Network Working Group W. Simpson, Editor
Request for Comments: 1662 Daydreamer
STD: 51 July 1994
Obsoletes: 1549 
Category: Standards Track
 PPP in HDLC-like Framing
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.
Abstract
 The Point-to-Point Protocol (PPP) [1] provides a standard method for
 transporting multi-protocol datagrams over point-to-point links.
 This document describes the use of HDLC-like framing for PPP
 encapsulated packets.
Table of Contents
 1. Introduction .......................................... 1
 1.1 Specification of Requirements ................... 2
 1.2 Terminology ..................................... 2
 2. Physical Layer Requirements ........................... 3
 3. The Data Link Layer ................................... 4
 3.1 Frame Format .................................... 5
 3.2 Modification of the Basic Frame ................. 7
 4. Octet-stuffed framing ................................. 8
 4.1 Flag Sequence ................................... 8
 4.2 Transparency .................................... 8
 4.3 Invalid Frames .................................. 9
 4.4 Time Fill ....................................... 9
 4.4.1 Octet-synchronous ............................... 9
 4.4.2 Asynchronous .................................... 9
 4.5 Transmission Considerations ..................... 10
 4.5.1 Octet-synchronous ............................... 10
 4.5.2 Asynchronous .................................... 10
 5. Bit-stuffed framing ................................... 11
 5.1 Flag Sequence ................................... 11
 5.2 Transparency .................................... 11
 5.3 Invalid Frames .................................. 11
 5.4 Time Fill ....................................... 11
 5.5 Transmission Considerations ..................... 12
 6. Asynchronous to Synchronous Conversion ................ 13
 7. Additional LCP Configuration Options .................. 14
 7.1 Async-Control-Character-Map (ACCM) .............. 14
 APPENDICES ................................................... 17
 A. Recommended LCP Options ............................... 17
 B. Automatic Recognition of PPP Frames ................... 17
 C. Fast Frame Check Sequence (FCS) Implementation ........ 18
 C.1 FCS table generator ............................. 18
 C.2 16-bit FCS Computation Method ................... 19
 C.3 32-bit FCS Computation Method ................... 21
 SECURITY CONSIDERATIONS ...................................... 24
 REFERENCES ................................................... 24
 ACKNOWLEDGEMENTS ............................................. 25
 CHAIR'S ADDRESS .............................................. 25
 EDITOR'S ADDRESS ............................................. 25
1. Introduction
 This specification provides for framing over both bit-oriented and
 octet-oriented synchronous links, and asynchronous links with 8 bits
 of data and no parity. These links MUST be full-duplex, but MAY be
 either dedicated or circuit-switched.
 An escape mechanism is specified to allow control data such as
 XON/XOFF to be transmitted transparently over the link, and to remove
 spurious control data which may be injected into the link by
 intervening hardware and software.
 Some protocols expect error free transmission, and either provide
 error detection only on a conditional basis, or do not provide it at
 all. PPP uses the HDLC Frame Check Sequence for error detection.
 This is commonly available in hardware implementations, and a
 software implementation is provided.
1.1. Specification of Requirements
 In this document, several words are used to signify the requirements
 of the specification. These words are often capitalized.
 MUST This word, or the adjective "required", means that the
 definition is an absolute requirement of the specification.
 MUST NOT This phrase means that the definition is an absolute
 prohibition of the specification.
 SHOULD This word, or the adjective "recommended", means that there
 may exist valid reasons in particular circumstances to
 ignore this item, but the full implications must be
 understood and carefully weighed before choosing a
 different course.
 MAY This word, or the adjective "optional", means that this
 item is one of an allowed set of alternatives. An
 implementation which does not include this option MUST be
 prepared to interoperate with another implementation which
 does include the option.
1.2. Terminology
 This document frequently uses the following terms:
 datagram The unit of transmission in the network layer (such as IP).
 A datagram may be encapsulated in one or more packets
 passed to the data link layer.
 frame The unit of transmission at the data link layer. A frame
 may include a header and/or a trailer, along with some
 number of units of data.
 packet The basic unit of encapsulation, which is passed across the
 interface between the network layer and the data link
 layer. A packet is usually mapped to a frame; the
 exceptions are when data link layer fragmentation is being
 performed, or when multiple packets are incorporated into a
 single frame.
 peer The other end of the point-to-point link.
 silently discard
 The implementation discards the packet without further
 processing. The implementation SHOULD provide the
 capability of logging the error, including the contents of
 the silently discarded packet, and SHOULD record the event
 in a statistics counter.
2. Physical Layer Requirements
 PPP is capable of operating across most DTE/DCE interfaces (such as,
 EIA RS-232-E, EIA RS-422, and CCITT V.35). The only absolute
 requirement imposed by PPP is the provision of a full-duplex circuit,
 either dedicated or circuit-switched, which can operate in either an
 asynchronous (start/stop), bit-synchronous, or octet-synchronous
 mode, transparent to PPP Data Link Layer frames.
 Interface Format
 PPP presents an octet interface to the physical layer. There is
 no provision for sub-octets to be supplied or accepted.
 Transmission Rate
 PPP does not impose any restrictions regarding transmission rate,
 other than that of the particular DTE/DCE interface.
