RC4#RC4-based random number generators

RC4 was designed by Ron Rivest of RSA Security in 1987. While it is officially termed "Rivest Cipher 4", the RC acronym is alternatively understood to stand for "Ron's Code"{{cite web| url = http://people.csail.mit.edu/rivest/faq.html#Ron| title = Rivest FAQ}} (see also RC2, RC5 and RC6).

RC4 was initially a trade secret, but in September 1994, a description of it was anonymously posted to the Cypherpunks mailing list.{{cite mailing list|url=http://cypherpunks.venona.com/date/1994/09/msg00304.html |title=Thank you Bob Anderson |date=9 September 1994 |access-date=2007-05-28 |mailing-list=Cypherpunks |url-status=dead |archive-url=https://web.archive.org/web/20010722163902/http://cypherpunks.venona.com/date/1994/09/msg00304.html |archive-date=22 July 2001 }} It was soon posted on the sci.crypt newsgroup, where it was broken within days by Bob Jenkins.{{cite newsgroup

| author = Bob Jenkins

| title = Re: RC4 ?

| date = 1994-09-15

| newsgroup = sci.crypt

| message-id = 359qjg$55v$1@mhadg.production.compuserve.com

| url = https://groups.google.com/d/msg/sci.crypt/JsO3xEATGFA/-wO4ttv7BCYJ

}} From there, it spread to many sites on the Internet. The leaked code was confirmed to be genuine, as its output was found to match that of proprietary software using licensed RC4. Because the algorithm is known, it is no longer a trade secret. The name RC4 is trademarked, so RC4 is often referred to as ARCFOUR or ARC4 (meaning alleged RC4){{cite web|title=Manual Pages: arc4random|url=https://man.openbsd.org/OpenBSD-5.4/arc4random.3|access-date=2 February 2018|date=5 June 2013}} to avoid trademark problems. RSA Security has never officially released the algorithm; Rivest has, however, linked to the English Wikipedia article on RC4 in his own course notes in 2008{{cite web| url = http://courses.csail.mit.edu/6.857/2008/lecture.html| title = 6.857 Computer and Network Security Spring 2008: Lectures and Handouts}} and confirmed the history of RC4 and its code in a 2014 paper by him.

RC4 became part of some commonly used encryption protocols and standards, such as WEP in 1997 and WPA in 2003/2004 for wireless cards; and SSL in 1995 and its successor TLS in 1999, until it was prohibited for all versions of TLS by RFC 7465 in 2015, due to the RC4 attacks weakening or breaking RC4 used in SSL/TLS. The main factors in RC4's success over such a wide range of applications have been its speed and simplicity: efficient implementations in both software and hardware were very easy to develop.

RC4 generates a pseudorandom stream of bits (a keystream). As with any stream cipher, these can be used for encryption by combining it with the plaintext using bitwise exclusive or; decryption is performed the same way (since exclusive or with given data is an involution). This is similar to the one-time pad, except that generated pseudorandom bits, rather than a prepared stream, are used.

To generate the keystream, the cipher makes use of a secret internal state which consists of two parts:

1. A permutation of all 256 possible bytes (denoted "S" below).
2. Two 8-bit index-pointers (denoted "i" and "j").

The permutation is initialized with a variable-length key, typically between 40 and 2048 bits, using the key-scheduling algorithm (KSA). Once this has been completed, the stream of bits is generated using the pseudo-random generation algorithm (PRGA).

The key-scheduling algorithm is used to initialize the permutation in the array "S". "keylength" is defined as the number of bytes in the key and can be in the range 1 ≤ keylength ≤ 256, typically between 5 and 16, corresponding to a key length of 40–128 bits. First, the array "S" is initialized to the identity permutation. S is then processed for 256 iterations in a similar way to the main PRGA, but also mixes in bytes of the key at the same time.

for i from 0 to 255

S[i] := i

endfor

j := 0

for i from 0 to 255

j := (j + S[i] + key[i mod keylength]) mod 256

swap values of S[i] and S[j]

endfor

Image:RC4.svg

For as many iterations as are needed, the PRGA modifies the state and outputs a byte of the keystream. In each iteration, the PRGA:

• increments {{mono|i}};
• looks up the {{mono|i}}th element of {{mono|S}}, {{mono|S[i]}}, and adds that to {{mono|j}};
• exchanges the values of {{mono|S[i]}} and {{mono|S[j]}}, then uses the sum {{mono|S[i] + S[j] (modulo 256)}} as an index to fetch a third element of {{mono|S}} (the keystream value {{mono|K}} below);
• then bitwise exclusive ORed (XORed) with the next byte of the message to produce the next byte of either ciphertext or plaintext.

Each element of S is swapped with another element at least once every 256 iterations.

i := 0

j := 0

while GeneratingOutput:

i := (i + 1) mod 256

j := (j + S[i]) mod 256

swap values of S[i] and S[j]

t := (S[i] + S[j]) mod 256

K := S[t]

output K

endwhile

Thus, this produces a stream of {{mono|K[0], K[1], ...}} which are XORed with the {{mono|plaintext}} to obtain the {{mono|ciphertext}}. So {{mono|ciphertext[l] {{=}} plaintext[l] ⊕ K[l]}}.

