using a keyestablishment scheme and is used as input to a (single-step) key

derivation function or an extraction-then-expansion procedure 

that derives keying material in a two-step process.

Support a security 

strength

A term applied to a method (e.g., an RBG, or a key with its 

associated cryptographic algorithm) that is capable of providing 

(at a minimum) the security strength required or desired for 

protecting data. 

Symmetric key See Secret key.

Symmetric-key 

algorithm

A cryptographic algorithm that uses the same secret key for its 

operation and, if applicable, for reversing the effects of the 

operation (e.g., an HMAC key for keyed hashing, or an AES 

key for encryption and decryption). Also known as a secret-key 

algorithm.

Target data The data that is ultimately to be protected (e.g., a key or other 

sensitive data).
9

Trusted Party A party that is trusted by its clients to generate cryptographic 

keys.

3.2 Acronyms

AES Advanced Encryption Standard. See [FIPS 197].

CMAC Cipher-based MAC. See [SP 800-38B].

CTR Counter mode for a block cipher algorithm. See [SP 800-38A].

DLC Discrete Logarithm Cryptography.

FIPS Federal Information Processing Standard.

HMAC Keyed-Hash Message Authentication Code. See [FIPS 198].

IFC Integer Factorization Cryptography.

KDF Key Derivation Function.

MAC Message Authentication Code.

NIST National Institute of Standards and Technology.

RBG Random Bit Generator.

RSA Rivest-Shamir-Adelman.

SP Special Publication.

3.3 Symbols

Symbol Meaning

⊕ Bit-wise exclusive-or. A mathematical operation that is defined as:

0 ⊕ 0 = 0,

0 ⊕ 1 = 1,

1 ⊕ 0 = 1, and

1 ⊕ 1 = 0.

|| Concatenation

H(x) A cryptographic hash function with x as an input.

T(x, k) Truncation of the bit string x to the leftmost k bits of x, where k ≤ the 

length of x in bits. 
10

4 General Discussion

4.1 Keys to Be Generated

This Recommendation addresses the generation of the cryptographic keys used in

cryptography. Key generation includes the generation of a key using the output of a 

random bit generator, the derivation of a key from another key, the derivation of a key 

from a password, and key agreement performed by two entities using an approved keyagreement scheme. All keys shall be based directly or indirectly on the output of an 

approved Random Bit Generator (RBG). For the purposes of this Recommendation, keys 

that are derived during a key-agreement transaction (see [SP 800-56A] and [SP 800-

56B]), derived from another key using a key derivation function (see [SP 800-108]) or 

derived from a password for storage applications (see [SP 800-132]) are considered to be 

indirectly generated from an RBG, since an ancestor key1

or random value (e.g., the 

random value used to generate a key-agreement key pair) was obtained directly from the 

output of an approved RBG. 

Two classes of cryptographic algorithms that require cryptographic keys have been 

approved for Federal government use: asymmetric-key algorithms and symmetric-key 

algorithms. The generation of keys for these algorithm classes is discussed in Sections 6 

and 7.

4.2 Where Keys are Generated

Cryptographic keys shall be generated within FIPS 1402-compliant cryptographic 

modules [FIPS 140]. For explanatory purposes, consider the cryptographic module in 

which a key is generated to be the key-generating module. Any random value required by 

the key-generating module shall be generated within that module; that is, the RBG (or 

portion of the RBG3

) that generates the random value shall be implemented within the 

FIPS 140 cryptographic module that generates the key. The generated keys shall be 

transported (when necessary) using secure channels and shall be used by their associated 

cryptographic algorithm within FIPS 140-compliant cryptographic modules.

4.3 Supporting a Security Strength

A method (e.g., an RBG, or a key and its associated cryptographic algorithm) supports a 

given security strength if the security strength provided by that method is equal to or 

greater than the security strength required for protecting the target data; the actual 

security strength provided can be higher than required.

 

1 Ancestor key: A key that is used in the generation of another key. For example, an ancestor key for a key generated 

by a key derivation function would be the key-derivation key used by that key derivation function.