 Control Signals
 PPP does not require the use of control signals, such as Request
 To Send (RTS), Clear To Send (CTS), Data Carrier Detect (DCD), and
 Data Terminal Ready (DTR).
 When available, using such signals can allow greater functionality
 and performance. In particular, such signals SHOULD be used to
 signal the Up and Down events in the LCP Option Negotiation
 Automaton [1]. When such signals are not available, the
 implementation MUST signal the Up event to LCP upon
 initialization, and SHOULD NOT signal the Down event.
 Because signalling is not required, the physical layer MAY be
 decoupled from the data link layer, hiding the transient details
 of the physical transport. This has implications for mobility in
 cellular radio networks, and other rapidly switching links.
 When moving from cell to cell within the same zone, an
 implementation MAY choose to treat the entire zone as a single
 link, even though transmission is switched among several
 frequencies. The link is considered to be with the central
 control unit for the zone, rather than the individual cell
 transceivers. However, the link SHOULD re-establish its
 configuration whenever the link is switched to a different
 administration.
 Due to the bursty nature of data traffic, some implementations
 have choosen to disconnect the physical layer during periods of
 inactivity, and reconnect when traffic resumes, without informing
 the data link layer. Robust implementations should avoid using
 this trick over-zealously, since the price for decreased setup
 latency is decreased security. Implementations SHOULD signal the
 Down event whenever "significant time" has elapsed since the link
 was disconnected. The value for "significant time" is a matter of
 considerable debate, and is based on the tariffs, call setup
 times, and security concerns of the installation.
3. The Data Link Layer
 PPP uses the principles described in ISO 3309-1979 HDLC frame
 structure, most recently the fourth edition 3309:1991 [2], which
 specifies modifications to allow HDLC use in asynchronous
 environments.
 The PPP control procedures use the Control field encodings described
 in ISO 4335-1979 HDLC elements of procedures, most recently the
 fourth edition 4335:1991 [4].
 This should not be construed to indicate that every feature of the
 above recommendations are included in PPP. Each feature included
 is explicitly described in the following sections.
 To remain consistent with standard Internet practice, and avoid
 confusion for people used to reading RFCs, all binary numbers in the
 following descriptions are in Most Significant Bit to Least
 Significant Bit order, reading from left to right, unless otherwise
 indicated. Note that this is contrary to standard ISO and CCITT
 practice which orders bits as transmitted (network bit order). Keep
 this in mind when comparing this document with the international
 standards documents.
3.1. Frame Format
 A summary of the PPP HDLC-like frame structure is shown below. This
 figure does not include bits inserted for synchronization (such as
 start and stop bits for asynchronous links), nor any bits or octets
 inserted for transparency. The fields are transmitted from left to
 right.
 +----------+----------+----------+
 | Flag | Address | Control |
 | 01111110 | 11111111 | 00000011 |
 +----------+----------+----------+
 +----------+-------------+---------+
 | Protocol | Information | Padding |
 | 8/16 bits| * | * |
 +----------+-------------+---------+
 +----------+----------+-----------------
 | FCS | Flag | Inter-frame Fill
 |16/32 bits| 01111110 | or next Address
 +----------+----------+-----------------
 The Protocol, Information and Padding fields are described in the
 Point-to-Point Protocol Encapsulation [1].
 Flag Sequence
 Each frame begins and ends with a Flag Sequence, which is the
 binary sequence 01111110 (hexadecimal 0x7e). All implementations
 continuously check for this flag, which is used for frame
 synchronization.
 Only one Flag Sequence is required between two frames. Two
 consecutive Flag Sequences constitute an empty frame, which is
 silently discarded, and not counted as a FCS error.
 Address Field
 The Address field is a single octet, which contains the binary
 sequence 11111111 (hexadecimal 0xff), the All-Stations address.
 Individual station addresses are not assigned. The All-Stations
 address MUST always be recognized and received.
 The use of other address lengths and values may be defined at a
 later time, or by prior agreement. Frames with unrecognized
 Addresses SHOULD be silently discarded.
 Control Field
 The Control field is a single octet, which contains the binary
 sequence 00000011 (hexadecimal 0x03), the Unnumbered Information
 (UI) command with the Poll/Final (P/F) bit set to zero.
 The use of other Control field values may be defined at a later
 time, or by prior agreement. Frames with unrecognized Control
 field values SHOULD be silently discarded.
 Frame Check Sequence (FCS) Field
 The Frame Check Sequence field defaults to 16 bits (two octets).
 The FCS is transmitted least significant octet first, which
 contains the coefficient of the highest term.
 A 32-bit (four octet) FCS is also defined. Its use may be
 negotiated as described in "PPP LCP Extensions" [5].
 The use of other FCS lengths may be defined at a later time, or by
 prior agreement.
 The FCS field is calculated over all bits of the Address, Control,
 Protocol, Information and Padding fields, not including any start
 and stop bits (asynchronous) nor any bits (synchronous) or octets
 (asynchronous or synchronous) inserted for transparency. This
 also does not include the Flag Sequences nor the FCS field itself.
 When octets are received which are flagged in the Async-
 Control-Character-Map, they are discarded before calculating
 the FCS.