Several operating systems include {{code|arc4random}}, an API originating in OpenBSD providing access to a random number generator originally based on RC4. The API allows no seeding, as the function initializes itself using /dev/random. The use of RC4 has been phased out in most systems implementing this API. Man pages for the new arc4random include the backronym "A Replacement Call for Random" for ARC4 as a mnemonic, as it provides better random data than rand() does.{{cite web |url=http://man.openbsd.org/arc4random.3 |title=arc4random(3) |publisher=OpenBSD}}

• In OpenBSD 5.5, released in May 2014, {{code|arc4random}} was modified to use ChaCha20.{{cite web |title=OpenBSD 5.5 |url=http://www.openbsd.org/55.html |access-date=21 September 2014}}{{cite web |url=http://bxr.su/OpenBSD/lib/libc/crypt/arc4random.c |title=libc/crypt/arc4random.c |website=BSD Cross Reference, OpenBSD src/lib/ |editor=deraadt |editor-link=Theo de Raadt |date=21 July 2014 |access-date=2015-01-13 |quote=ChaCha based random number generator for OpenBSD.}} The implementations of arc4random in FreeBSD, NetBSD{{cite web |url=http://bxr.su/NetBSD/lib/libc/gen/arc4random.c |title=libc/gen/arc4random.c |website=BSD Cross Reference, NetBSD src/lib/ |editor=riastradh |date=16 November 2014 |access-date=2015-01-13 |quote=Legacy arc4random(3) API from OpenBSD reimplemented using the ChaCha20 PRF, with per-thread state.}}{{cite web |title=arc4random – NetBSD Manual Pages |url=http://netbsd.gw.com/cgi-bin/man-cgi?arc4random++NetBSD-current |access-date=6 January 2015 |archive-date=6 July 2020 |archive-url=https://web.archive.org/web/20200706210612/https://netbsd.gw.com/cgi-bin/man-cgi?arc4random++NetBSD-current |url-status=dead}} also use ChaCha20.
• Linux typically uses glibc, which did not offer arc4random until 2022. Instead, a separate library, libbsd, offers the function; it was updated to use ChaCha20 in 2016.{{cite web |title=Update arc4random module from OpenBSD and LibreSSL |url=https://cgit.freedesktop.org/libbsd/commit/?id=874a0e5 |access-date=6 January 2016}} In 2022, glibc added its own version of arc4random, also based on ChaCha20.{{cite web |title=GNU C Library Finally Adds arc4random Functions For Linux |url=https://www.phoronix.com/news/GNU-Glibc-arc4random-Functions |website=www.phoronix.com |language=en}}
• According to manual pages shipped with the operating system, in the 2017 release of macOS and iOS operating systems, Apple replaced RC4 with AES in its implementation of arc4random.

Proposed new random number generators are often compared to the RC4 random number generator.

Bartosz Zoltak.

[//eprint.iacr.org/2013/768.pdf "VMPC-R: Cryptographically Secure Pseudo-Random Number Generator, Alternative to RC4"].

2010?

Chefranov, A. G.

[https://ieeexplore.ieee.org/document/4022919/ "Pseudo-Random Number Generator RC4 Period Improvement"].

2006.

Several attacks on RC4 are able to distinguish its output from a random sequence.

Many stream ciphers are based on linear-feedback shift registers (LFSRs), which, while efficient in hardware, are less so in software. The design of RC4 avoids the use of LFSRs and is ideal for software implementation, as it requires only byte manipulations. It uses 256 bytes of memory for the state array, S[0] through S[255], k bytes of memory for the key, key[0] through key[k−1], and integer variables, i, j, and K. Performing a modular reduction of some value modulo 256 can be done with a bitwise AND with 255 (which is equivalent to taking the low-order byte of the value in question).

These test vectors are not official, but convenient for anyone testing their own RC4 program. The keys and plaintext are ASCII, the keystream and ciphertext are in hexadecimal.

Unlike a modern stream cipher (such as those in eSTREAM), RC4 does not take a separate nonce alongside the key. This means that if a single long-term key is to be used to securely encrypt multiple streams, the protocol must specify how to combine the nonce and the long-term key to generate the stream key for RC4. One approach to addressing this is to generate a "fresh" RC4 key by hashing a long-term key with a nonce. However, many applications that use RC4 simply concatenate key and nonce; RC4's weak key schedule then gives rise to related-key attacks, like the Fluhrer, Mantin and Shamir attack (which is famous for breaking the WEP standard).{{cite web |date=1 September 2001 |title=RSA Security Response to Weaknesses in Key Scheduling Algorithm of RC4 |publisher=RSA Laboratories |url=http://www.emc.com/emc-plus/rsa-labs/historical/rsa-security-response-weaknesses-algorithm-rc4.htm }}

