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<title>Key derivation function</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Key derivation function</span></span>

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<p>In <a href="Cryptography" title="Cryptography">cryptography</a>, a <b>key derivation function</b> (<b>KDF</b>) is a cryptographic algorithm that derives one or more <a href="Key_(cryptography)" title="Key (cryptography)">secret keys</a> from a secret value such as a master key, a <a href="Password" title="Password">password</a>, or a <a href="Passphrase" title="Passphrase">passphrase</a> using a <a href="Pseudorandom_function" class="mw-redirect" title="Pseudorandom function">pseudorandom function</a> (which typically uses a <a href="Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash function</a> or <a href="Block_cipher" title="Block cipher">block cipher</a>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-rfc8018_2-0" class="reference"><a href="#cite_note-rfc8018-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a <a href="Diffie%E2%80%93Hellman_key_exchange" title="Diffie–Hellman key exchange">Diffie–Hellman key exchange</a> into a symmetric key for use with <a href="Advanced_Encryption_Standard" title="Advanced Encryption Standard">AES</a>. <a href="HMAC" title="HMAC">Keyed cryptographic hash functions</a> are popular examples of pseudorandom functions used for key derivation.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>The first deliberately slow (key stretching) password-based key derivation function was called "<a href="Crypt_(C)" title="Crypt (C)">crypt</a>" (or "crypt(3)" after its <a href="Manual_page_(Unix)" class="mw-redirect" title="Manual page (Unix)">man page</a>), and was invented by <a href="Robert_Morris_(cryptographer)" title="Robert Morris (cryptographer)">Robert Morris</a> in 1978. It would encrypt a constant (zero), using the first 8 characters of the user's password as the key, by performing 25 iterations of a modified <a href="Data_Encryption_Standard" title="Data Encryption Standard">DES</a> encryption algorithm (in which a 12-bit number read from the real-time computer clock is used to perturb the calculations). The resulting 64-bit number is encoded as 11 printable characters and then stored in the <a href="Unix" title="Unix">Unix</a> password file.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> While it was a great advance at the time, increases in processor speeds since the <a href="PDP-11" title="PDP-11">PDP-11</a> era have made <a href="Brute-force_attack" title="Brute-force attack">brute-force attacks</a> against crypt <a href="Feasible_computability" class="mw-redirect" title="Feasible computability">feasible</a>, and advances in storage have rendered the 12-bit <a href="Salt_(cryptography)" title="Salt (cryptography)">salt</a> inadequate. The crypt function's design also limits the user password to 8 characters, which limits the keyspace and makes strong <a href="Passphrase" title="Passphrase">passphrases</a> impossible.

</p><p>Although high throughput is a desirable property in general-purpose hash functions, the opposite is true in password security applications in which defending against brute-force cracking is a primary concern. The growing use of <a href="Massively_parallel" title="Massively parallel">massively-parallel</a> hardware such as <a href="Graphics_processing_unit" title="Graphics processing unit">GPUs</a>, <a href="Field-programmable_gate_array" title="Field-programmable gate array">FPGAs</a>, and even <a href="Application-specific_integrated_circuit" title="Application-specific integrated circuit">ASICs</a> for brute-force cracking has made the selection of a suitable algorithms even more critical because the good algorithm should enforce a certain amount of computational cost not only on CPUs, but also resist the cost/performance advantages of modern massively-parallel platforms for such tasks. Various algorithms have been designed specifically for this purpose, including <a href="Bcrypt" title="Bcrypt">bcrypt</a>, <a href="Scrypt" title="Scrypt">scrypt</a> and, more recently, <a href="Lyra2" title="Lyra2">Lyra2</a> and <a href="Argon2" title="Argon2">Argon2</a> (the latter being the winner of the <a href="Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a>). The large-scale <a href="Ashley_Madison_data_breach" title="Ashley Madison data breach">Ashley Madison data breach</a> in which roughly 36 million passwords hashes were stolen by attackers illustrated the importance of algorithm selection in securing passwords. Although bcrypt was employed to protect the hashes (making large scale brute-force cracking expensive and time-consuming), a significant portion of the accounts in the compromised data also contained a password hash based on the fast, general-purpose, and <a href="MD5#Security" title="MD5">insecure</a> <a href="MD5" title="MD5">MD5</a> algorithm, which made it possible for over 11 million of the passwords to be cracked in a matter of weeks.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p><p>In June 2017, The U.S. National Institute of Standards and Technology (NIST) issued a new revision of their digital authentication guidelines, NIST SP 800-63B-3,<sup id="cite_ref-sp800-63B_7-0" class="reference"><a href="#cite_note-sp800-63B-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 5.1.1.2">: 5.1.1.2 </span></sup> stating that: "Verifiers SHALL store memorized secrets [i.e. passwords] in a form that is resistant to offline attacks. Memorized secrets SHALL be salted and hashed using a suitable one-way key derivation function. Key derivation functions take a password, a salt, and a cost factor as inputs then generate a password hash. Their purpose is to make each password guessing trial by an attacker who has obtained a password hash file expensive and therefore the cost of a guessing attack high or prohibitive."