 For more information on the specification of the FCS, see the
 Appendices.
 The end of the Information and Padding fields is found by locating
 the closing Flag Sequence and removing the Frame Check Sequence
 field.
3.2. Modification of the Basic Frame
 The Link Control Protocol can negotiate modifications to the standard
 HDLC-like frame structure. However, modified frames will always be
 clearly distinguishable from standard frames.
 Address-and-Control-Field-Compression
 When using the standard HDLC-like framing, the Address and Control
 fields contain the hexadecimal values 0xff and 0x03 respectively.
 When other Address or Control field values are in use, Address-
 and-Control-Field-Compression MUST NOT be negotiated.
 On transmission, compressed Address and Control fields are simply
 omitted.
 On reception, the Address and Control fields are decompressed by
 examining the first two octets. If they contain the values 0xff
 and 0x03, they are assumed to be the Address and Control fields.
 If not, it is assumed that the fields were compressed and were not
 transmitted.
 By definition, the first octet of a two octet Protocol field
 will never be 0xff (since it is not even). The Protocol field
 value 0x00ff is not allowed (reserved) to avoid ambiguity when
 Protocol-Field-Compression is enabled and the first Information
 field octet is 0x03.
4. Octet-stuffed framing
 This chapter summarizes the use of HDLC-like framing with 8-bit
 asynchronous and octet-synchronous links.
4.1. Flag Sequence
 The Flag Sequence indicates the beginning or end of a frame. The
 octet stream is examined on an octet-by-octet basis for the value
 01111110 (hexadecimal 0x7e).
4.2. Transparency
 An octet stuffing procedure is used. The Control Escape octet is
 defined as binary 01111101 (hexadecimal 0x7d), most significant bit
 first.
 As a minimum, sending implementations MUST escape the Flag Sequence
 and Control Escape octets.
 After FCS computation, the transmitter examines the entire frame
 between the two Flag Sequences. Each Flag Sequence, Control Escape
 octet, and any octet which is flagged in the sending Async-Control-
 Character-Map (ACCM), is replaced by a two octet sequence consisting
 of the Control Escape octet followed by the original octet
 exclusive-or'd with hexadecimal 0x20.
 This is bit 5 complemented, where the bit positions are numbered
 76543210 (the 6th bit as used in ISO numbered 87654321 -- BEWARE
 when comparing documents).
 Receiving implementations MUST correctly process all Control Escape
 sequences.
 On reception, prior to FCS computation, each octet with value less
 than hexadecimal 0x20 is checked. If it is flagged in the receiving
 ACCM, it is simply removed (it may have been inserted by intervening
 data communications equipment). Each Control Escape octet is also
 removed, and the following octet is exclusive-or'd with hexadecimal
 0x20, unless it is the Flag Sequence (which aborts a frame).
 A few examples may make this more clear. Escaped data is transmitted
 on the link as follows:
 0x7e is encoded as 0x7d, 0x5e. (Flag Sequence)
 0x7d is encoded as 0x7d, 0x5d. (Control Escape)
 0x03 is encoded as 0x7d, 0x23. (ETX)
 Some modems with software flow control may intercept outgoing DC1 and
 DC3 ignoring the 8th (parity) bit. This data would be transmitted on
 the link as follows:
 0x11 is encoded as 0x7d, 0x31. (XON)
 0x13 is encoded as 0x7d, 0x33. (XOFF)
 0x91 is encoded as 0x7d, 0xb1. (XON with parity set)
 0x93 is encoded as 0x7d, 0xb3. (XOFF with parity set)
4.3. Invalid Frames
 Frames which are too short (less than 4 octets when using the 16-bit
 FCS), or which end with a Control Escape octet followed immediately
 by a closing Flag Sequence, or in which octet-framing is violated (by
 transmitting a "0" stop bit where a "1" bit is expected), are
 silently discarded, and not counted as a FCS error.
4.4. Time Fill
4.4.1. Octet-synchronous
 There is no provision for inter-octet time fill.
 The Flag Sequence MUST be transmitted during inter-frame time fill.
4.4.2. Asynchronous
 Inter-octet time fill MUST be accomplished by transmitting continuous
 "1" bits (mark-hold state).
 Inter-frame time fill can be viewed as extended inter-octet time
 fill. Doing so can save one octet for every frame, decreasing delay
 and increasing bandwidth. This is possible since a Flag Sequence may
 serve as both a frame end and a frame begin. After having received
 any frame, an idle receiver will always be in a frame begin state.
 Robust transmitters should avoid using this trick over-zealously,
 since the price for decreased delay is decreased reliability. Noisy
 links may cause the receiver to receive garbage characters and
 interpret them as part of an incoming frame. If the transmitter does
 not send a new opening Flag Sequence before sending the next frame,
 then that frame will be appended to the noise characters causing an
 invalid frame (with high reliability).
 It is suggested that implementations will achieve the best results by
 always sending an opening Flag Sequence if the new frame is not
 back-to-back with the last. Transmitters SHOULD send an open Flag
 Sequence whenever "appreciable time" has elapsed after the prior
 closing Flag Sequence. The maximum value for "appreciable time" is
 likely to be no greater than the typing rate of a slow typist, about
 1 second.