Because RC4 is a stream cipher, it is more malleable than common block ciphers. If not used together with a strong message authentication code (MAC), then encryption is vulnerable to a bit-flipping attack. The cipher is also vulnerable to a stream cipher attack if not implemented correctly.{{cite book |url=https://books.google.com/books?id=dQE6LGep6wEC |pages=92–93 |title=Hidden Keys to Software Break-Ins and Unauthorized Entry |first=Dmitry |last=Sklyarov |publisher=A-List Publishing |year=2004 |isbn=978-1931769303}}

It is noteworthy, however, that RC4, being a stream cipher, was for a period of time the only common cipher that was immune[http://serverfault.com/questions/315042/ "ssl - Safest ciphers to use with the BEAST? (TLS 1.0 exploit) I've read that RC4 is immune"]. serverfault.com. to the 2011 BEAST attack on TLS 1.0. The attack exploits a known weakness in the way cipher-block chaining mode is used with all of the other ciphers supported by TLS 1.0, which are all block ciphers.

In March 2013, there were new attack scenarios proposed by Isobe, Ohigashi, Watanabe and Morii,{{cite web |url=http://home.hiroshima-u.ac.jp/ohigashi/rc4/ |title=Security of RC4 Stream Cipher |last1=Isobe |first1=Takanori |last2=Ohigashi |first2=Toshihiro |date=10–13 Mar 2013 |publisher=Hiroshima University |access-date=2014-10-27 }} as well as AlFardan, Bernstein, Paterson, Poettering and Schuldt that use new statistical biases in RC4 key table{{cite book |author1=Pouyan Sepehrdad |author2=Serge Vaudenay |author3=Martin Vuagnoux |title=Selected Areas in Cryptography |chapter=Discovery and Exploitation of New Biases in RC4 |series=Lecture Notes in Computer Science | year=2011 | volume=6544 | pages=74–91 | doi=10.1007/978-3-642-19574-7_5|isbn = 978-3-642-19573-0}} to recover plaintext with large number of TLS encryptions.{{cite web | url=http://blog.cryptographyengineering.com/2013/03/attack-of-week-rc4-is-kind-of-broken-in.html | title=Attack of the week: RC4 is kind of broken in TLS | work=Cryptography Engineering | access-date=12 March 2013 | author=Green, Matthew | date=2013-03-12 }}{{cite web | title=On the Security of RC4 in TLS | url=http://www.isg.rhul.ac.uk/tls/ | publisher=Royal Holloway University of London | access-date=13 March 2013 |author1=Nadhem AlFardan |author2=Dan Bernstein |author3=Kenny Paterson |author4=Bertram Poettering |author5=Jacob Schuldt }}

The use of RC4 in TLS is prohibited by RFC 7465 published in February 2015.

In 1995, Andrew Roos experimentally observed that the first byte of the keystream is correlated with the first three bytes of the key, and the first few bytes of the permutation after the KSA are correlated with some linear combination of the key bytes.Andrew Roos. A Class of Weak Keys in the RC4 Stream Cipher. Two posts in sci.crypt, message-id 43u1eh$1j3@hermes.is.co.za and 44ebge$llf@hermes.is.co.za, 1995. These biases remained unexplained until 2007, when Goutam Paul, Siddheshwar Rathi and Subhamoy MaitraGoutam Paul, Siddheshwar Rathi and Subhamoy Maitra. On Non-negligible Bias of the First Output Byte of RC4 towards the First Three Bytes of the Secret Key. Proceedings of the International Workshop on Coding and Cryptography (WCC) 2007, pages 285–294 and Designs, Codes and Cryptography Journal, pages 123–134, vol. 49, no. 1-3, December 2008. proved the keystream–key correlation and, in another work, Goutam Paul and Subhamoy MaitraGoutam Paul and Subhamoy Maitra. Permutation after RC4 Key Scheduling Reveals the Secret Key. SAC 2007, pages 360–377, vol. 4876, Lecture Notes in Computer Science, Springer. proved the permutation–key correlations. The latter work also used the permutation–key correlations to design the first algorithm for complete key reconstruction from the final permutation after the KSA, without any assumption on the key or initialization vector. This algorithm has a constant probability of success in a time, which is the square root of the exhaustive key search complexity. Subsequently, many other works have been performed on key reconstruction from RC4 internal states.Eli Biham and Yaniv Carmeli. Efficient Reconstruction of RC4 Keys from Internal States. FSE 2008, pages 270–288, vol. 5086, Lecture Notes in Computer Science, Springer.Mete Akgun, Pinar Kavak, Huseyin Demirci. New Results on the Key Scheduling Algorithm of RC4. INDOCRYPT 2008, pages 40–52, vol. 5365, Lecture Notes in Computer Science, Springer.Riddhipratim Basu, Subhamoy Maitra, Goutam Paul and Tanmoy Talukdar. On Some Sequences of the Secret Pseudo-random Index j in RC4 Key Scheduling. Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error Correcting Codes (AAECC), 8–12 June 2009, Tarragona, Spain, pages 137–148, vol. 5527, Lecture Notes in Computer Science, Springer. Subhamoy Maitra and Goutam PaulSubhamoy Maitra and Goutam Paul. New Form of Permutation Bias and Secret Key Leakage in Keystream Bytes of RC4. Proceedings of the 15th Fast Software Encryption (FSE) Workshop, 10–13 February 2008, Lausanne, Switzerland, pages 253–269, vol. 5086, Lecture Notes in Computer Science, Springer. also showed that the Roos-type biases still persist even when one considers nested permutation indices, like {{mono|S[S[i]]}} or {{mono|S[S[S[i]]]}}. These types of biases are used in some of the later key reconstruction methods for increasing the success probability.