</p><p>Modern password-based key derivation functions, such as <a href="PBKDF2" title="PBKDF2">PBKDF2</a>,<sup id="cite_ref-rfc8018_2-1" class="reference"><a href="#cite_note-rfc8018-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> are based on a recognized cryptographic hash, such as <a href="SHA-2" title="SHA-2">SHA-2</a>, use more salt (at least 64 bits and chosen randomly) and a high iteration count. NIST recommends a minimum iteration count of 10,000.<sup id="cite_ref-sp800-63B_7-1" class="reference"><a href="#cite_note-sp800-63B-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 5.1.1.2">: 5.1.1.2 </span></sup>

"For especially critical keys, or for very powerful systems or systems where user-perceived performance is not critical, an iteration count of 10,000,000 may be appropriate.”

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<div class="mw-heading mw-heading2"><h2 id="Key_derivation">Key derivation</h2></div>

<p>The original use for a KDF is key derivation, the generation of keys from secret passwords or passphrases. Variations on this theme include:

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<ul><li>In conjunction with non-secret parameters to derive one or more keys from a common secret value (which is sometimes also referred to as "<b>key diversification</b>"). Such use may prevent an attacker who obtains a derived key from learning useful information about either the input secret value or any of the other derived keys. A KDF may also be used to ensure that derived keys have other desirable properties, such as avoiding "weak keys" in some specific encryption systems.</li>

<li>As components of multiparty <a href="Key-agreement_protocol" title="Key-agreement protocol">key-agreement protocols</a>. Examples of such key derivation functions include KDF1, defined in <a href="IEEE_P1363" title="IEEE P1363">IEEE Std 1363-2000</a>, and similar functions in ANSI X9.42.</li>

<li>To derive keys from secret passwords or passphrases (a <i>password-based KDF</i>).</li>

<li>To derive keys of different length from the ones provided. KDFs designed for this purpose include <a href="HKDF" title="HKDF">HKDF</a> and SSKDF. These take an 'info' bit string as an additional optional 'info' parameter, which may be crucial to bind the derived key material to application- and context-specific information.<sup id="cite_ref-info_9-0" class="reference"><a href="#cite_note-info-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Key_stretching" title="Key stretching">Key stretching</a> and key strengthening.</li></ul>

<div class="mw-heading mw-heading3"><h3 id="Key_stretching_and_key_strengthening">Key stretching and key strengthening</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Key_stretching" title="Key stretching">Key stretching</a></div>

<p>Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys. In such applications, it is generally recommended that the key derivation function be made deliberately slow so as to frustrate <a href="Brute-force_attack" title="Brute-force attack">brute-force attack</a> or <a href="Dictionary_attack" title="Dictionary attack">dictionary attack</a> on the password or passphrase input value.

