# Needham–Schroeder protocol

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The term Needham–Schroeder protocol can refer to one of the two key transport protocols intended for use over an insecure network, both proposed by Roger Needham and Michael Schroeder.[1] These are:

• The Needham–Schroeder Symmetric Key Protocol is based on a symmetric encryption algorithm. It forms the basis for the Kerberos protocol. This protocol aims to establish a session key between two parties on a network, typically to protect further communication.
• 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.

## The symmetric protocol

Here, Alice (A) initiates the communication to Bob (B). S is a server trusted by both parties. In the communication:

• A and B are identities of Alice and Bob respectively
• KAS is a symmetric key known only to A and S
• KBS is a symmetric key known only to B and S
• NA and NB are nonces generated by A and B respectively
• KAB is a symmetric, generated key, which will be the session key of the session between A and B

The protocol can be specified as follows in security protocol notation:

${\displaystyle A\rightarrow S:\left.A,B,N_{A}\right.}$

Alice sends a message to the server identifying herself and Bob, telling the server she wants to communicate with Bob.

${\displaystyle S\rightarrow A:\{N_{A},K_{AB},B,\{K_{AB},A\}_{K_{BS}}\}_{K_{AS}}}$

The server generates ${\displaystyle {K_{AB}}}$ and sends back to Alice a copy encrypted under ${\displaystyle {K_{BS}}}$ 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.

${\displaystyle A\rightarrow B:\{K_{AB},A\}_{K_{BS}}}$

Alice forwards the key to Bob who can decrypt it with the key he shares with the server, thus authenticating the data.

${\displaystyle B\rightarrow A:\{N_{B}\}_{K_{AB}}}$

Bob sends Alice a nonce encrypted under ${\displaystyle {K_{AB}}}$ to show that he has the key.

${\displaystyle A\rightarrow B:\{N_{B}-1\}_{K_{AB}}}$

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.

### Attacks on the protocol

The protocol is vulnerable to a replay attack (as identified by Denning and Sacco[2]). If an attacker uses an older, compromised value for KAB, he can then replay the message ${\displaystyle \{K_{AB},A\}_{K_{BS}}}$ to Bob, who will accept it, being unable to tell that the key is not fresh.

### Fixing the attack

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.[3] At the beginning of the protocol:

${\displaystyle A\rightarrow B:A}$
Alice sends to Bob a request.
${\displaystyle B\rightarrow A:\{A,\mathbf {N_{B}'} \}_{K_{BS}}}$
Bob responds with a nonce encrypted under his key with the Server.
${\displaystyle A\rightarrow S:\left.A,B,N_{A},\{A,\mathbf {N_{B}'} \}_{K_{BS}}\right.}$
Alice sends a message to the server identifying herself and Bob, telling the server she wants to communicate with Bob.
${\displaystyle S\rightarrow A:\{N_{A},K_{AB},B,\{K_{AB},A,\mathbf {N_{B}'} \}_{K_{BS}}\}_{K_{AS}}}$
Note the inclusion of the nonce.

The protocol then continues as described through the final three steps as described in the original protocol above. Note that ${\displaystyle N_{B}'}$ is a different nonce from ${\displaystyle N_{B}}$.The inclusion of this new nonce prevents the replaying of a compromised version of ${\displaystyle \{K_{AB},A\}_{K_{BS}}}$ since such a message would need to be of the form ${\displaystyle \{K_{AB},A,\mathbf {N_{B}'} \}_{K_{BS}}}$ which the attacker can't forge since she does not have ${\displaystyle K_{BS}}$.

## The public-key protocol

This assumes the use of a public-key encryption algorithm.

Here, Alice (A) and Bob (B) use a trusted server (S) to distribute public keys on request. These keys are:

• KPA and KSA, respectively public and private halves of an encryption key-pair belonging to A (S stands for "secret key" here)
• KPB and KSB, similar belonging to B
• KPS and KSS, similar belonging to S. (Note this has the property that KSS is used to encrypt and KPS to decrypt).

The protocol runs as follows:

${\displaystyle A\rightarrow S:\left.A,B\right.}$

A requests B's public keys from S

${\displaystyle S\rightarrow A:\{K_{PB},B\}_{K_{SS}}}$

S responds with public key KPB alongside B's identity, signed by the server for authentication purposes.

${\displaystyle A\rightarrow B:\{N_{A},A\}_{K_{PB}}}$

A chooses a random NA and sends it to B.

${\displaystyle B\rightarrow S:\left.B,A\right.}$

B now knows A wants to communicate, so B requests A's public keys.

${\displaystyle S\rightarrow B:\{K_{PA},A\}_{K_{SS}}}$

Server responds.

${\displaystyle B\rightarrow A:\{N_{A},N_{B}\}_{K_{PA}}}$

B chooses a random NB, and sends it to A along with NA to prove ability to decrypt with KSB.

${\displaystyle A\rightarrow B:\{N_{B}\}_{K_{PB}}}$

A confirms NB to B, to prove ability to decrypt with KSA

At the end of the protocol, A and B know each other's identities, and know both NA and NB. These nonces are not known to eavesdroppers.

### An attack on the protocol

Unfortunately, this protocol is vulnerable to a man-in-the-middle attack. If an impostor I 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.

Ignoring the traffic to and from S, which is unchanged, the attack runs as follows:

${\displaystyle A\rightarrow I:\{N_{A},A\}_{K_{PI}}}$

A sends NA to I, who decrypts the message with KSI

${\displaystyle I\rightarrow B:\{N_{A},A\}_{K_{PB}}}$

I relays the message to B, pretending that A is communicating

${\displaystyle B\rightarrow I:\{N_{A},N_{B}\}_{K_{PA}}}$

B sends NB

${\displaystyle I\rightarrow A:\{N_{A},N_{B}\}_{K_{PA}}}$

I relays it to A

${\displaystyle A\rightarrow I:\{N_{B}\}_{K_{PI}}}$

A decrypts NB and confirms it to I, who learns it

${\displaystyle I\rightarrow B:\{N_{B}\}_{K_{PB}}}$

I re-encrypts NB, and convinces B that he's decrypted it

At the end of the attack, B falsely believes that A is communicating with him, and that NA and NB are known only to A and B.

### Fixing the man-in-the-middle attack

The attack was first described in a 1995 paper by Gavin Lowe.[4] 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 to include the responder's identity, that is we replace:

${\displaystyle B\rightarrow A:\{N_{A},N_{B}\}_{K_{PA}}}$

with the fixed version:

${\displaystyle B\rightarrow A:\{N_{A},N_{B},B\}_{K_{PA}}}$