The keystream generated by the RC4 is biased to varying degrees towards certain sequences, making it vulnerable to distinguishing attacks. The best such attack is due to Itsik Mantin and Adi Shamir, who showed that the second output byte of the cipher was biased toward zero with probability 1/128 (instead of 1/256). This is due to the fact that if the third byte of the original state is zero, and the second byte is not equal to 2, then the second output byte is always zero. Such bias can be detected by observing only 256 bytes.{{cite conference |author1=Itsik Mantin |author2=Adi Shamir |date=2001 |title=A Practical Attack on Broadcast RC4 |conference=FSE 2001 |pages=152–164 |url=https://link.springer.com/content/pdf/10.1007%2F3-540-45473-X_13.pdf |doi=10.1007/3-540-45473-X_13}}

Souradyuti Paul and Bart Preneel of COSIC showed that the first and the second bytes of the RC4 were also biased. The number of required samples to detect this bias is 2²⁵ bytes.{{cite conference |author1=Souradyuti Paul |author2=Bart Preneel |title=Analysis of Non-fortuitous Predictive States of the RC4 Keystream Generator |conference=Indocrypt 2003 |pages=52–67 |url=http://www.cosic.esat.kuleuven.be/publications/article-86.pdf }}

Scott Fluhrer and David McGrew also showed attacks that distinguished the keystream of the RC4 from a random stream given a gigabyte of output.{{cite conference |author1=Scott R. Fluhrer |author2=David A. McGrew |title=Statistical Analysis of the Alleged RC4 Keystream Generator |conference=FSE 2000 |pages=19–30 |url=http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/FluhrerMcgrew.pdf |url-status=dead |archive-url=https://web.archive.org/web/20140502020708/http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/FluhrerMcgrew.pdf |archive-date=2 May 2014 |df=dmy-all }}

The complete characterization of a single step of RC4 PRGA was performed by Riddhipratim Basu, Shirshendu Ganguly, Subhamoy Maitra, and Goutam Paul.{{cite journal |first1=Riddhipratim |last1=Basu |first2=Shirshendu |last2=Ganguly |first3=Subhamoy |last3=Maitra |first4=Goutam |last4=Paul |title=A Complete Characterization of the Evolution of RC4 Pseudo Random Generation Algorithm |journal=Journal of Mathematical Cryptology |pages=257–289 |volume=2 |issue=3 |year=2008 |doi=10.1515/JMC.2008.012 |s2cid=9613837 |doi-access=free }} Considering all the permutations, they proved that the distribution of the output is not uniform given i and j, and as a consequence, information about j is always leaked into the output.

{{Main article|Fluhrer, Mantin and Shamir attack}}

In 2001, a new and surprising discovery was made by Fluhrer, Mantin and Shamir: over all the possible RC4 keys, the statistics for the first few bytes of output keystream are strongly non-random, leaking information about the key. If the nonce and long-term key are simply concatenated to generate the RC4 key, this long-term key can be discovered by analysing a large number of messages encrypted with this key.{{cite journal |first1=Scott R. |last1=Fluhrer |first2=Itsik |last2=Mantin |first3=Adi |last3=Shamir |title=Weaknesses in the Key Scheduling Algorithm of RC4 |journal=Selected Areas in Cryptography |year=2001 |pages=1–24 |url=http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/Rc4_ksa.ps |archive-url=https://web.archive.org/web/20040602051734/http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/Rc4_ksa.ps |archive-date=2 June 2004}} This and related effects were then used to break the WEP ("wired equivalent privacy") encryption used with 802.11 wireless networks. This caused a scramble for a standards-based replacement for WEP in the 802.11 market and led to the IEEE 802.11i effort and WPA.{{cite web |url=http://findarticles.com/p/articles/mi_m0DIS/is_2003_Jan/ai_n27590035/ |archive-url=https://archive.today/20120709120158/http://findarticles.com/p/articles/mi_m0DIS/is_2003_Jan/ai_n27590035/ |url-status=dead |archive-date=2012-07-09 |title=Interim technology for wireless LAN security: WPA to replace WEP while industry develops new security standard}}

