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| The term '''Needham–Schroeder protocol''' can refer to one of the two [[communications protocol|communication protocols]] intended for use over an insecure network, both proposed by [[Roger Needham]] and [[Michael Schroeder]].<ref name="needham-schroeder">
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| {{Cite journal | last1=Needham | first1=Roger | last2=Schroeder | first2=Michael |
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| title=Using encryption for authentication in large networks of computers. |
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| journal=Communications of the ACM |
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| volume=21 | issue=12 | date=December 1978 | pages=993–999 |
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| doi=10.1145/359657.359659 | postscript=<!--None-->
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| }}
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| </ref> These are:
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| * The ''Needham–Schroeder Symmetric Key Protocol'' is based on a [[Symmetric-key algorithm|symmetric encryption algorithm]]. It forms the basis for the [[Kerberos (protocol)|Kerberos]] protocol. This protocol aims to establish a [[session key]] between two parties on a network, typically to protect further communication.
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| * The ''Needham–Schroeder Public-Key Protocol'', based on [[public-key cryptography]]. This protocol is intended to provide mutual [[authentication]] between two parties communicating on a network, but in its proposed form is insecure.
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| ==The symmetric protocol==
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| Here, [[Alice and Bob|Alice]] (A) initiates the communication to Bob (B). S is a server trusted by both parties. In the communication:
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| * A and B are identities of Alice and Bob respectively
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| * K<sub>AS</sub> is a symmetric key known only to A and S
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| * K<sub>BS</sub> is a symmetric key known only to B and S
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| * N<sub>A</sub> and N<sub>B</sub> are [[cryptographic nonce|nonces]] generated by A and B respectively
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| * K<sub>AB</sub> is a symmetric, generated key, which will be the [[session key]] of the session between A and B
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| The protocol can be specified as follows in [[security protocol notation]]:
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| <math>A \rightarrow S: \left . A,B,N_A \right .</math>
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| :Alice sends a message to the server identifying herself and Bob, telling the server she wants to communicate with Bob.
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| <math>S \rightarrow A: \{N_A, K_{AB}, B, \{K_{AB}, A\}_{K_{BS}}\}_{K_{AS}}</math>
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| :The server generates <math>{K_{AB}}</math> and sends back to Alice a copy encrypted under <math>{K_{BS}}</math> for Alice to forward to Bob and also a copy for Alice. Since Alice may be requesting keys for several different people, the nonce assures Alice that the message is fresh and that the server is replying to that particular message and the inclusion of Bob's name tells Alice who she is to share this key with.
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| <math>A \rightarrow B: \{K_{AB}, A\}_{K_{BS}}</math> | |
| :Alice forwards the key to Bob who can decrypt it with the key he shares with the server, thus authenticating the data.
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| <math>B \rightarrow A: \{N_B\}_{K_{AB}}</math>
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| :Bob sends Alice a nonce encrypted under <math>{K_{AB}}</math> to show that he has the key.
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| <math>A \rightarrow B: \{N_B-1\}_{K_{AB}}</math>
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| :Alice performs a simple operation on the nonce, re-encrypts it and sends it back verifying that she is still alive and that she holds the key.
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| === Attacks on the protocol ===
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| The protocol is vulnerable to a [[replay attack]] (as identified by [[Dorothy E. Denning|Denning]] and Sacco<ref>{{cite journal |last=Denning |first=Dorothy E. | last2=Sacco | first2=Giovanni Maria |authorlink=Dorothy E. Denning |year=1981 |title=Timestamps in key distributed protocols |journal=Communication of the ACM |volume=24 |issue=8 |pages=533–535 |doi=10.1145/358722.358740 }}</ref>). If an attacker uses an older, compromised value for K<sub>AB</sub>, he can then replay the message <math>\{K_{AB}, A\}_{K_{BS}}</math> to Bob, who will accept it, being unable to tell that the key is not fresh.
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| === Fixing the attack ===
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| This flaw is fixed in the [[Kerberos protocol]] by the inclusion of a [[timestamp]]. It can also be fixed with the use of nonces as described below.<ref>{{cite journal |last=Needham |first=R. M. |authorlink=Roger Needham | last2=Schroeder | first2= M. D. | authorlink2=Michael Schroeder |year=1987 |title=Authentication revisited |journal=ACM SIGOPS Operating Systems Review |volume=21 |issue=1 |pages=7 |doi=10.1145/24592.24593 }}</ref> At the beginning of the protocol:
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| :: <math>A \rightarrow B: A</math>
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| :Alice sends to Bob a request.
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| :: <math>B \rightarrow A: \{A,\mathbf{N_B'}\}_{K_{BS}}</math>
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| :Bob responds with a nonce encrypted under his key with the Server.
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| :: <math>A \rightarrow S: \left . A,B,N_A,\{A,\mathbf{N_B'}\}_{K_{BS}} \right .</math>
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| :Alice sends a message to the server identifying herself and Bob, telling the server she wants to communicate with Bob.
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| :: <math>S \rightarrow A: \{N_A, K_{AB}, B, \{K_{AB}, A,\mathbf{N_B'}\}_{K_{BS}}\}_{K_{AS}}</math>
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| :Note the inclusion of the nonce.
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| The protocol then continues as described through the final three steps as described in the original protocol [[#The symmetric protocol|above]]. Note that <math> N_B' </math> is a different nonce from <math> N_B</math>.The inclusion of this new nonce prevents the replaying of a compromised version of <math>\{K_{AB}, A\}_{K_{BS}}</math> since such a message would need to be of the form <math>\{K_{AB}, A,\mathbf{N_B'}\}_{K_{BS}}</math> which the attacker can't forge since she does not have <math>K_{BS}</math>.