2 “FIPS 140” without a reference to a particular version is intended to mean the version(s) of the FIPS that are currently 

being validated (e.g., FIPS 140-2).

3 The RBG itself might be distributed (e.g., the entropy source may not co-reside with the algorithm that generates the 

(pseudo) random output). See [FIPS 800-90].
11

Security strength supported by an RBG: A well-designed RBG supports a given security 

strength if the amount of entropy (i.e., randomness) available in the RBG is equal to or 

greater than that security strength. The security strength supported depends on the 

secrecy of the information designated as the entropy bits and, when used for the 

generation of keys and other secret values, on the secrecy of the RBG output. For 

information regarding the security strength that can be supported by approved RBGs, see 

[SP 800-90].

Security strength supported by an algorithm: Discussions of cryptographic algorithms 

and the security strengths they can support, given certain choices of parameters and/or

key lengths, are provided in [SP 800-57-1]. The security strength of a cryptographic 

algorithm that uses keys of a certain size (i.e., length) is assessed under the assumption 

that those keys are generated using an approved process that provides entropy equal to or 

greater than the security strength assessed for that algorithm and key size (where both the 

entropy and the security strength are measured in bits).

Security strength supported by a key: The security strength that can be supported by a key 

depends on 1) the algorithm with which it is used, 2) the size of the key (see [SP 800-57-

1]), 3) the process that generated the key (e.g., the security strength supported by the 

RBG that was used to generate the key), and 4) how the key was handled (e.g., the 

security strength available in the method used to transport the key)4

. The use of such 

terms as “security strength supported by a key” or “key supports a security strength”

assumes that these factors have been taken into account. For example, if an approved

RBG that supports a security strength of 128 bits has been used to generate a 128-bit key, 

and if (immediately after generation) the key is used with AES-128 to encrypt target data, 

then the key may be said to support a security strength of 128 bits in that encryption 

operation (for as long as the key is kept secret).

5 Using the Output of a Random Bit Generator 

Random bit strings required for the generation of cryptographic keys shall be obtained 

from the output of an approved Random Bit Generator (RBG); approved RBGs are 

specified in [SP 800-90], [FIPS 186-2], [X9.31] and [X9.62].5 The RBG shall be 

instantiated at a security strength that supports the security strength required to protect 

the target data (i.e., the data that will be protected by the generated keys).

The output of an approved RBG may be used as specified in this section to obtain either 

a symmetric key or the random value needed to generate an asymmetric key pair.

Asymmetric key pairs require the use of an approved algorithm for their generation. 

 

4 Note that the security strength that can be supported by a key is not solely dependent on its length; for example, even 

though a 128-bit key is used with AES, an AES operation using that key can only provide 112 bits of security strength 

if the key was generated using an RBG that supports a security strength of only 112 bits.

5 [SP 800-90] addresses the issues associated with security strengths, whereas [FIPS 186-2], [X9.31] and [X9.62] do 

not. Note that in [SP 800-131A], the use of the RBGs specified in [FIPS 186-2], [X9.31] and [X9.62] have been 

deprecated. Their security strengths may be limited by either the RBG algorithm or the amount of entropy in the 

RBG seed.
12

Examples are those included in [FIPS 186-3] for generating DSA, ECDSA and RSA 

keys. The generation of asymmetric key pairs from a random value is discussed in 

Section 6.

Methods for the generation of symmetric keys are discussed in Section 7.

Let K be either a symmetric key or the random value to be used as input to an approved

asymmetric-key pair generation algorithm. K shall be a bit string value of the following 

form: 

K = U ⊕ V, (1)

where 

• U is a bit string of the desired length that is obtained as the output of an approved

Random Bit Generator (RBG) that is capable of supporting the desired security 

strength required to protect the target data,

• V is a bit string of the same length as U, and

• The value of V is determined in a manner that is independent of the value of U

(and vice-versa).