Protocols can defend against this attack by discarding the initial portion of the keystream. Such a modified algorithm is traditionally called "RC4-drop[{{mvar|n}}]", where {{mvar|n}} is the number of initial keystream bytes that are dropped. The SCAN default is {{mvar|n}} = 768 bytes, but a conservative value would be {{mvar|n}} = 3072 bytes.{{cite web |url=http://www.users.zetnet.co.uk/hopwood/crypto/scan/cs.html#RC4-drop |title=RC4-drop(nbytes) in the Standard Cryptographic Algorithm Naming database}}

The Fluhrer, Mantin and Shamir attack does not apply to RC4-based SSL, since SSL generates the encryption keys it uses for RC4 by hashing, meaning that different SSL sessions have unrelated keys.{{cite web |first=Ron |last=Rivest |url=https://www.rsa.com/rsalabs/node.asp?id=2009 |title=RSA Security Response to Weaknesses in Key Scheduling Algorithm of RC4}}

In 2005, Andreas Klein presented an analysis of the RC4 stream cipher, showing more correlations between the RC4 keystream and the key.A. Klein, Attacks on the RC4 stream cipher, Designs, Codes and Cryptography (2008) 48:269–286. Erik Tews, Ralf-Philipp Weinmann, and Andrei Pychkine used this analysis to create aircrack-ptw, a tool that cracks 104-bit RC4 used in 128-bit WEP in under a minute.Erik Tews, Ralf-Philipp Weinmann, Andrei Pyshkin. [//eprint.iacr.org/2007/120 Breaking 104-bit WEP in under a minute]. Whereas the Fluhrer, Mantin, and Shamir attack used around 10 million messages, aircrack-ptw can break 104-bit keys in 40,000 frames with 50% probability, or in 85,000 frames with 95% probability.

A combinatorial problem related to the number of inputs and outputs of the RC4 cipher was first posed by Itsik Mantin and Adi Shamir in 2001, whereby, of the total 256 elements in the typical state of RC4, if x number of elements (x ≤ 256) are only known (all other elements can be assumed empty), then the maximum number of elements that can be produced deterministically is also {{mvar|x}} in the next 256 rounds. This conjecture was put to rest in 2004 with a formal proof given by Souradyuti Paul and Bart Preneel.Souradyuti Paul and Bart Preneel, [http://www.cosic.esat.kuleuven.be/publications/article-40.pdf A New Weakness in the RC4 Keystream Generator and an Approach to Improve the Security of the Cipher]. Fast Software Encryption – FSE 2004, pp. 245–259.

In 2013, a group of security researchers at the Information Security Group at Royal Holloway, University of London reported an attack that can become effective using only 2³⁴ encrypted messages.{{cite news |url=https://www.theregister.co.uk/2013/03/15/tls_broken/ |title=HTTPS cookie crypto CRUMBLES AGAIN in hands of stats boffins |author=John Leyden |website=The Register |date=15 March 2013}}{{cite web |url=http://www.isg.rhul.ac.uk/tls/RC4biases.pdf |title=On the Security of RC4 in TLS and WPA |last=AlFardan |publisher=Information Security Group, Royal Holloway, University of London |date=8 July 2013 |display-authors=etal |access-date=6 September 2013 |archive-date=22 September 2013 |archive-url=https://web.archive.org/web/20130922170155/http://www.isg.rhul.ac.uk/tls/RC4biases.pdf |url-status=dead }}{{cite web |title=On the Security of RC4 in TLS and WPA |url=http://www.isg.rhul.ac.uk/tls/ |publisher=Information Security Group, Royal Holloway, University of London |access-date=2013-09-06}} While yet not a practical attack for most purposes, this result is sufficiently close to one that it has led to speculation that it is plausible that some state cryptologic agencies may already have better attacks that render RC4 insecure.{{cite web |url=https://www.theregister.co.uk/2013/09/06/nsa_cryptobreaking_bullrun_analysis/ |title=That earth-shattering NSA crypto-cracking: Have spooks smashed RC4? |author=John Leyden |date=6 September 2013 |website=The Register}} Given that, {{asof|2013|lc=yes}}, a large amount of TLS traffic uses RC4 to avoid attacks on block ciphers that use cipher block chaining, if these hypothetical better attacks exist, then this would make the TLS-with-RC4 combination insecure against such attackers in a large number of practical scenarios.

