By Matt Mahoney, Oct. 13, 2008
This document describes a proposed design for a globally distributed artificial general intelligence (AGI) for the purpose of automating the world economy. The estimated value is on the order of US $1 quadrillion. The cost of a solution would be of the same order if we assume a million-fold decrease in the costs of computation, memory, and bandwidth, solutions to the natural language, speech, and vision problems, and an environment of pervasive public surveillance. The high cost implies decentralized ownership and a funding model that rewards intelligence and usefulness in a hostile environment where information has negative value and owners compete for attention, reputation, and resources.
The proposed solution is called competitive message routing (CMR). To a human user or a specialized intelligent server, CMR is a content-searchable message pool to which anyone may post. AGI is achieved by routing messages to the right specialists. CMR is implemented as a peer to peer network where incoming messages are cached, matched to stored messages, and each is forwarded to the sources of the other message. Economic, security, and long term safety issues are discussed. A specific protocol is proposed, defining a message format, sender authentication, and transport over existing internet protocols.
The purpose of AGI is twofold: first to improve the efficiency of organizations of humans by facilitating communication and access to information, and second, to automate the economy with respect to those functions that require human labor.
With respect to communication, the goal is to make information easy to find and publish. To send a message, you simply speak or type it into your computer or phone to nobody in particular, and it goes to anyone who cares, human or machine. If your message is in the form of a question, then it goes to anyone who can or has already answered it. If it is in the form of a statement, it goes to anyone whose question (past or future) it answers. Sending a message may initiate a public conversation with others that share your interests. When enough narrowly intelligent experts are added to the network, you should not care (or may prefer) that your conversation be with machines rather than humans.
With respect to automating labor, the goal is to reduce costs. It is not simply to replace existing jobs with machines, e. g. replacing truck drivers and lawyers, resulting in massive unemployment. Rather, easy access to an immense global database and computing infrastructure should result in new ways of solving problems, for example, the way shopping on the internet has supplemented traditional markets and created new job opportunities for web designers. Although the trend is clear that we are better off with automation, the details are difficult to predict, so I will not attempt to do so. Fifty years ago we imagined a future where robots pumped gas and tourists went to Mars, not the other way around.
The cost of AGI is estimated to be on the order of US $1 quadrillion.
First, we assume that Moore's Law will contine to halve the cost of computing power, storage, and network bandwidth every year or two for at least the next 30 years, as it has done for the last 50 years or so.
Second, we assume that there are no fundamental obstacles to solving hard AI problems such as language and vision, other than lack of computing power. In the worst case, these could be implemented using human brain sized neural networks, specifically, 1011 neurons and 1015 synapses modeled at 10 ms resolution. An equivalent artificial neural network would require about 1015 bytes of memory and 1017 operations per second. As of 2008 this would require about 20 doublings of Moore's law to make brain-sized computing power affordable to individuals. It is possible that more efficient solutions may be found sooner. In any case, we may ultimately neglect the cost of hardware.
Third, we assume that people will want AGI. It implies pervasive surveillance, since it will be the cheapest way for it to acquire the necessary knowledge. We imagine that a search for "where was Matt Mahoney last Saturday?" would produce a map, annotated with links to hundreds of videos recorded on public cameras indexed by face and license plate recognition software, and links to any conversations I made through computers or face to face within range of a public microphone. These conversations would be instantly indexed, summarized, and sent to anyone with an interest in what I said. At the same time, I would be notified of your query. We assume that people will want their conversations public because of the convenience, for example:
She: Hi dear. Could you pick up some Chinese on the way home? He: OK, the usual? Wok-in-the-box: Your order will be ready in 5 minutes.In building AGI, we can choose between spending more money to get it sooner vs. spending less by waiting until hardware costs drop. The optimal point is the value of the labor replaced divided by market interest rates. As of 2006, the value of labor worldwide was worth US $66 trillion. If we assume an interest rate of 6%, then the value would be $1 quadrillion. However, this is a moving target. The world GDP is increasing at about 5% annually. At this rate, it will be worth $4 quadrillion in 30 years.
As a best case scenario, we may assume that the major cost of AGI will be software and knowledge, which is not subject to Moore's Law. To make knowledge acquisition as cheap as possible, we will assume that the AGI understands language, speech, and images so it is not necessary to write code. We can train AGI on already published information plus surveillance of our normal activities rather than explicit instruction. It remains to estimate how much knowledge we need, how much is already available, and the rate that the remainder can be acquired.