The algorithm with which K will be used, and the security strength that this usage is 

intended to support will determine the required bit length and/or the minimum security 

strength that this process must provide. Since there are no restrictions on the selection of 

V (other than its length and its independence from U), a conservative approach 

necessitates an assumption that the process used to select U provides most (if not all) of 

the required entropy. 

The independence requirement on U and V is interpreted in a computational and a 

statistical sense; that is, the computation of U does not depend on V, the computation of V

does not depend on U, and knowing one of the values (U or V) must yield no information 

that can be used to gain insight into the other value. Assuming that U is the output of an 

approved RBG, the following are examples of independently selected V values:

1. V is a constant (selected independently from the value of U). (Note, that if V is a 

string of binary zeroes, then K = U, i.e., the output of an approved RBG.)

2. V is a key obtained using an approved key-derivation method from a keyderivation key and other input that is independent of U; see SP 800-108.

3. V is a key that was independently generated in another cryptographic module. V

was protected using an approved key-wrapping algorithm or transported using an 

approved key transport scheme during subsequent transport. Upon receipt, the 

protection on V is removed within the key-generating module that generated U

before combining V with U. 

4. V is produced by hashing another bit string (V ′) using an approved hash function 

and (if necessary) truncating the result to the appropriate length before combining 

it with U. That is, V = T(H(V ′), k) where T(x, k) denotes the truncation of bit 

string x to its k leftmost bits, and k is the length of U. The bit string V ′ may be a) 
13

a constant; b) a key derived from a shared secret during an approved keyagreement scheme between the key-generating module and another cryptographic 

module; or c) a key that was i) independently generated by another module, ii) 

sent using an approved key wrapping algorithm or transported using an 

approved key transport scheme, and iii) upon receipt, the protection on the key

was removed.

6 Generation of Key Pairs for Asymmetric-Key Algorithms

Asymmetric-key algorithms, also known as public-key algorithms, require the use of 

asymmetric key pairs, consisting of a private key and a corresponding public key. The 

key to be used for each operation depends on the cryptographic process being performed 

(e.g., digital-signature generation or verification). Each public/private key pair is 

associated with only one entity; this entity is known as the key-pair owner. The public 

key may be known by anyone, whereas the private key must be known and used only by 

the key-pair owner. Key pairs shall be generated by:

• The key-pair owner, or

• A Trusted Party that provides the key pair to the owner in a secure manner. The 

Trusted Party must be trusted by all parties that use the public key.

6.1 Key Pairs for Digital Signature Schemes

Digital signatures are generated on data to provide origin authentication, assurance of 

data integrity or signatory non-repudiation. Digital signatures are generated by a signer 

using a private key, and verified by a receiver using a public key. The generation of key

pairs for digital signature applications is addressed in [FIPS 186-3] for the DSA, RSA 

and ECDSA digital signature algorithms. 

A value of K, computed as shown in Section 5, shall be used to provide the random value

needed to generate a key pair for DSA, ECDSA or RSA as specified in [FIPS 186-3]. The 

maximum security strength that can be supported by these algorithms and the key lengths

used by these algorithms are provided in [SP 800-57-1]. 

For example, [SP 800-57-1] states that a DSA key pair with a public-key length of 2048

bits and a private-key length of 224 bits can support (at most) a security strength of 112 

bits. [FIPS 186-3] specifies that for such DSA key pairs, the random value used to 

determine a private key must be obtained using an RBG that supports a security strength 

of 112 bits. Using the method in Section 5, a random value K that is to be used for the 

generation of the key pair is determined by U (a value of an appropriate bit length 

obtained from an RBG that supports a security strength of at least 112 bits) and V (which 

could be zero). The value K is then used to determine the DSA key pair, as specified in 

[FIPS 186-3].

6.2 Key Pairs for Key Establishment

Key establishment includes both key agreement and key transport. Key agreement is a 

method of key establishment in which the resultant secret keying material is a function of 
14

information contributed by the participants, so that no party can predetermine the value of 

the keying material independent of any other party’s contribution. For key-transport, one 

party (the sender) selects a value for the secret keying material and then securely 

distributes that value to another party (the receiver).