In March 2015, researcher to Royal Holloway announced improvements to their attack, providing a 2²⁶ attack against passwords encrypted with RC4, as used in TLS.{{Cite web |title=RC4 must die |url=http://www.isg.rhul.ac.uk/tls/RC4mustdie.html}}

{{main article|Bar mitzvah attack}}

At the Black Hat Asia 2015 Conference, Itsik Mantin presented another attack against SSL using RC4 cipher.{{Cite web| url=https://www.blackhat.com/asia-15/briefings.html#bar-mitzva-attack-breaking-ssl-with-13-year-old-rc4-weakness| title=Briefings – March 26 & 27| access-date=November 19, 2016| date=2015}}{{Cite web| title=Attacking SSL when using RC4| date=2015| url=https://www.imperva.com/docs/HII_Attacking_SSL_when_using_RC4.pdf| access-date=November 19, 2016}}

In 2015, security researchers from KU Leuven presented new attacks against RC4 in both TLS and WPA-TKIP.{{cite web |url=https://www.rc4nomore.com/ |title=RC4 NOMORE: Numerous Occurrence MOnitoring & Recovery Exploit |author1=Mathy Vanhoef |author2=Frank Piessens |date=9 August 2015}} Dubbed the Numerous Occurrence MOnitoring & Recovery Exploit (NOMORE) attack, it is the first attack of its kind that was demonstrated in practice. Their attack against TLS can decrypt a secure HTTP cookie within 75 hours. The attack against WPA-TKIP can be completed within an hour and allows an attacker to decrypt and inject arbitrary packets.

As mentioned above, the most important weakness of RC4 comes from the insufficient key schedule; the first bytes of output reveal information about the key. This can be corrected by simply discarding some initial portion of the output stream.{{Citation |chapter-url=http://eprint.iacr.org/2002/067 |chapter=(Not So) Random Shuffles of RC4 |author=Ilya Mironov |date=1 June 2002 |title=Advances in Cryptology – CRYPTO 2002 |pages=304–319 |series=Lecture Notes in Computer Science |volume=2442 |publisher=Springer-Verlag |isbn=978-3-540-44050-5 |doi=10.1007/3-540-45708-9_20 |id=Cryptology ePrint Archive: Report 2002/067 |access-date=2011-11-04|url=http://www.iacr.org/archive/crypto2002/24420305/24420305.pdf |doi-access=free }} This is known as RC4-dropN, where N is typically a multiple of 256, such as 768 or 1024.

A number of attempts have been made to strengthen RC4, notably Spritz, RC4A, VMPC, and RC4⁺.

Souradyuti Paul and Bart Preneel have proposed an RC4 variant, which they call RC4A.{{Citation |chapter=A New Weakness in the RC4 Keystream Generator and an Approach to Improve the Security of the Cipher |author1=Souradyuti Paul |author-link1=Souradyuti Paul |author2=Bart Preneel |author-link2=Bart Preneel |chapter-url=http://homes.esat.kuleuven.be/~psourady/publication-info/PP04-bias_rc4.htm |year=2004 |title=Fast Software Encryption, FSE 2004 |series=Lecture Notes in Computer Science |volume=3017 |publisher=Springer-Verlag |isbn=978-3-540-22171-5 |pages=245–259 |doi=10.1007/978-3-540-25937-4_16 |access-date=2011-11-04|doi-access=free }}

RC4A uses two state arrays {{mono|S1}} and {{mono|S2}}, and two indexes {{mono|j1}} and {{mono|j2}}. Each time {{mono|i}} is incremented, two bytes are generated:

1. First, the basic RC4 algorithm is performed using {{mono|S1}} and {{mono|j1}}, but in the last step, {{mono|S1[i]+S1[j1]}} is looked up in {{mono|S2}}.
2. Second, the operation is repeated (without incrementing {{mono|i}} again) on {{mono|S2}} and {{mono|j2}}, and {{mono|S1[S2[i]+S2[j2]]}} is output.

Thus, the algorithm is:

All arithmetic is performed modulo 256

i := 0

j1 := 0

j2 := 0

while GeneratingOutput:

i := i + 1

j1 := j1 + S1[i]

swap values of S1[i] and S1[j1]

output S2[S1[i] + S1[j1]]

j2 := j2 + S2[i]

swap values of S2[i] and S2[j2]

output S1[S2[i] + S2[j2]]

endwhile

Although the algorithm required the same number of operations per output byte, there is greater parallelism than RC4, providing a possible speed improvement.

Although stronger than RC4, this algorithm has also been attacked, with Alexander Maximov{{Citation |title=Two Linear Distinguishing Attacks on VMPC and RC4A and Weakness of RC4 Family of Stream Ciphers |author=Alexander Maximov |url=http://eprint.iacr.org/2007/070 |date=22 February 2007 |id=Cryptology ePrint Archive: Report 2007/070 |access-date=2011-11-04}} and a team from NEC{{Citation |title=The Most Efficient Distinguishing Attack on VMPC and RC4A |url=http://www.ecrypt.eu.org/stream/papersdir/037.pdf |year=2005 |author1=Yukiyasu Tsunoo |author2=Teruo Saito |author3=Hiroyasu Kubo |author4=Maki Shigeri |author5=Tomoyasu Suzaki |author6=Takeshi Kawabata}} developing ways to distinguish its output from a truly random sequence.