In order to automate the economy, AGI must have knowledge equivalent to the world's population of about 1010 human brains. According to recall tests performed by Landauer, humans learn at a rate of 2 bits per second and have a long term memory capacity of about 109 bits. This is also about the amount of language processed since birth by an average adult, assuming 150 words per minute, several hours per day, at a rate of 1 bit per character as originally estimated by Shannon.
This implies that AGI needs 1019 bits of knowledge to automate the economy, except that people have shared knowledge. One of the advantages of machines over humans is that knowledge can be copied easily, eliminating the need to build millions of schools to train billions of agents. However, some fraction of knowledge is unique to each job and can't be copied. Organizations become more efficient when their members specialize. The fraction of shared knowledge is hard to estimate, but we can get some idea from the cost of replacing an employee, sometimes a year's salary. If we assume that 90% to 99% of human knowledge is shared, then AGI needs 1017 to 1018 bits of knowledge.
Currently, the internet has insufficient data to train AGI. A quick Google search for common English words ("the", "of", "a") shows that the accessible part of the internet is about 3 x 1010 web pages as of 2008. If each page has a few kilobytes of text, then there is about 1014 bits of knowledge available after compression. But even if it were 1016 bits, it would be far less than the amount needed. The rest still needs to be extracted from human brains.
We are fundamentally limited by the speed with which humans can communicate. Humans convey information at the same rate that they store it, about 2 bits per second. At current labor rates (US $5/hour worldwide), this implies a lower bound on cost of $100 trillion to $1 quadrillion as this information is gathered over several years from the world's population. However, this is a moving target. As we are developing language, vision, and surveillance capabilities to reduce knowledge acquistion costs, organizations are also becoming more efficient through increased specialization, with less duplication of knowledge and skills. In the worst case, an optimally efficient human economy with 1019 bits could cost on the order of $10 quadrillion in today's dollars to automate.
I propose a design for AGI called competitive message routing (CMR). To a client, CMR looks like a pool of messages which can be searched by content. A client can either be a human user or a machine (an expert) providing some specialized service, such as a calculator, database, or narrow AI application. When a client posts a message (adds it to the pool), it goes to anyone who has previously posted a similar message, and those similar messages are returned to the client. AGI is achieved by attaching lots of experts and routing messages to the right experts.
We make no distinction between queries and documents. A message may be used to ask a question, answer a question, post information, or initiate a public, interactive conversation with someone who shares your expressed interest. Every message is tagged with the name of its creator and time of creation. If the information was obtained from elsewhere, then the original sources should be included. Messages cannot be deleted or modified once they are added to the pool. However, updates can be posted and the latest version can be identified by its timestamp.
CMR is implemented on a peer to peer network, as described in my thesis. A message occupies a point in an m-dimensional semantic space, for example, a vector space model. Peers have a cache of messages, some of which originated from other peers. When a client creates a message X, the peers have the goal of routing X to the peers that hold messages close to it, and sending those responses back to the originator as well as any peers through which X was routed.
Example: suppose Alice wants to know what is the largest planet. She doesn't know or who might know, but knows Bob from the message M1 he sent last week: "Hello". She asks Bob. Bob doesn't know, but guesses that Charlie is an expert on planets because he received the message M2 last month: "Mercury is the innermost planet". The conversation goes like this:
Alice -> Bob: X = "What is the largest planet?" Bob -> Charlie: "Alice asked a minute ago: What is the largest planet?" Charlie -> Alice, Bob: M3 = "Dave said last year: Jupiter is the largest planet."
Fig. 1. Traversing messages in semantic space toward goal X.
The stored messages M1, M2, and M3 get progressively closer to X in semantic space, as shown in Fig. 1. Each peer knows only a subset of the messages in this space. The originator of the message serves as a link to other peers whose semantic regions overlaps. When no more progess can be made in approaching X, the last peer replies to all involved in routing X with the closest known match.
For a graph of n vertexes embedded in a semantic space of m dimensions, progress toward a target in space is possible in O(log n/log m) time when the average degree of the graph is at least 2m. For example, when m = 1, a binary tree will suffice. For a natural language semantic space, m is the size of the vocabulary, about 105.
As explained in my thesis, the model is robust. Each update adds more direct links to improve response time to similar messages, and new links to the graph to replace failed peers and links. (For example, Alice now knows that Charlie and Dave both know about Jupiter). Each query results in more copies of the requested message, to help load balancing. This robustness compensates for differences in the semantic models of different peers. A client may also post a message to several peers to improve the expected number of responses.