Approved methods for generating the (asymmetric) key pairs used by approved keyestablishment schemes between two parties are specified in [SP 800-56A] (for schemes 

that use finite-field or elliptic-curve cryptography) and in [SP 800-56B] (for schemes that 

use integer-factorization cryptography, e.g., RSA).

A value of K, computed as shown in Section 5, shall be used to provide the random 

value6 needed to generate key pairs for the finite field or elliptic curve schemes in [SP 

800-56A], or to generate a key pair for the integer-factorization schemes specified in [SP 

800-56B]. The maximum security strength that can be supported by the approved keyestablishment schemes and the key sizes used by these schemes is provided in [SP 800-

57-1].

6.3 Distributing the Key Pairs

A general discussion of the distribution of asymmetric key pairs is provided in [SP 800-

57-1]. 

The private key shall be kept secret. It shall either be generated 1) within the key-pair 

owner’s cryptographic module (i.e., the key-pair owner’s key-generating module), or 2)

within the cryptographic module of an entity trusted by the key-pair owner and any 

relying party not to misuse the private key or reveal it to other entities (i.e., generated 

within the key-generating module of a Trusted Party, and securely transferred to the keypair owner’s cryptographic module). 

If a private key is ever output from a cryptographic module, the key shall be output and 

transferred in a form and manner that provides appropriate assurance7 of its 

confidentiality and integrity. The protection shall provide appropriate assurance that only 

the key-pair owner and/or the party that generated the key pair will be able to determine 

the value of the plaintext private key (e.g., the confidentiality and integrity protection for 

the private key uses a cryptographic mechanism that is at least as strong as the 

(maximum) security strength that must be supported by the asymmetric algorithm that 

will use the private key).

The public key of a key pair may be made public. However, it shall be distributed and 

verified in a manner that assures its integrity and association with the key-pair owner 

(e.g., using a X.509 certificate that provides a level of cryptographic protection that is at 

least as strong as the security strength associated with the key pair).

 

6 Note that in Section 5, if V is all zeroes, then K (the random value) is the output of an RBG.

7 The term “provide appropriate assurance” is used to allow various methods for the input and output of critical security 

parameters to/from the different security levels that may be implemented for a cryptographic module (see [FIPS 140]

and Section 7.8 of [ImpGuide]). 
15

7 Generation of Keys for Symmetric-Key Algorithms

Symmetric-key algorithms use the same (secret) key to both apply cryptographic 

protection to information8 and to remove or verify the protection9. Keys used with

symmetric-key algorithms must be known by only the entities authorized to apply, 

remove or verify the protection, and are commonly known as secret keys. A secret key is 

often known by multiple entities that are said to share or own the secret key, although it is 

not uncommon for a key to be generated, owned and used by a single entity (e.g., for 

secure storage). A secret key shall be generated by:

• One or more of the entities that will share the key, or 

• A Trusted Party that provides the key to the intended sharing entities in a secure 

manner. The Trusted Party must be trusted by all entities that will share the key

not to disclose the key to unauthorized parties or otherwise misuse the key.

A symmetric key K could be used, for example, to:

• Encrypt and decrypt data in an appropriate mode (e.g., using AES in the CTR 

mode as specified in [FIPS 197] and SP [800-38A]), 

• Generate Message Authentication Codes (e.g., using AES in the CMAC mode, as 

specified in [FIPS 197] and [SP 800-38B], or HMAC, as specified in [FIPS 198], 

or

• Derive additional keys using a key derivation function specified in [SP 800-108], 

where K is the pre-shared key that is used as the key-derivation key.

7.1 The “Direct Generation” of Symmetric Keys

Symmetric keys that are to be directly generated from the output of an RBG shall be 

generated as specified in Section 5, where K is the desired key. The length of the key to 

be generated is determined by the algorithm with which it will be used and the desired 

security strength to be provided; see [SP 800-57-1] for discussions on key lengths and the 

(maximum) security strengths supported by symmetric-key algorithms.