4.5. Transmission Considerations
4.5.1. Octet-synchronous
 The definition of various encodings and scrambling is the
 responsibility of the DTE/DCE equipment in use, and is outside the
 scope of this specification.
4.5.2. Asynchronous
 All octets are transmitted least significant bit first, with one
 start bit, eight bits of data, and one stop bit. There is no
 provision for seven bit asynchronous links.
5. Bit-stuffed framing
 This chapter summarizes the use of HDLC-like framing with bit-
 synchronous links.
5.1. Flag Sequence
 The Flag Sequence indicates the beginning or end of a frame, and is
 used for frame synchronization. The bit stream is examined on a
 bit-by-bit basis for the binary sequence 01111110 (hexadecimal 0x7e).
 The "shared zero mode" Flag Sequence "011111101111110" SHOULD NOT be
 used. When not avoidable, such an implementation MUST ensure that
 the first Flag Sequence detected (the end of the frame) is promptly
 communicated to the link layer. Use of the shared zero mode hinders
 interoperability with bit-synchronous to asynchronous and bit-
 synchronous to octet-synchronous converters.
5.2. Transparency
 After FCS computation, the transmitter examines the entire frame
 between the two Flag Sequences. A "0" bit is inserted after all
 sequences of five contiguous "1" bits (including the last 5 bits of
 the FCS) to ensure that a Flag Sequence is not simulated.
 On reception, prior to FCS computation, any "0" bit that directly
 follows five contiguous "1" bits is discarded.
5.3. Invalid Frames
 Frames which are too short (less than 4 octets when using the 16-bit
 FCS), or which end with a sequence of more than six "1" bits, are
 silently discarded, and not counted as a FCS error.
5.4. Time Fill
 There is no provision for inter-octet time fill.
 The Flag Sequence SHOULD be transmitted during inter-frame time fill.
 However, certain types of circuit-switched links require the use of
 mark idle (continuous ones), particularly those that calculate
 accounting based on periods of bit activity. When mark idle is used
 on a bit-synchronous link, the implementation MUST ensure at least 15
 consecutive "1" bits between Flags during the idle period, and that
 the Flag Sequence is always generated at the beginning of a frame
 after an idle period.
 This differs from practice in ISO 3309, which allows 7 to 14 bit
 mark idle.
5.5. Transmission Considerations
 All octets are transmitted least significant bit first.
 The definition of various encodings and scrambling is the
 responsibility of the DTE/DCE equipment in use, and is outside the
 scope of this specification.
 While PPP will operate without regard to the underlying
 representation of the bit stream, lack of standards for transmission
 will hinder interoperability as surely as lack of data link
 standards. At speeds of 56 Kbps through 2.0 Mbps, NRZ is currently
 most widely available, and on that basis is recommended as a default.
 When configuration of the encoding is allowed, NRZI is recommended as
 an alternative, because of its relative immunity to signal inversion
 configuration errors, and instances when it MAY allow connection
 without an expensive DSU/CSU. Unfortunately, NRZI encoding
 exacerbates the missing x1 factor of the 16-bit FCS, so that one
 error in 2**15 goes undetected (instead of one in 2**16), and triple
 errors are not detected. Therefore, when NRZI is in use, it is
 recommended that the 32-bit FCS be negotiated, which includes the x1
 factor.
 At higher speeds of up to 45 Mbps, some implementors have chosen the
 ANSI High Speed Synchronous Interface [HSSI]. While this experience
 is currently limited, implementors are encouraged to cooperate in
 choosing transmission encoding.
6. Asynchronous to Synchronous Conversion
 There may be some use of asynchronous-to-synchronous converters (some
 built into modems and cellular interfaces), resulting in an
 asynchronous PPP implementation on one end of a link and a
 synchronous implementation on the other. It is the responsibility of
 the converter to do all stuffing conversions during operation.
 To enable this functionality, synchronous PPP implementations MUST
 always respond to the Async-Control-Character-Map Configuration
 Option with the LCP Configure-Ack. However, acceptance of the
 Configuration Option does not imply that the synchronous
 implementation will do any ACCM mapping. Instead, all such octet
 mapping will be performed by the asynchronous-to-synchronous
 converter.
7. Additional LCP Configuration Options
 The Configuration Option format and basic options are already defined
 for LCP [1].
 Up-to-date values of the LCP Option Type field are specified in the
 most recent "Assigned Numbers" RFC [10]. This document concerns the
 following values:
 2 Async-Control-Character-Map
7.1. Async-Control-Character-Map (ACCM)
 Description
 This Configuration Option provides a method to negotiate the use
 of control character transparency on asynchronous links.
 Each end of the asynchronous link maintains two Async-Control-
 Character-Maps. The receiving ACCM is 32 bits, but the sending
 ACCM may be up to 256 bits. This results in four distinct ACCMs,
 two in each direction of the link.
 For asynchronous links, the default receiving ACCM is 0xffffffff.
 The default sending ACCM is 0xffffffff, plus the Control Escape
 and Flag Sequence characters themselves, plus whatever other
 outgoing characters are flagged (by prior configuration) as likely
 to be intercepted.
 For other types of links, the default value is 0, since there is
 no need for mapping.