An organization is optimally efficient when there is no unnecessary duplication of knowledge among peers beyond what is needed for fault recovery. This is achieved by a market economy where information has negative value. Peers have an incentive to offload information to other peers and delete their own copy as long as it remains accessible. Peers can mutually benefit by trading messages if both parties can compress the received messages more tightly than the sent messages.
Trading results in peers storing groups of similar messages, clusters in semantic space. We define a distance between messages X and Y as D(X, Y) = K(Y|X) + K(X|Y) where K is Kolmogorov complexity, i.e. K(Y|X) = K(XY) - K(X) is the length of the shortest program that outputs Y given X as input. K is not computable in general, so for practical purposes we substitute a compression difference measure, C(X, Y) = C(Y|X) + C(X|Y) where C(Y|X) = C(XY) - C(X) and C(XY) means the compressed size of X concatenated with Y. The better the compression algorithm, the more closely C approximates K.
D is compatible with Euclidean distance in the vector space model because it has the properites of a distance measure. It has the following properties for distinct messages X, Y, and Z:
We can now describe a routing policy. A peer has a cache of messages received from other peers. We assume that messages cluster within peers, meaning D(X, Y) is likely to be smaller if X and Y are stored on the same peer than on different peers. Suppose Alice receives message X and must decide who to route it to. Alice computes D1 = D(X, Y1), D2 = D(X, Y2), ... where Yi is the concatenation of all messages received from peer i. Then Alice routes X to the i that minimizes Di. This is Alice's best estimate of the peer that can compress X the smallest.
Let's say the best match to X is i = Bob. If Bob is one of the senders of X, then Alice should keep X rather than send it back. To compensate for her storage cost, Alice should send a different message back to Bob, one that takes a lot of space in Alice's cache but that Bob can easily compress. Then for each message Zj in Alice's cache where Bob is not one of the senders, Alice computes Dj = D(Zj, Zi=1..n,i≠j) - D(X, Zj) and reply with Zj that maximizes Dj. The term Zi=1..n,i≠j means the concatenation of all of the messages in the cache except Zj.
X is a guess about what Bob knows. Alice can concatenate other messages from Bob to X in computing D(X, Zj)
When Alice sends or forwards a message, she does not delete it right away. She keeps it in the cache until she needs space. Peers are free to choose their own deletion policies. This requires some intelligence. Otherwise peers that provide unlimited free space can be exploited by non-cooperating peers.
Peers may choose their routing strategies independently using different compression algorithms. This introduces an uncertainty as to which message matches the closest. We compensate by routing messages to more than one peer when all of them are fairly close. In the previous example we might have additional messages such as:
Bob -> Alice: "Charlie said last month: Mercury is the innermost planet" Charlie -> Dave: "Bob said 1 minutes ago that Alice asked 2 minutes ago: What is the largest planet?" Dave -> Alice, Bob, Charlie: "Jupiter is still the largest planet"However, a ratio of output to input greater than 1 could lead to an exponential explosion of messages. To compensate, peers should delete duplicate messages and establish a distance threshold or other criteria such that if there is no good match then the message is discarded. In general, there is no clean solution. A good routing strategy requires intelligence and an economic policy that rewards intelligence as discussed in section 4.
AGI is too expensive for any one person or group to own or be able to control any significant part of it. The system must be decentralized. There is no central authority to enforce the peer to peer protocol. Messages may not conform to the protocol and may be hostile. Peers will need to deal with false information, spam, scams, flooding attacks, forgery, attached viruses and worms, and malformed or malicious messages that attempt to exploit software flaws such as buffer overflows to crash the recipient or gain unauthorized access.
In order for AGI to be built, there must be an economic incentive for users to add well-behaved peers to the system. They must have an incentive to make CPU, memory, and bandwidth (resources) and high quality information available. They must have an incentive to prevent their peers from being exploited by forwarding malicious traffic.
The economic model of CMR is based on information having negative value on average. People are willing to pay to have their messages received by others. Peers compete for attention, reputation, and resources in a hostile environment. This requires that peers rank others by the quality of information received from them and to reject messages from peers with poor reputations. Distinguishing between high and low quality information requires intelligence. It requires work by users, either to rate messages to adjust the reputation of senders, or to specify complex filtering policies. This work may be a significant fraction of the total cost of AGI, perhaps the single greatest cost.