7.2 Distributing the Generated Symmetric Key

The symmetric key generated within the key-generating module often needs to be shared 

with one or more other entities that have their own cryptographic modules. The key may 

be distributed manually, or using an approved key transport or key wrapping method

(see [SP 800-56A], [SP 800-56B] and [SP 800-38F]). See [SP 800-57-1] for further 

discussion. The method used for key transport or key wrapping shall support the desired 

security strength needed to protect the target data (i.e., the data to be protected using the 

 

8 For example, transform plaintext data into ciphertext data using an encryption operation or compute a message 

authentication code (MAC).

9 For example, remove the protection by transforming the ciphertext data back to the original plaintext data using a 

decryption operation, or verify the protection by computing a message authentication code and comparing the newly 

computed MAC with a received MAC)
16

symmetric key). The requirements for outputting a key from a cryptographic module are 

discussed in [FIPS 140]. 

7.3 Symmetric Keys Generated Using Key-Agreement Schemes

When an approved key-agreement scheme is available within an entity’s key-generating 

module, a symmetric key may be established with another entity that has the same 

capability; this process results in a symmetric key that is shared between the two entities 

participating in the key-agreement transaction; further distribution of this symmetric key 

is not required between the two entities. 

Figure 1 depicts a typical key-agreement process. Asymmetric key-agreement keys are 

used with a key-agreement primitive to generate a shared secret. The shared secret is 

provided to a key-derivation method (e.g., a single-step key derivation function or an 

extraction-then-expansion (E-E) procedure) to derive keying material. [SP 800-56A] 

specifies approved key-agreement methods based on DLC; [SP 800-56B] includes 

specifications for approved key-agreement methods based on IFC. Approved single-step 

key derivation functions are specified in [SP 800-56A] and [SP 800-56B]; approved

extraction-then-expansion procedures are specified in [SP 800-56C] and may be used by 

the key-agreement schemes, as specified in [SP 800-56A].

Figure 1: Key-agreement Process per SP 800-56A, B and C
17

The key-agreement schemes used by many widely used internet security protocols do not 

fully comply with [SP 800-56A] and [SP 800-56B]. For example, the key-derivation 

method used to derive keying material from the shared secret may be different. [SP 800-

135] discusses some of these protocols, conditionally approves the use of the key

derivation functions employed by those protocols, and specifies requirements for that 

approved use.

The maximum security strength that can be supported by a key derived in this manner is 

dependent on 1) the security strength supported by the asymmetric key pairs (as used 

during key establishment), 2) the key-derivation method used, 3) the length of the derived 

key and 4) the algorithm with which the derived key will be used. See [SP 800-57-1] for 

items 1, 3 and 4. For item 2, see [SP 800-56A], [SP 800-56B] and [SP 800-56C] when 

the key-derivation method specified therein is used; no statement is made at this time 

concerning the security strengths that may be supported by a key derived using the 

methods specified in [SP 800-135].

7.4 Symmetric Keys Derived From a Pre-shared Key

Symmetric keys are often derived using a key derivation function (KDF) and a pre-shared 

key known as a key-derivation key. The pre-shared key may have been:

• Generated from an approved RBG (see Section 5) and distributed as specified in 

Section 7.2, if required, 

• Agreed upon using a key-agreement scheme (see Section 7.3), or

• Derived using a KDF and a (different) pre-shared key as specified in [SP 800-

108]. 

Approved methods are provided in [SP 800-108], which specifies approved KDFs for 

deriving keys from a pre-shared key (i.e., a key-derivation key). The KDFs are based on 

HMAC [FIPS 198] and CMAC [SP 800-38B]. 

If the derived keys need to be distributed to other entities, this may be accomplished as 

discussed in Section 7.2.

In addition to the symmetric algorithm with which a derived key will be used, the 

security strength that can be supported by the derived key depends on the security 

strength supported by the key-derivation key and the KDF method used (see [SP 800-57-

1] for the maximum security strength that can be supported by HMAC and CMAC, and 

[SP 800-107] for further discussions about the security strength of HMAC).