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| ==The public-key protocol==
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| This assumes the use of a [[public-key cryptography|public-key encryption algorithm]].
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| Here, Alice (A) and Bob (B) use a trusted server (S) to distribute public keys on request. These keys are:
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| * K<sub>PA</sub> and K<sub>SA</sub>, respectively public and private halves of an encryption key-pair belonging to A (S stands for "secret key" here)
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| * K<sub>PB</sub> and K<sub>SB</sub>, similar belonging to B
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| * K<sub>PS</sub> and K<sub>SS</sub>, similar belonging to S. (Note this has the property that K<sub>SS</sub> is used to ''encrypt'' and K<sub>PS</sub> to ''decrypt'').
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| The protocol runs as follows:
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| <math>A \rightarrow S: \left . A, B \right .</math>
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| :A requests B's public keys from S
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| <math>S \rightarrow A: \{K_{PB}, B\}_{K_{SS}}</math> | |
| :S responds with public key K<sub>PB</sub> alongside B's identity, signed by the server for authentication purposes.
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| <math>B \rightarrow S: \left. B, A \right .</math>
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| : B requests A's public keys.
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| <math>S \rightarrow B: \{K_{PA}, A\}_{K_{SS}}</math>
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| : Server responds.
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| <math>A \rightarrow B: \{N_A, A\}_{K_{PB}}</math>
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| : A invents N<sub>A</sub> and sends it to B.
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| <math>B \rightarrow A: \{N_A, N_B\}_{K_{PA}}</math>
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| :B invents N<sub>B</sub>, and sends it to A along with N<sub>A</sub> to prove ability to decrypt with K<sub>SB</sub>.
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| <math>A \rightarrow B: \{N_B\}_{K_{PB}}</math>
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| :A confirms N<sub>B</sub> to B, to prove ability to decrypt with K<sub>SA</sub>
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| At the end of the protocol, A and B know each other's identities, and know both N<sub>A</sub> and N<sub>B</sub>. These nonces are not known to eavesdroppers.
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| ===An attack on the protocol===
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| Unfortunately, this protocol is vulnerable to a [[man-in-the-middle attack]]. If an impostor can persuade A to initiate a session with him, he can relay the messages to B and convince B that he is communicating with A.
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| Ignoring the traffic to and from S, which is unchanged, the attack runs as follows:
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| <math>A \rightarrow I: \{N_A, A\}_{K_{PI}}</math> | |
| :A sends N<sub>A</sub> to I, who decrypts the message with K<sub>SI</sub>
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| <math>I \rightarrow B: \{N_A, A\}_{K_{PB}}</math>
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| :I relays the message to B, pretending that A is communicating
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| <math>B \rightarrow I: \{N_A, N_B\}_{K_{PA}}</math>
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| :B sends N<sub>B</sub>
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| <math>I \rightarrow A: \{N_A, N_B\}_{K_{PA}}</math>
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| :I relays it to A
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| <math>A \rightarrow I: \{N_B\}_{K_{PI}}</math>
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| :A decrypts N<sub>B</sub> and confirms it to I, who learns it
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| <math>I \rightarrow B: \{N_B\}_{K_{PB}}</math>
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| :I re-encrypts N<sub>B</sub>, and convinces B that he's decrypted it
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| At the end of the attack, B falsely believes that A is communicating with him, and that N<sub>A</sub> and N<sub>B</sub> are known only to A and B.
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| === Fixing the man-in-the-middle attack ===
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| The attack was first described in a 1995 paper by Gavin Lowe.<ref name="lowe">
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| {{Cite journal | last1=Lowe | first1=Gavin |
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| title=An attack on the Needham-Schroeder public key authentication protocol. |
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| journal=Information Processing Letters |
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| volume=56 |
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| issue=3 |
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| pages=131–136 |
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| date=November 1995 |
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| url=http://web.comlab.ox.ac.uk/oucl/work/gavin.lowe/Security/Papers/NSPKP.ps |
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| doi=10.1016/0020-0190(95)00144-2 |
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| accessdate=2008-04-17 | postscript=<!--None-->
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| }}
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| </ref>
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| The paper also describes a fixed version of the scheme, referred to as the '''Needham–Schroeder–Lowe protocol'''. The fix involves the modification of message six, that is we replace:
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| <math>B \rightarrow A: \{N_A, N_B\}_{K_{PA}}</math>
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| with the fixed version:
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| <math>B \rightarrow A: \{N_A, N_B, B\}_{K_{PA}}</math>
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| ==See also==
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| * [[Kerberos (protocol)|Kerberos]]
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| * [[Otway–Rees protocol]]
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| * [[Yahalom (protocol)|Yahalom]]
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| * [[Wide Mouth Frog protocol]]
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| * [[Neuman–Stubblebine protocol]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * http://www.lsv.ens-cachan.fr/spore/nspk.html - description of the Public-key protocol
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| * http://www.lsv.ens-cachan.fr/spore/nssk.html - the Symmetric-key protocol
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| * http://www.lsv.ens-cachan.fr/spore/nspkLowe.html - the public-key protocol amended by Lowe
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| {{DEFAULTSORT:Needham-Schroeder Protocol}}
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| [[Category:Authentication protocols]]
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| [[Category:Key transport protocols]]
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| [[Category:Symmetric-key cryptography]]
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| [[Category:Computer access control protocols]]
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| {{Link GA|ru}}
| |
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