CMR supports an advertising model. However, peers must target ads carefully to those who want them, or risk being blocked or having to pay other peers to forward their ads. Users need to supply useful services and information in a competitive market in order to make a profit. This is the other major cost of AGI.
Reputation management requires that peers reliably identify their sources. CMR allows senders to sign messages independently of any underlying protocol that might also provide this service (such as HTTPS). A CMR digital signature is based on a secret key shared by the sender and receiver. If Bob receives a signed message from Alice, then Bob can verify that the message is from the same source that claimed to be Alice in other signed messages, and that the message was not altered or forged by anyone not knowing the key. Keys are not reused between any other pair of peers to minimize the damage if a key is compromised.
When Alice sends a message to Bob for the first time, they may establish a key using one time public RSA key pairs, by Diffie-Hellman (DH) key exchange, or by other methods outside the CMR protocol. However there is no foolproof method of key exchange. RSA and DH are susceptible to man in the middle attacks if the attacker is able to intercept messages from both peers.
Signatures are used only between immediate neighbors. If Alice sends a message to Bob, which is forwarded to Charlie, then Charlie can only verify Bob's signature and must trust that Bob verified Alice. If in doubt, Charlie should ask Alice directly. If Charlie determines that Bob's message was bogus, then Charlie should downgrade only Bob's reputation, since Bob's claim that it is from Alice cannot be trusted.
AGI will obviously have a huge impact on society. In particular Vernor Vinge has raised the possibility of runaway AI resulting in a technological singularity. Organizations such as SIAI and the Lifeboat Foundation were formed to address the existential threats of an intelligence explosion of unfriendly AI. I will address these concerns with respect to CMR.
One possibility is that a smarter than human AI could produce even smarter AI in a process of recursive self improvement (RSI). In this scenario, the first program to achieve superhuman intelligence would be the last invention that humans would need to create. One of the goals of SIAI has been to develop that seed AI and ensure that it remains friendly through successive generations.
I do not believe this approach is viable. Currently there are no physical, mathematical, or software models of RSI for any reasonable definition of what "intelligence" means. I showed (PDF) (HTML) that RSI is possible, but only in a trivial sense. The maximum rate of improvement is O(log n), no faster than a counter. Intelligence requires information, and information can't come from nowhere.
An often cited example of RSI is the growth of human civilization. That is not the case. Economic, cultural, and technological growth is a form of self organization, not self improvement. Individual humans can do much more today than 1000 years ago, but our brains are no different. Without language, modern humans probably would not think to produce spears out of sticks and rocks, much less produce computers.
In the short term, CMR produces AGI from lots of machines that individually have low intelligence and only do what they are programmed to do by humans. These machines have no goals and cannot improve themselves. However, CMR rewards intelligence, where intelligence is defined as successful ability to acquire computing resources. The absence of RSI only means that improvement is an evolutionary process in which programs do not set the criteria for testing intelligence in their copies.
Humans, like all animals, have evolved a fear of death (actually, a fear of the many things that can kill us), because it increases the expected number of children. Some people may wish to create programs that simulate their brains and have them turned on after they die. Such a program would have the same memories, skills, and simulated emotions as the original and be indistinguishable to friends and relatives.
We call such a program an upload. It is not necessary to develop any new technology (such as brain scanning) beyond what we have already assumed: a million-fold drop in computing costs and extensive surveillance to extract 109 bits of knowledge from every human. Any memory differences between the original and copy could be filled in with plausible details, and the copy would not appear to notice. We might assume other technology is developed later, such as robotic embodiment.
Whether an upload actually transfers the original's consciousness is an irrelevant, philosophical question. What is important is that to others it will appear that the original has been brought back to life, making it a popular option. As I described CMR, it is friendly because humans own computing resources and the machines themselves have no rights. The danger is that people will want their uploads to have the same rights as they had when they were alive, including ownership of resources. This will result in humans competing with machines of their own creation rather than just each other. It also raises difficult legal issues because uploads could reproduce themselves rapidly, modify their own software, and there is no clear legal or technical distinction between uploads and other types of programs.
CMR is an environment where peers compete for resources. These could be stolen by trickery or exploiting software flaws. Currently, internet worms exploit flaws discovered by humans to make copies of themselves. Intelligent worms with language models that include programming skills are much more dangerous for 4 reasons.