</p><p>Such use may be expressed as <span class="texhtml">DK = KDF(key, salt, iterations)</span>, where <span class="texhtml">DK</span> is the derived key, <span class="texhtml">KDF</span> is the key derivation <a href="Subroutine" class="mw-redirect" title="Subroutine">function</a>, <span class="texhtml">key</span> is the original key or password, <span class="texhtml">salt</span> is a random number which acts as <a href="Salt_(cryptography)" title="Salt (cryptography)">cryptographic salt</a>, and <span class="texhtml">iterations</span> refers to the number of <a href="Iteration" title="Iteration">iterations</a> of a sub-function. The derived key is used instead of the original key or password as the key to the system. The values of the salt and the number of iterations (if it is not fixed) are stored with the hashed password or sent as <a href="Plaintext" title="Plaintext">cleartext</a> (unencrypted) with an encrypted message.<sup id="cite_ref-salthash_10-0" class="reference"><a href="#cite_note-salthash-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>The difficulty of a brute force attack is increased with the number of iterations. A practical limit on the iteration count is the unwillingness of users to tolerate a perceptible delay in logging into a computer or seeing a decrypted message. The use of <a href="Salt_(cryptography)" title="Salt (cryptography)">salt</a> prevents the attackers from precomputing a dictionary of derived keys.<sup id="cite_ref-salthash_10-1" class="reference"><a href="#cite_note-salthash-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>An alternative approach, called <b>key strengthening</b>, extends the key with a random salt, but then (unlike in key stretching) securely deletes the salt.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This forces both the attacker and legitimate users to perform a brute-force search for the salt value.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Although the paper that introduced key stretching<sup id="cite_ref-low-entropy_13-0" class="reference"><a href="#cite_note-low-entropy-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> referred to this earlier technique and intentionally chose a different name, the term "key strengthening" is now often (arguably incorrectly) used to refer to key stretching.

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<div class="mw-heading mw-heading2"><h2 id="Password_hashing">Password hashing</h2></div>

<p>Despite their original use for key derivation, KDFs are possibly better known for their use in <b>password hashing</b> (<a href="Cryptographic_hash_function#Password_verification" title="Cryptographic hash function">password verification by hash comparison</a>), as used by the <a href="Passwd" title="Passwd">passwd</a> file or <a href="Shadow_password" class="mw-redirect" title="Shadow password">shadow password</a> file. Password hash functions should be relatively expensive to calculate in case of brute-force attacks, and the <a href="Key_stretching" title="Key stretching">key stretching</a> of KDFs happen to provide this characteristic. The non-secret parameters are called "<a href="Salt_(cryptography)" title="Salt (cryptography)">salt</a>" in this context.

</p><p>In 2013 a <a href="Password_Hashing_Competition" title="Password Hashing Competition">Password Hashing Competition</a> was announced to choose a new, standard algorithm for password hashing. On 20 July 2015 the competition ended and <a href="Argon2" title="Argon2">Argon2</a> was announced as the final winner. Four other algorithms received special recognition: Catena, <a href="Lyra2" title="Lyra2">Lyra2</a>, Makwa and <a href="Yescrypt" title="Yescrypt">yescrypt</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

</p><p>As of May 2023, the <a href="OWASP" title="OWASP">Open Worldwide Application Security Project</a> (OWASP) recommends the following KDFs for password hashing, listed in order of priority:<sup id="cite_ref-owasp_15-0" class="reference"><a href="#cite_note-owasp-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>

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<ol><li><a href="Argon2" title="Argon2">Argon2id</a></li>