{{Main article|Variably Modified Permutation Composition}}

Variably Modified Permutation Composition (VMPC) is another RC4 variant.{{Citation |chapter=VMPC One-Way Function and Stream Cipher |chapter-url=http://www.vmpcfunction.com/vmpc.pdf |author=Bartosz Zoltak |year=2004 |title=Fast Software Encryption, FSE 2004 |series=Lecture Notes in Computer Science |volume=3017 |publisher=Springer-Verlag |doi=10.1007/978-3-540-25937-4_14 |isbn=978-3-540-22171-5 |pages=210–225 |access-date=2011-11-04|url=https://www.iacr.org/archive/fse2004/30170209/30170209.pdf |citeseerx=10.1.1.469.8297 }} It uses similar key schedule as RC4, with

{{mono|1=j := S[(j + S[i] + key[i mod keylength]) mod 256]}} iterating 3 × 256 = 768 times rather than 256, and with an optional additional 768 iterations to incorporate an initial vector. The output generation function operates as follows:

All arithmetic is performed modulo 256.

i := 0

while GeneratingOutput:

j := S[j + S[i]]

output S[S[S[j]] + 1]

Swap S[i] and S[j] (b := S[j]; S[j] := S[i]; S[i] := b))

i := i + 1

endwhile

This was attacked in the same papers as RC4A, and can be distinguished within 2³⁸ output bytes.{{Cite web |url=http://www.cryptolounge.org/wiki/RC4A |title=CryptoLounge: RC4A |access-date=4 November 2011 |archive-url=https://web.archive.org/web/20111001012601/http://www.cryptolounge.org/wiki/RC4A |archive-date=1 October 2011 |url-status=dead |df=dmy-all }}

RC4⁺ is a modified version of RC4 with a more complex three-phase key schedule (taking about three times as long as RC4, or the same as RC4-drop512), and a more complex output function which performs four additional lookups in the S array for each byte output, taking approximately 1.7 times as long as basic RC4.{{Citation |chapter=Analysis of RC4 and Proposal of Additional Layers for Better Security Margin |chapter-url=http://eprint.iacr.org/2008/396 |author1=Subhamoy Maitra |author2=Goutam Paul |title=Progress in Cryptology - INDOCRYPT 2008 |date=19 September 2008 |pages=27–39 |series=Lecture Notes in Computer Science |volume=5365 |publisher=Springer-Verlag |isbn=978-3-540-89753-8 |doi=10.1007/978-3-540-89754-5_3 |id=Cryptology ePrint Archive: Report 2008/396 |access-date=2011-11-04|url=http://eprint.iacr.org/2008/396.pdf |citeseerx=10.1.1.215.7178 }}

All arithmetic modulo 256. << and >> are left and right shift, ⊕ is exclusive OR

while GeneratingOutput:

i := i + 1

a := S[i]

j := j + a

Swap S[i] and S[j] (b := S[j]; S[j] := S[i]; S[i] := b;)

c := S[i<<5 ⊕ j>>3] + S[j<<5 ⊕ i>>3]

output (S[a+b] + S[c⊕0xAA]) ⊕ S[j+b]

endwhile

This algorithm has not been analyzed significantly.

In 2014, Ronald Rivest gave a talk and co-wrote a paper{{cite news |last1=Rivest |first1=Ron |last2=Schuldt |first2=Jacob |date=27 October 2014 |title=Spritz – a spongy RC4-like stream cipher and hash function |url=http://people.csail.mit.edu/rivest/pubs/RS14.pdf |access-date=26 October 2014}} on an updated redesign called Spritz. A hardware accelerator of Spritz was published in Secrypt, 2016{{cite web | title=Hardware Accelerator for Stream Cipher Spritz | url=https://blogs.ntu.edu.sg/debjyoti001/files/2016/07/paper-1rf0pxd.pdf | publisher=Secrypt 2016 | access-date=29 July 2016 |author1=Debjyoti Bhattacharjee |author2=Anupam Chattopadhyay}} and shows that due to multiple nested calls required to produce output bytes, Spritz performs rather slowly compared to other hash functions such as SHA-3 and the best known hardware implementation of RC4.

Like other sponge functions, Spritz can be used to build a cryptographic hash function, a deterministic random bit generator (DRBG), an encryption algorithm that supports authenticated encryption with associated data (AEAD), etc.

In 2016, Banik and Isobe proposed an attack that can distinguish Spritz from random noise.{{Cite book|last1=Banik|first1=Subhadeep|last2=Isobe|first2=Takanori|title=Fast Software Encryption |chapter=Cryptanalysis of the Full Spritz Stream Cipher |date=2016-03-20|publisher=Springer Berlin Heidelberg|isbn=9783662529928|editor-last=Peyrin|editor-first=Thomas|series=Lecture Notes in Computer Science|volume=9783 |pages=63–77|language=en|doi=10.1007/978-3-662-52993-5_4|s2cid=16296315}} In 2017, Banik, Isobe, and Morii proprosed a simple fix that removes the distinguisher in the first two keystream bytes, requiring only one additional memory access without diminishing software performance substantially.{{Cite journal|last1=Banik|first1=Subhadeep|last2=Isobe|first2=Takanori|last3=Morii|first3=Masakatu|date=2017-06-01|title=Analysis and Improvements of the Full Spritz Stream Cipher|url=https://www.jstage.jst.go.jp/article/transfun/E100.A/6/E100.A_1296/_article|journal=IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences|volume=E100.A|issue=6|pages=1296–1305|doi=10.1587/transfun.E100.A.1296|bibcode=2017IEITF.100.1296B |hdl=10356/81487|hdl-access=free}}

