Network Working Group T. Wu Request for Comments: 2945 Stanford University Category: Standards Track September 2000 The SRP Authentication and Key Exchange System Status of this Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (2000). All Rights Reserved. Abstract This document describes a cryptographically strong network authentication mechanism known as the Secure Remote Password (SRP) protocol. This mechanism is suitable for negotiating secure connections using a user-supplied password, while eliminating the security problems traditionally associated with reusable passwords. This system also performs a secure key exchange in the process of authentication, allowing security layers (privacy and/or integrity protection) to be enabled during the session. Trusted key servers and certificate infrastructures are not required, and clients are not required to store or manage any long-term keys. SRP offers both security and deployment advantages over existing challenge-response techniques, making it an ideal drop-in replacement where secure password authentication is needed. 1. Introduction The lack of a secure authentication mechanism that is also easy to use has been a long-standing problem with the vast majority of Internet protocols currently in use. The problem is two-fold: Users like to use passwords that they can remember, but most password-based authentication systems offer little protection against even passive attackers, especially if weak and easily-guessed passwords are used. Eavesdropping on a TCP/IP network can be carried out very easily and very effectively against protocols that transmit passwords in the clear. Even so-called "challenge-response" techniques like the one described in [RFC 2095] and [RFC 1760], which are designed to defeat Wu Standards Track [Page 1] RFC 2945 SRP Authentication & Key Exchange System September 2000 simple sniffing attacks, can be compromised by what is known as a "dictionary attack". This occurs when an attacker captures the messages exchanged during a legitimate run of the protocol and uses that information to verify a series of guessed passwords taken from a precompiled "dictionary" of common passwords. This works because users often choose simple, easy-to-remember passwords, which invariably are also easy to guess. Many existing mechanisms also require the password database on the host to be kept secret because the password P or some private hash h(P) is stored there and would compromise security if revealed. That approach often degenerates into "security through obscurity" and goes against the UNIX convention of keeping a "public" password file whose contents can be revealed without destroying system security. SRP meets the strictest requirements laid down in [RFC 1704] for a non-disclosing authentication protocol. It offers complete protection against both passive and active attacks, and accomplishes this efficiently using a single Diffie-Hellman-style round of computation, making it feasible to use in both interactive and non- interactive authentication for a wide range of Internet protocols. Since it retains its security when used with low-entropy passwords, it can be seamlessly integrated into existing user applications. 2. Conventions and Terminology The protocol described by this document is sometimes referred to as "SRP-3" for historical purposes. This particular protocol is described in [SRP] and is believed to have very good logical and cryptographic resistance to both eavesdropping and active attacks. This document does not attempt to describe SRP in the context of any particular Internet protocol; instead it describes an abstract protocol that can be easily fitted to a particular application. For example, the specific format of messages (including padding) is not specified. Those issues have been left to the protocol implementor to decide. The one implementation issue worth specifying here is the mapping between strings and integers. Internet protocols are byte-oriented, while SRP performs algebraic operations on its messages, so it is logical to define at least one method by which integers can be converted into a string of bytes and vice versa. An n-byte string S can be converted to an integer as follows: i = S[n-1] + 256 * S[n-2] + 256^2 * S[n-3] + ... + 256^(n-1) * S[0] Wu Standards Track [Page 2] RFC 2945 SRP Authentication & Key Exchange System September 2000 where i is the integer and S[x] is the value of the x'th byte of S. In human terms, the string of bytes is the integer expressed in base 256, with the most significant digit first. When converting back to a string, S[0] must be non-zero (padding is considered to be a separate, independent process). This conversion method is suitable for file storage, in-memory representation, and network transmission of large integer values. Unless otherwise specified, this mapping will be assumed. If implementations require padding a string that represents an integer value, it is recommended that they use zero bytes and add them to the beginning of the string. The conversion back to integer automatically discards leading zero bytes, making this padding scheme less prone to error. The SHA hash function, when used in this document, refers to the SHA-1 message digest algorithm described in [SHA1]. 3. The SRP-SHA1 mechanism This section describes an implementation of the SRP authentication and key-exchange protocol that employs the SHA hash function to generate session keys and authentication proofs. The host stores user passwords as triplets of the form { , , } Password entries are generated as follows: = random() x = SHA( | SHA( | ":" | )) = v = g^x % N The | symbol indicates string concatenation, the ^ operator is the exponentiation operation, and the % operator is the integer remainder operation. Most implementations perform the exponentiation and remainder in a single stage to avoid generating unwieldy intermediate results. Note that the 160-bit output of SHA is implicitly converted to an integer before it is operated upon. Authentication is generally initiated by the client. Client Host -------- ------ U = --> Wu Standards Track [Page 3] RFC 2945 SRP Authentication & Key Exchange System September 2000 Upon identifying himself to the host, the client will receive the salt stored on the host under his username. a = random() A = g^a % N --> v = b = random() x = SHA(s | SHA(U | ":" | p)) S = (B - g^x) ^ (a + u * x) % N S = (A * v^u) ^ b % N K = SHA_Interleave(S) K = SHA_Interleave(S) (this function is described in the next section) The client generates a random number, raises g to that power modulo the field prime, and sends the result to the host. The host does the same thing and also adds the public verifier before sending it to the client. Both sides then construct the shared session key based on the respective formulae. The parameter u is a 32-bit unsigned integer which takes its value from the first 32 bits of the SHA1 hash of B, MSB first. The client MUST abort authentication if B % N is zero. The host MUST abort the authentication attempt if A % N is zero. The host MUST send B after receiving A from the client, never before. At this point, the client and server should have a common session key that is secure (i.e. not known to an outside party). To finish authentication, they must prove to each other that their keys are identical. M = H(H(N) XOR H(g) | H(U) | s | A | B | K) -->