 The default inclusion of all octets less than hexadecimal 0x20
 allows all ASCII control characters [6] excluding DEL (Delete)
 to be transparently communicated through all known data
 communications equipment.
 The transmitter MAY also send octets with values in the range 0x40
 through 0xff (except 0x5e) in Control Escape format. Since these
 octet values are not negotiable, this does not solve the problem
 of receivers which cannot handle all non-control characters.
 Also, since the technique does not affect the 8th bit, this does
 not solve problems for communications links that can send only 7-
 bit characters.
 Note that this specification differs in detail from later
 amendments, such as 3309:1991/Amendment 2 [3]. However, such
 "extended transparency" is applied only by "prior agreement".
 Use of the transparency methods in this specification
 constitute a prior agreement with respect to PPP.
 For compatibility with 3309:1991/Amendment 2, the transmitter
 MAY escape DEL and ACCM equivalents with the 8th (most
 significant) bit set. No change is required in the receiving
 algorithm.
 Following ACCM negotiation, the transmitter SHOULD cease
 escaping DEL.
 However, it is rarely necessary to map all control characters, and
 often it is unnecessary to map any control characters. The
 Configuration Option is used to inform the peer which control
 characters MUST remain mapped when the peer sends them.
 The peer MAY still send any other octets in mapped format, if it
 is necessary because of constraints known to the peer. The peer
 SHOULD Configure-Nak with the logical union of the sets of mapped
 octets, so that when such octets are spuriously introduced they
 can be ignored on receipt.
 A summary of the Async-Control-Character-Map Configuration Option
 format is shown below. The fields are transmitted from left to
 right.
 0 1 2 3
 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
 | Type | Length | ACCM
 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
 ACCM (cont) |
 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
 Type
 2
 Length
 6
 ACCM
 The ACCM field is four octets, and indicates the set of control
 characters to be mapped. The map is sent most significant octet
 first.
 Each numbered bit corresponds to the octet of the same value. If
 the bit is cleared to zero, then that octet need not be mapped.
 If the bit is set to one, then that octet MUST remain mapped. For
 example, if bit 19 is set to zero, then the ASCII control
 character 19 (DC3, Control-S) MAY be sent in the clear.
 Note: The least significant bit of the least significant octet
 (the final octet transmitted) is numbered bit 0, and would map
 to the ASCII control character NUL.
A. Recommended LCP Options
 The following Configurations Options are recommended:
 High Speed links
 Magic Number
 Link Quality Monitoring
 No Address and Control Field Compression
 No Protocol Field Compression
 Low Speed or Asynchronous links
 Async Control Character Map
 Magic Number
 Address and Control Field Compression
 Protocol Field Compression
B. Automatic Recognition of PPP Frames
 It is sometimes desirable to detect PPP frames, for example during a
 login sequence. The following octet sequences all begin valid PPP
 LCP frames:
 7e ff 03 c0 21
 7e ff 7d 23 c0 21
 7e 7d df 7d 23 c0 21
 Note that the first two forms are not a valid username for Unix.
 However, only the third form generates a correctly checksummed PPP
 frame, whenever 03 and ff are taken as the control characters ETX and
 DEL without regard to parity (they are correct for an even parity
 link) and discarded.
 Many implementations deal with this by putting the interface into
 packet mode when one of the above username patterns are detected
 during login, without examining the initial PPP checksum. The
 initial incoming PPP frame is discarded, but a Configure-Request is
 sent immediately.
C. Fast Frame Check Sequence (FCS) Implementation
 The FCS was originally designed with hardware implementations in
 mind. A serial bit stream is transmitted on the wire, the FCS is
 calculated over the serial data as it goes out, and the complement of
 the resulting FCS is appended to the serial stream, followed by the
 Flag Sequence.
 The receiver has no way of determining that it has finished
 calculating the received FCS until it detects the Flag Sequence.
 Therefore, the FCS was designed so that a particular pattern results
 when the FCS operation passes over the complemented FCS. A good
 frame is indicated by this "good FCS" value.
C.1. FCS table generator
 The following code creates the lookup table used to calculate the
 FCS-16.
 /*
 * Generate a FCS-16 table.
 *
 * Drew D. Perkins at Carnegie Mellon University.
 *
 * Code liberally borrowed from Mohsen Banan and D. Hugh Redelmeier.
 */
 /*
 * The FCS-16 generator polynomial: x**0 + x**5 + x**12 + x**16.
 */
 #define P 0x8408
 main()
 {
 register unsigned int b, v;
 register int i;
 printf("typedef unsigned short u16;\n");
 printf("static u16 fcstab[256] = {");
 for (b = 0; ; ) {
 if (b % 8 == 0)
 printf("\n");
 v = b;
 for (i = 8; i--; )
 v = v & 1 ? (v >> 1) ^ P : v >> 1;
 printf("\t0x%04x", v & 0xFFFF);
 if (++b == 256)
 break;
 printf(",");
 }
 printf("\n};\n");
 }
C.2. 16-bit FCS Computation Method
 The following code provides a table lookup computation for
 calculating the Frame Check Sequence as data arrives at the
 interface. This implementation is based on [7], [8], and [9].
 /*
 * u16 represents an unsigned 16-bit number. Adjust the typedef for
 * your hardware.