• WEP
• TKIP (default algorithm for WPA, but can be configured to use AES-CCMP instead of RC4)
• BitTorrent protocol encryption
• Microsoft Office XP (insecure implementation since nonce remains unchanged when documents get modifiedHongjun Wu, "The Misuse of RC4 in Microsoft Word and Excel". https://eprint.iacr.org/2005/007)
• Microsoft Point-to-Point Encryption
• Transport Layer Security / Secure Sockets Layer (was optional and then the use of RC4 was prohibited in RFC 7465)
• Secure Shell (optionally)
• Remote Desktop Protocol (optionally)
• Kerberos (optionally)
• SASL Mechanism Digest-MD5 (optionally, historic, obsoleted in RFC 6331)
• Gpcode.AK, an early June 2008 computer virus for Microsoft Windows, which takes documents hostage for ransom by obscuring them with RC4 and RSA-1024 encryption
• PDF
• Skype (in modified form){{cite web

| url=http://www.h-online.com/security/news/item/Skype-s-encryption-procedure-partly-exposed-1034577.html

| archive-url=https://web.archive.org/web/20100711062958/http://www.h-online.com/security/news/item/Skype-s-encryption-procedure-partly-exposed-1034577.html

| archive-date=11 July 2010

| title=Skype's encryption procedure partly exposed

| publisher=www.h-online.com

| access-date=2010-07-08}}

Where a protocol is marked with "(optionally)", RC4 is one of multiple ciphers the system can be configured to use.

• TEA, Block TEA also known as eXtended TEA and Corrected Block TEA – A family of block ciphers that, like RC4, are designed to be very simple to implement.
• Advanced Encryption Standard
• CipherSaber

{{reflist|30em}}

• {{cite book |title=RC4 Stream Cipher and Its Variants |last1=Paul |first1=Goutam |author2=Subhamoy Maitra |year= 2011 |publisher=CRC Press |isbn=9781439831359 |url=http://www.crcpress.com/product/isbn/9781439831359 }}
• {{cite book

|title=Applied Cryptography: Protocols, Algorithms, and Source Code in C

|last1=Schneier |first1=Bruce |author-link1=Bruce Schneier

|year=1995

|publisher=Wiley

|isbn=978-0471117094

|chapter-url=https://www.schneier.com/book-applied.html

|chapter=Chapter 17 – Other Stream Ciphers and Real Random-Sequence Generators

|edition=2nd

}}

• [http://cypherpunks.venona.com/archive/1994/09/msg00304.html Original posting of RC4 algorithm to Cypherpunks mailing list], [https://web.archive.org/web/20080207125928/http://cypherpunks.venona.com/archive/1994/09/msg00304.html Archived version]
• {{IETF RFC|4345|link=no}} – Improved Arcfour Modes for the Secure Shell (SSH) Transport Layer Protocol
• {{IETF RFC|6229|link=no}} – Test Vectors for the Stream Cipher RC4
• {{IETF RFC|7465|link=no}} – Prohibiting RC4 Cipher Suites
• {{cite IETF|draft=draft-kaukonen-cipher-arcfour-03|title=A Stream Cipher Encryption Algorithm "Arcfour"|last1=Kaukonen|last2=Thayer}}
• [http://www.users.zetnet.co.uk/hopwood/crypto/scan/cs.html#RC4 Entry for RC4 on SCAN (Standard Cryptographic Algorithm Naming)]
• {{webarchive|url=https://web.archive.org/web/20150221230645/http://www.wisdom.weizmann.ac.il/~itsik/RC4/rc4.html|title=Attacks on RC4|date=21 February 2015}}
• {{webarchive|url=https://web.archive.org/web/20161118145850/http://www.emc.com/emc-plus/rsa-labs/historical/rsa-security-response-weaknesses-algorithm-rc4.htm|title=RSA Security Response to Weaknesses in Key Scheduling Algorithm of RC4|date=18 November 2016}}

;RC4 in WEP

• {{webarchive|url=https://web.archive.org/web/20200119101604/http://www.isaac.cs.berkeley.edu/isaac/wep-faq.html|title=Security of the WEP algorithm|date=19 January 2020}}
• {{cite journal|url=http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/rc4_wep.ps|last1=Fluhrer|last2=Mantin|last3=Shamir|title=Attacks On RC4 and WEP|format=PostScript|journal=CryptoBytes|volume=5|number=2|date=Summer–Fall 2002|archive-url=https://web.archive.org/web/20150102135713/http://www.wisdom.weizmann.ac.il/~itsik/RC4/Papers/rc4_wep.ps|archive-date=2 January 2015}}

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