7.5 Symmetric Keys Derived From Passwords

In a number of popular applications, keys are generated from passwords. This is a 

questionable practice, as the passwords usually contain very little entropy (i.e., 

randomness), and are, therefore, easily guessed. However, approved methods for 

deriving keys from passwords for storage applications are provided in [SP 800-132]. For 

these applications, users are strongly advised to select passwords with a very large 

amount of entropy.
18

When a key is generated from a password, the entropy provided (and thus, the maximum 

security strength that can be supported by the generated key) shall be considered to be 

zero unless the password is generated using an approved RBG. In this case, the security 

strength that can be supported by the password (password_strength) is no greater than the 

minimum of the security strength supported by the RBG (RBG_strength) and the actual 

number of bits of RBG output (RBG_outlen) used in the password. That is,

password_strength ≤ min(RBG_strength, RBG_outlen).

7.6 Symmetric Keys Produced by Combining Multiple Keys and Other 

Data

When symmetric keys K1, ..., Kn are generated and/or established independently, they 

may be combined within a key-generating module to form a key K. Other items of data

(V1, ..., Vm) that are independent of these keys can also be combined with the Ki to form 

K, under the conditions specified below. Note that, while the Ki values are required to be 

secret, the Vi values need not be kept secret.

The independent generation/establishment of the component keys K1, ..., Kn is 

interpreted in a computational and a statistical sense; that is, the computation of any 

particular Ki value does not depend on any one or more of the other Ki values, and it is 

not feasible to use knowledge of any proper subset of the Ki values to obtain any 

information about the remaining Ki values.

The independence of the component keys from the other items of data is also interpreted 

in a computational and a statistical sense. This means that the computation of the Ki

values does not depend on any of the Vj values, the computation of the Vj values does not 

depend on any of the Ki values, and knowledge of the Vj values yields no information that 

can feasibly be used to gain insight into the Ki values. In cases where some (or all) of the 

Vj values are secret, and the rest of the Vj values (if any) are public, “independence” also 

means that knowledge of the Ki values and public Vj values yields no information that can 

feasibly be used to gain insight into the secret Vj values.

The component symmetric keys K1, ..., Kn shall be generated and/or established 

independently using approved methods10. The other items of data (i.e., V1, ..., Vm) may 

be generated or obtained using any method that ensures their independence from those 

keys. 

The approved methods for combining these symmetric keys (and other items of data) 

are:

1. Concatenating two or more keys, i.e., K = K1 || ...|| Kn. The sum of the bit lengths 

of the n component keys shall be equal to the required bit length of K.

2. Exclusive-Oring one or more symmetric keys, i.e., K = K1 ⊕ ... ⊕ Kn. The length 

of each component key (Ki) shall be equal to the length required for K. 

 

10 See Sections 7.1, 7.3, 7.4 and 7.5.
19

3. Exclusive-Oring one or more symmetric keys and one or more other items of data, 

i.e., K = K1 ⊕ ... ⊕ Kn ⊕ V1 ⊕ ... ⊕ Vm. The length of each component key (Ki) 

and each item of data (Vi) shall be equal to the length required for K.

Each Ki used in one of the three methods above shall be kept secret, shall be considered a 

key-derivation key, and shall not be used for any purpose other than the computation of a 

specific symmetric key K (i.e., a given Ki shall not be used to generate more than one 

key).

7.7 Replacement of Symmetric Keys

Sometimes, a symmetric key may need to be replaced. This may be due to a compromise

of the key or the end of the key’s cryptoperiod (see [SP 800-57-1]). Replacement may be 

accomplished by a rekeying process or by a key-update process. Rekeying is the 

replacement of a key with a new key that is generated in a manner that is entirely 

independent of the value of the old key (i.e., knowledge of the old key provides no 

knowledge of the value of the replaced key and vice versa). In a key-update process, the 

new key is usually related in some way to the old key that it replaces. 