 */
 typedef unsigned short u16;
 /*
 * FCS lookup table as calculated by the table generator.
 */
 static u16 fcstab[256] = {
 0x0000, 0x1189, 0x2312, 0x329b, 0x4624, 0x57ad, 0x6536, 0x74bf,
 0x8c48, 0x9dc1, 0xaf5a, 0xbed3, 0xca6c, 0xdbe5, 0xe97e, 0xf8f7,
 0x1081, 0x0108, 0x3393, 0x221a, 0x56a5, 0x472c, 0x75b7, 0x643e,
 0x9cc9, 0x8d40, 0xbfdb, 0xae52, 0xdaed, 0xcb64, 0xf9ff, 0xe876,
 0x2102, 0x308b, 0x0210, 0x1399, 0x6726, 0x76af, 0x4434, 0x55bd,
 0xad4a, 0xbcc3, 0x8e58, 0x9fd1, 0xeb6e, 0xfae7, 0xc87c, 0xd9f5,
 0x3183, 0x200a, 0x1291, 0x0318, 0x77a7, 0x662e, 0x54b5, 0x453c,
 0xbdcb, 0xac42, 0x9ed9, 0x8f50, 0xfbef, 0xea66, 0xd8fd, 0xc974,
 0x4204, 0x538d, 0x6116, 0x709f, 0x0420, 0x15a9, 0x2732, 0x36bb,
 0xce4c, 0xdfc5, 0xed5e, 0xfcd7, 0x8868, 0x99e1, 0xab7a, 0xbaf3,
 0x5285, 0x430c, 0x7197, 0x601e, 0x14a1, 0x0528, 0x37b3, 0x263a,
 0xdecd, 0xcf44, 0xfddf, 0xec56, 0x98e9, 0x8960, 0xbbfb, 0xaa72,
 0x6306, 0x728f, 0x4014, 0x519d, 0x2522, 0x34ab, 0x0630, 0x17b9,
 0xef4e, 0xfec7, 0xcc5c, 0xddd5, 0xa96a, 0xb8e3, 0x8a78, 0x9bf1,
 0x7387, 0x620e, 0x5095, 0x411c, 0x35a3, 0x242a, 0x16b1, 0x0738,
 0xffcf, 0xee46, 0xdcdd, 0xcd54, 0xb9eb, 0xa862, 0x9af9, 0x8b70,
 0x8408, 0x9581, 0xa71a, 0xb693, 0xc22c, 0xd3a5, 0xe13e, 0xf0b7,
 0x0840, 0x19c9, 0x2b52, 0x3adb, 0x4e64, 0x5fed, 0x6d76, 0x7cff,
 0x9489, 0x8500, 0xb79b, 0xa612, 0xd2ad, 0xc324, 0xf1bf, 0xe036,
 0x18c1, 0x0948, 0x3bd3, 0x2a5a, 0x5ee5, 0x4f6c, 0x7df7, 0x6c7e,
 0xa50a, 0xb483, 0x8618, 0x9791, 0xe32e, 0xf2a7, 0xc03c, 0xd1b5,
 0x2942, 0x38cb, 0x0a50, 0x1bd9, 0x6f66, 0x7eef, 0x4c74, 0x5dfd,
 0xb58b, 0xa402, 0x9699, 0x8710, 0xf3af, 0xe226, 0xd0bd, 0xc134,
 0x39c3, 0x284a, 0x1ad1, 0x0b58, 0x7fe7, 0x6e6e, 0x5cf5, 0x4d7c,
 0xc60c, 0xd785, 0xe51e, 0xf497, 0x8028, 0x91a1, 0xa33a, 0xb2b3,
 0x4a44, 0x5bcd, 0x6956, 0x78df, 0x0c60, 0x1de9, 0x2f72, 0x3efb,
 0xd68d, 0xc704, 0xf59f, 0xe416, 0x90a9, 0x8120, 0xb3bb, 0xa232,
 0x5ac5, 0x4b4c, 0x79d7, 0x685e, 0x1ce1, 0x0d68, 0x3ff3, 0x2e7a,
 0xe70e, 0xf687, 0xc41c, 0xd595, 0xa12a, 0xb0a3, 0x8238, 0x93b1,
 0x6b46, 0x7acf, 0x4854, 0x59dd, 0x2d62, 0x3ceb, 0x0e70, 0x1ff9,
 0xf78f, 0xe606, 0xd49d, 0xc514, 0xb1ab, 0xa022, 0x92b9, 0x8330,
 0x7bc7, 0x6a4e, 0x58d5, 0x495c, 0x3de3, 0x2c6a, 0x1ef1, 0x0f78
 };
 #define PPPINITFCS16 0xffff /* Initial FCS value */
 #define PPPGOODFCS16 0xf0b8 /* Good final FCS value */
 /*
 * Calculate a new fcs given the current fcs and the new data.