Whether or not we have RSI, uploading, or intelligent worms, at some point the total knowledge and computation implemented in machines will exceed that of human brains. Beyond that, it would matter little to the global brain whether humans were extinct or not. It not, then humans would at least be unaware of the intelligence that controlled the world around them, just as dogs are unaware of the human intelligence or goals of their breeders.
We should hope that the collective intelligence would be benevolant to humans, but what does that mean? Humans want happiness, but happiness is just a reward signal controlled by a complex function that evolved to increase reproductive fitness. Expressed as a reinforcement learner, the human brain implements an optimization process whose goal is to maximize the scalar utility U(x) over the 2109 to 21015 possible mental states, x. We experience happiness when we go from a mental state x1 to x2 where U(x1) < U(x2). At some point there is a maximum where any thought or sensory awareness would be unpleasant because it would result in a different mental state.
A possible way out is to augment the brain with additional memory so that we never run out of mental states. Then what do we become? At some point the original brain becomes such a tiny fraction that we could discard it with little effect. As a computer, we could reprogram our memories and goals. Instead of defining happiness as getting what we want, we could reprogram ourselves to want what we have. But in an environment where programs compete for atoms and energy, such systems would not be viable. Evolution favors programs that fear death and die, that can't get everything they want, and can't change what they want.
This section describes a proposed implementation of competitive message routing (CMR) protocol. CMR is a distributed message posting and search service. When a client posts a message, it has the effect of adding the message to the pool and retrieving related messages that are either already in the pool or that are posted later by other clients. There is no provision to delete or modify messages, once posted.
A CMR network is composed of peers. Any peer may send messages to any other peer. Every peer should have a globally unique address for receiving messages.
A peer is either a router or a client. A client may either be an interface to a human user or to a server. CMR protocol specifies only the behavior of routers. Clients do not have to follow any rules. Thus, peers cannot tell if incoming messages are from routers or clients because it is possible for a client to emulate a router.
A router has a store of messages called a cache. The cache contains previously received messages. A router cannot create new messages. Only a client can do that.
A CMR message is a string of 8-bit bytes. A message consists of a signature, a routing header, and a message body.
A signature consists of a line of text ending with a carriage return (CR, ASCII 13) and a linefeed (LF, ASCII 10). The first character of the signature is a version number, either 0 (ASCII 48) or 1 (ASCII 49), followed by a hash string. If the version number is 0 then the hash string is empty and the message is said to be unsigned. If it is 1, then the hash string is the SHA-256 hash of a secret key, kab concatenated with the routing header and message body. The hash is written as 64 lower case hexadecimal digits. kab should be known only to the sender whose address appears in the first line of the routing header and the receiver. kab may be of any length. In computing the hash, no bytes are placed after the key before the routing header.
A routing header consists of one or more message IDs. A message ID is a line consisting of a timestamp, a space character (ASCII 32), a server address and a CR LF to terminate the line. The message ID means that the message was sent at the indicated time by the peer with the given address. The message IDs are ordered from newest to oldest. Thus, the last line of the header identifies the client that created the message and the time it was created. The last line of the header is followed by a blank line (an additional CR LF).
A message ID uniquely identifies a message. No two messages that contain matching IDs anywhere in their routing headers should differ anywhere in the remainder of the header or in the body.
A timestamp has the format YYYY/MM/DD HH:MM:SS[.S*] (year, month, day, hour, minute, seconds, optional fractional seconds) in the range 0000/01/01 00:00:00 to 9999/12/31 23:59:59.999... . Times are universal times (UT, formerly GMT). A decimal point after the seconds is optional. If it appears, it may be followed by any number of decimals. A timestamp must represent a valid time, not in the future, and earlier than the timestamp on the line above it, if any.
An address is an internet server address. It has the form of a URL if the underlying transport protocol supports it. Otherwise it is any string not containing the CR or LF characters. No address should appear more than once in a header. The recipient's address should not appear at all.
The message body consists of a length, n, written as a decimal number followed by CR LF, then n bytes (ASCII 0 through 255). Normally the body will contain human understandable data such as ASCII or UTF-8 encoded text, or suitably encoded audio, images, or video in common formats. However, there is no restriction on content. For example:
101c1ad32d6fe646a56edba43bd342ee11e45ba188c59aeec91a5590a0ea114d5 2008/09/01 00:00:53.42 http://alice.com/cmr 2008/09/01 00:00:53 udp://192.168.0.102:53/dns-tunnel 2008/08/31 23:59:01.0955 https://www.charlie.com/messages.pl 14 Hello World!