<li><a href="Scrypt" title="Scrypt">scrypt</a> if Argon2id is unavailable</li>

<li><a href="Bcrypt" title="Bcrypt">bcrypt</a> for legacy systems</li>

<li><a href="PBKDF2" title="PBKDF2">PBKDF2</a> if <a href="FIPS-140" class="mw-redirect" title="FIPS-140">FIPS-140</a> compliance is required</li></ol>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-sp800-63B-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-sp800-63B_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-sp800-63B_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFGrassi_Paul_A.2017" class="citation book cs1">Grassi Paul A. (June 2017). <i>SP 800-63B-3 – Digital Identity Guidelines, Authentication and Lifecycle Management</i>. NIST. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.6028%2FNIST.SP.800-63b">10.6028/NIST.SP.800-63b</a>.</cite></span>

</li>

<li id="cite_note-sp800-132-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-sp800-132_8-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMeltem_Sönmez_TuranElaine_BarkerWilliam_BurrLily_Chen2010" class="citation book cs1">Meltem Sönmez Turan; Elaine Barker; William Burr; Lily Chen (December 2010). <a rel="nofollow" class="external text" href="http://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-132.pdf"><i>SP 800-132 – Recommendation for Password-Based Key Derivation, Part 1: Storage Applications</i></a> <span class="cs1-format">(PDF)</span>. NIST. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.6028%2FNIST.SP.800-132">10.6028/NIST.SP.800-132</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:56801929">56801929</a>.</cite></span>

</li>

<li id="cite_note-info-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-info_9-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFKrawczykEronen2010" class="citation journal cs1">Krawczyk, Hugo; Eronen, Pasi (May 2010). <a rel="nofollow" class="external text" href="https://datatracker.ietf.org/doc/html/rfc5869#section-3.2">"The 'info' Input to HKDF"</a>. <i>datatracker.ietf.org</i>.</cite> RFC 5869 (2010)</span>

</li>

<li id="cite_note-salthash-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-salthash_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-salthash_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://crackstation.net/hashing-security.htm">"Salted Password Hashing – Doing it Right"</a>. <i>CrackStation.net</i><span class="reference-accessdate">. Retrieved <span class="nowrap">29 January</span> 2015</span>.</cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Abadi, Martın, T. Mark A. Lomas, and Roger Needham. "Strengthening passwords." Digital System Research Center, Tech. Rep 33 (1997): 1997.</span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">U. Manber, "A Simple Scheme to Make Passwords Based on One-Way Functions Much Harder to Crack," Computers & Security, v.15, n.2, 1996, pp.171–176.</span>

</li>

<li id="cite_note-low-entropy-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-low-entropy_13-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.schneier.com/paper-low-entropy.html">Secure Applications of Low-Entropy Keys</a>, <a href="John_Kelsey_(cryptanalyst)" title="John Kelsey (cryptanalyst)">J. Kelsey</a>, <a href="Bruce_Schneier" title="Bruce Schneier">B. Schneier</a>, C. Hall, and <a href="David_A._Wagner" title="David A. Wagner">D. Wagner</a> (1997)</span>

</li>

<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://password-hashing.net/">"Password Hashing Competition"</a></span>

</li>

<li id="cite_note-owasp-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-owasp_15-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://cheatsheetseries.owasp.org/cheatsheets/Password_Storage_Cheat_Sheet.html">"Password Storage Cheat Sheet"</a>. <i>OWASP Cheat Sheet Series</i>. <a href="OWASP" title="OWASP">OWASP</a><span class="reference-accessdate">. Retrieved <span class="nowrap">17 May</span> 2023</span>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFPercival2009" class="citation web cs1"><a href="Colin_Percival" title="Colin Percival">Percival, Colin</a> (May 2009). <a rel="nofollow" class="external text" href="http://www.tarsnap.com/scrypt/scrypt.pdf">"Stronger Key Derivation via Sequential Memory-Hard Functions"</a> <span class="cs1-format">(PDF)</span>. <i>BSDCan'09 Presentation</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 May</span> 2009</span>.</cite></li>

<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150228035021/http://di-mgt.com.au/cryptoKDFs.html">Key Derivation Functions</a></li></ul>

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