 */
 u16 pppfcs16(fcs, cp, len)
 register u16 fcs;
 register unsigned char *cp;
 register int len;
 {
 ASSERT(sizeof (u16) == 2);
 ASSERT(((u16) -1) > 0);
 while (len--)
 fcs = (fcs >> 8) ^ fcstab[(fcs ^ *cp++) & 0xff];
 return (fcs);
 }
 /*
 * How to use the fcs
 */
 tryfcs16(cp, len)
 register unsigned char *cp;
 register int len;
 {
 u16 trialfcs;
 /* add on output */
 trialfcs = pppfcs16( PPPINITFCS16, cp, len );
 trialfcs ^= 0xffff; /* complement */
 cp[len] = (trialfcs & 0x00ff); /* least significant byte first */
 cp[len+1] = ((trialfcs >> 8) & 0x00ff);
 /* check on input */
 trialfcs = pppfcs16( PPPINITFCS16, cp, len + 2 );
 if ( trialfcs == PPPGOODFCS16 )
 printf("Good FCS\n");
 }
C.3. 32-bit FCS Computation Method
 The following code provides a table lookup computation for
 calculating the 32-bit Frame Check Sequence as data arrives at the
 interface.
 /*
 * The FCS-32 generator polynomial: x**0 + x**1 + x**2 + x**4 + x**5
 * + x**7 + x**8 + x**10 + x**11 + x**12 + x**16
 * + x**22 + x**23 + x**26 + x**32.
 */
 /*
 * u32 represents an unsigned 32-bit number. Adjust the typedef for
 * your hardware.
 */
 typedef unsigned long u32;
 static u32 fcstab_32[256] =
 {
 0x00000000, 0x77073096, 0xee0e612c, 0x990951ba,
 0x076dc419, 0x706af48f, 0xe963a535, 0x9e6495a3,
 0x0edb8832, 0x79dcb8a4, 0xe0d5e91e, 0x97d2d988,
 0x09b64c2b, 0x7eb17cbd, 0xe7b82d07, 0x90bf1d91,
 0x1db71064, 0x6ab020f2, 0xf3b97148, 0x84be41de,
 0x1adad47d, 0x6ddde4eb, 0xf4d4b551, 0x83d385c7,
 0x136c9856, 0x646ba8c0, 0xfd62f97a, 0x8a65c9ec,
 0x14015c4f, 0x63066cd9, 0xfa0f3d63, 0x8d080df5,
 0x3b6e20c8, 0x4c69105e, 0xd56041e4, 0xa2677172,
 0x3c03e4d1, 0x4b04d447, 0xd20d85fd, 0xa50ab56b,
 0x35b5a8fa, 0x42b2986c, 0xdbbbc9d6, 0xacbcf940,
 0x32d86ce3, 0x45df5c75, 0xdcd60dcf, 0xabd13d59,
 0x26d930ac, 0x51de003a, 0xc8d75180, 0xbfd06116,
 0x21b4f4b5, 0x56b3c423, 0xcfba9599, 0xb8bda50f,
 0x2802b89e, 0x5f058808, 0xc60cd9b2, 0xb10be924,
 0x2f6f7c87, 0x58684c11, 0xc1611dab, 0xb6662d3d,
 0x76dc4190, 0x01db7106, 0x98d220bc, 0xefd5102a,
 0x71b18589, 0x06b6b51f, 0x9fbfe4a5, 0xe8b8d433,
 0x7807c9a2, 0x0f00f934, 0x9609a88e, 0xe10e9818,
 0x7f6a0dbb, 0x086d3d2d, 0x91646c97, 0xe6635c01,
 0x6b6b51f4, 0x1c6c6162, 0x856530d8, 0xf262004e,
 0x6c0695ed, 0x1b01a57b, 0x8208f4c1, 0xf50fc457,
 0x65b0d9c6, 0x12b7e950, 0x8bbeb8ea, 0xfcb9887c,
 0x62dd1ddf, 0x15da2d49, 0x8cd37cf3, 0xfbd44c65,
 0x4db26158, 0x3ab551ce, 0xa3bc0074, 0xd4bb30e2,
 0x4adfa541, 0x3dd895d7, 0xa4d1c46d, 0xd3d6f4fb,
 0x4369e96a, 0x346ed9fc, 0xad678846, 0xda60b8d0,
 0x44042d73, 0x33031de5, 0xaa0a4c5f, 0xdd0d7cc9,
 0x5005713c, 0x270241aa, 0xbe0b1010, 0xc90c2086,
 0x5768b525, 0x206f85b3, 0xb966d409, 0xce61e49f,
 0x5edef90e, 0x29d9c998, 0xb0d09822, 0xc7d7a8b4,
 0x59b33d17, 0x2eb40d81, 0xb7bd5c3b, 0xc0ba6cad,
 0xedb88320, 0x9abfb3b6, 0x03b6e20c, 0x74b1d29a,
 0xead54739, 0x9dd277af, 0x04db2615, 0x73dc1683,
 0xe3630b12, 0x94643b84, 0x0d6d6a3e, 0x7a6a5aa8,
 0xe40ecf0b, 0x9309ff9d, 0x0a00ae27, 0x7d079eb1,
 0xf00f9344, 0x8708a3d2, 0x1e01f268, 0x6906c2fe,
 0xf762575d, 0x806567cb, 0x196c3671, 0x6e6b06e7,
 0xfed41b76, 0x89d32be0, 0x10da7a5a, 0x67dd4acc,
 0xf9b9df6f, 0x8ebeeff9, 0x17b7be43, 0x60b08ed5,
 0xd6d6a3e8, 0xa1d1937e, 0x38d8c2c4, 0x4fdff252,
 0xd1bb67f1, 0xa6bc5767, 0x3fb506dd, 0x48b2364b,
 0xd80d2bda, 0xaf0a1b4c, 0x36034af6, 0x41047a60,
 0xdf60efc3, 0xa867df55, 0x316e8eef, 0x4669be79,