Compromised keys shall only be rekeyed, rather than updated. When a compromised key 

is replaced, the new key shall be generated in a manner that provides assurance of its 

independence from the compromised key. The new key may be generated using any

method in Section 7 with the following restrictions:

1. The method used shall provide assurance that there is no feasibly detectable 

relationship between the new key and the compromised key. To that end, the new 

key shall not be derived or updated using the compromised key.

2. If the compromised key was generated in a manner that depended (in whole or in 

part) on a password (see Sections 7.5 and 7.6), then that password shall be 

changed prior to the generation of any new key; in particular, the new key(s) shall

be generated in a manner that is independent of the old password value.

If an uncompromised symmetric key is to be replaced, it shall be replaced using any 

method in Section 7 that supports the required amount of security strength. However, if 

the key to be replaced was generated in a manner that depended (in whole or in part) on a 

password (see Sections 7.5 and 7.6), that password shall be changed prior to the 

generation of the new key. 
20

Appendix A: References

[FIPS 140] FIPS 140-2, Security Requirements for Cryptographic Modules, May 

2001, available at http://csrc.nist.gov/publications/PubsFIPS.html.

[FIPS 180] FIPS 180-4, Secure Hash Standard, March 2012.

[FIPS 186-2] Digital Signature Standard, January 2000.

[FIPS 186-3] FIPS 186-3, Digital Signature Standard, June 2009.

[FIPS 197] Advanced Encryption Standard (AES), November 2001.

[FIPS 198] FIPS 198-1, Keyed-Hash Message Authentication Code (HMAC), July 

2008.

[SP 800-38A] Recommendation for Block Cipher Modes of Operation - Methods and 

Techniques, December 2001.

[SP 800-38B] SP 800-38B, Recommendation for Block Cipher Modes of Operation: The 

CMAC Mode for Authentication, May 2005.

[SP 800-38F] DRAFT Recommendation for Block Cipher Modes of Operation: Methods 

for Key Wrapping, August 2011 (Draft).

[SP 800-56A] SP 800-56A, Recommendation for Pair-Wise Key Establishment Schemes 

Using Discrete Logarithm Cryptography, March 2007.

[SP 800-56B] SP 800-56B, Recommendation for Pair-Wise Key Establishment Using 

Integer Factorization Cryptography, August 2009.

[SP 800-56C] SP 800-56C, Recommendation for Key Derivation through Extractionthen-Expansion, November 2011.

[SP 800-57-1] SP 800-57, Part 1, Recommendation for Key Management: General, July 

2012.

[SP 800-67] Recommendation for the Triple Data Encryption Algorithm (TDEA) 

Block Cipher, January 2012.

[SP 800-90] SP 800-90A, Recommendation for Random Number Generation Using 

Deterministic Random Bit Generators, January 2012.

Draft SP 800-90B, Recommendation for the Validation of Entropy 

Sources for Random Bit Generation, September 5, 2012.

Draft SP 800-90C, Recommendation for Random Bit Generator (RBG) 

Constructions, September 5, 2012.

[SP 800-108] SP 800-108, Recommendation for Key Derivation Using Pseudorandom 

Functions (Revised), October 2009.
21

[SP 800-131A] Recommendation for the Transitioning of Cryptographic Algorithms and 

Key Lengths, January 2011.

[SP 800-132] SP 800-132, Recommendation for Password-Based Key Derivation, Part 

1: Storage Applications, December 2010.

[SP 800-135] SP 800-135, Recommendation for Existing Application-Specific Key 

Derivation Functions, December 2010.

[ImpGuide] Implementation Guidance for FIPS PUB 140-2 and the Cryptographic 

Module Validation Program, available at 

http://csrc.nist.gov/groups/STM/cmvp/standards.html.

[X9.31] American National Standard (ANS) X9.31-1998, Digital Signatures Using 

Reversible Public Key Cryptography for the Financial Services Industry 

(rDSA), Withdrawn, but available from X9.org.

[X9.62] American National Standard X9.62-2005, Public Key Cryptography for the 

Financial Services Industry: The Elliptic Curve Digital Signature Algorithm 

(ECDSA), available at x9.org.