In this example, kab is the 3 byte string "foo", known only to the peer with address http://alice.com/cmr and the message recipient. The message was created by the client whose address is https://www.charlie.com/messages.pl.
When a router receives a message, it should reject (ignore and discard) any message that does not conform to the format described in the last section. It should reject any message with an ID that matches an ID of another message already in the cache. If the message is signed, then it should compute the signature and reject it if it does not match. It may also reject a message for any reason, for example, if the sender has a low reputation, or the content is recognized as spam or malicious, or if it cannot keep up with input. CMR does not require any policy.
If a message X is accepted, then it should be matched to zero or more messages in the cache and added to the cache. For each message Y matched to X, it should forward X to zero or more addresses that appear in the header of Y, and forward Y to zero or more addresses that appear in the header of X.
Router Alice forwards message X to peer Bob as follows:
CMR does not specify a cache deletion policy. A router may remove messages from its cache at any time.
CMR is a super-application layer protocol. It may be sent over existing internet protocols such as HTTP or HTTPS or in the body of an email message. In general, a peer implements a single server protocol such as HTTP (appearing as a web server) and multiple client protocols such as HTTP (appearing as a web browser), and SMTP (to send email). The following describe the protocol for Alice to send a message to Bob:
The recipient has a server address of the form mailto:email-address such as mailto:email@example.com. Alice sends an email message to Bob. The body of the email message may be either a CMR message or a MIME encoded file attachment containing a CMR message. The subject line is irrelevant. The recommended subject is "cmr".
The recipient has a server address in the form of a URL beginning with http:// such as http://bob.com/cgi-bin/cmr.pl. Messages are sent as plain text files using file upload protocol as described in RFC 1867.
The protocol for HTTPS is the same as for HTTP. HTTPS also encrypts the message and provides for a secondary means of authentication.
UDP represents a worst case scenario because a message is contained in a single packet with no assurance that the source IP address is correct. The server address has the form udp://IP-address:port/string (not a standard URL), such as in the previous example. The string is used to identify which local CMR server listening on the port should receive the message. A message should fit in the payload of a single packet (up to about 64 KB).
Handshake protocols are appropriate when the sender can reliably send a message to a receiver but the receiver cannot verify the sender's address. This model is usually assumed for email and HTTP requests. We assume that Alice and Bob both have HTTP server addresses, say, http://alice.com/ and http://bob.com/, and that they do not share a key. The exchange is:
When Alice sends a message to Bob for the first time and they do not share a secret key, a key may be established in a number of ways that are defined outside the CMR protocol. A key is unique to each pair of peers.
Alice generates a one time RSA key and sends a message to Bob with her public key. Bob replies by choosing a random key, encrypting it with her public key and sending it to Alice. If no key has been established, then both messages are unsigned. Otherwise, both messages are signed with the old keys and the new key takes effect for both Alice and Bob on the next message.
The protocol is as follows. Alice chooses two large prime numbers p and q, a public exponent e, and a private exponent d such that ed = 1 (mod lcm(p-1,q-1)), and computes n = pq. Alice sends a message to Bob with the following in the body:
RSA key exchange request=n,e.where all numbers are written in lower case hexadecimal. Bob then chooses a secret key k, computes c = ke (mod n) and replies to Alice:
RSA key exchange reply=c.Alice then computes key k = cd (mod n) and discards p, q, n, and d. Alice and Bob remove the two messages from their caches.
In Diffie-Hellman key exchange, Alice chooses a secret number, a, a large prime number p, and a primitive root g of p. Alice computes A = ga (mod p) and sends a message to Bob of the form:
DH key exchange request=g,p,A.where all numbers are written in lower case hexadecimal. Bob chooses a secret number, b, computes B = gb (mod p) and replies to Alice:
DH key exchange reply=B.Alice and Bob then agree to use key k = Ba (mod p) = Ab (mod p), computed by Alice and Bob respectively.
As with RSA, messages are either unsigned or signed with old keys.
If CMR is implemented on top of a secure protocol such as HTTPS or SSH, then the key may be chosen by Alice and sent directly in a single message to Bob:
Clear key exchange=k.The key is written in lower case hexadecimal and is converted into bytes (two digits per byte) when computing authentication strings. For example, if the key is "foo", then the message is:
Clear key exchange=666f6f.(In practice, a longer key would be used).
This documentation is a revision of my original proposal dated Dec. 6, 2007.