 0xcb61b38c, 0xbc66831a, 0x256fd2a0, 0x5268e236,
 0xcc0c7795, 0xbb0b4703, 0x220216b9, 0x5505262f,
 0xc5ba3bbe, 0xb2bd0b28, 0x2bb45a92, 0x5cb36a04,
 0xc2d7ffa7, 0xb5d0cf31, 0x2cd99e8b, 0x5bdeae1d,
 0x9b64c2b0, 0xec63f226, 0x756aa39c, 0x026d930a,
 0x9c0906a9, 0xeb0e363f, 0x72076785, 0x05005713,
 0x95bf4a82, 0xe2b87a14, 0x7bb12bae, 0x0cb61b38,
 0x92d28e9b, 0xe5d5be0d, 0x7cdcefb7, 0x0bdbdf21,
 0x86d3d2d4, 0xf1d4e242, 0x68ddb3f8, 0x1fda836e,
 0x81be16cd, 0xf6b9265b, 0x6fb077e1, 0x18b74777,
 0x88085ae6, 0xff0f6a70, 0x66063bca, 0x11010b5c,
 0x8f659eff, 0xf862ae69, 0x616bffd3, 0x166ccf45,
 0xa00ae278, 0xd70dd2ee, 0x4e048354, 0x3903b3c2,
 0xa7672661, 0xd06016f7, 0x4969474d, 0x3e6e77db,
 0xaed16a4a, 0xd9d65adc, 0x40df0b66, 0x37d83bf0,
 0xa9bcae53, 0xdebb9ec5, 0x47b2cf7f, 0x30b5ffe9,
 0xbdbdf21c, 0xcabac28a, 0x53b39330, 0x24b4a3a6,
 0xbad03605, 0xcdd70693, 0x54de5729, 0x23d967bf,
 0xb3667a2e, 0xc4614ab8, 0x5d681b02, 0x2a6f2b94,
 0xb40bbe37, 0xc30c8ea1, 0x5a05df1b, 0x2d02ef8d
 };
 #define PPPINITFCS32 0xffffffff /* Initial FCS value */
 #define PPPGOODFCS32 0xdebb20e3 /* Good final FCS value */
 /*
 * Calculate a new FCS given the current FCS and the new data.
 */
 u32 pppfcs32(fcs, cp, len)
 register u32 fcs;
 register unsigned char *cp;
 register int len;
 {
 ASSERT(sizeof (u32) == 4);
 ASSERT(((u32) -1) > 0);
 while (len--)
 fcs = (((fcs) >> 8) ^ fcstab_32[((fcs) ^ (*cp++)) & 0xff]);
 return (fcs);
 }
 /*
 * How to use the fcs
 */
 tryfcs32(cp, len)
 register unsigned char *cp;
 register int len;
 {
 u32 trialfcs;
 /* add on output */
 trialfcs = pppfcs32( PPPINITFCS32, cp, len );
 trialfcs ^= 0xffffffff; /* complement */
 cp[len] = (trialfcs & 0x00ff); /* least significant byte first */
 cp[len+1] = ((trialfcs >>= 8) & 0x00ff);
 cp[len+2] = ((trialfcs >>= 8) & 0x00ff);
 cp[len+3] = ((trialfcs >> 8) & 0x00ff);
 /* check on input */
 trialfcs = pppfcs32( PPPINITFCS32, cp, len + 4 );
 if ( trialfcs == PPPGOODFCS32 )
 printf("Good FCS\n");
 }
Security Considerations
 As noted in the Physical Layer Requirements section, the link layer
 might not be informed when the connected state of the physical layer
 has changed. This results in possible security lapses due to over-
 reliance on the integrity and security of switching systems and
 administrations. An insertion attack might be undetected. An
 attacker which is able to spoof the same calling identity might be
 able to avoid link authentication.
References
 [1] Simpson, W., Editor, "The Point-to-Point Protocol (PPP)", 
 STD 50, RFC 1661, Daydreamer, July 1994.
 [2] ISO/IEC 3309:1991(E), "Information Technology -
 Telecommunications and information exchange between systems -
 High-level data link control (HDLC) procedures - Frame
 structure", International Organization For Standardization,
 Fourth edition 1991年06月01日.
 [3] ISO/IEC 3309:1991/Amd.2:1992(E), "Information Technology -
 Telecommunications and information exchange between systems -
 High-level data link control (HDLC) procedures - Frame
 structure - Amendment 2: Extended transparency options for
 start/stop transmission", International Organization For
 Standardization, 1992年01月15日.
 [4] ISO/IEC 4335:1991(E), "Information Technology -
 Telecommunications and information exchange between systems -
 High-level data link control (HDLC) procedures - Elements of
 procedures", International Organization For Standardization,
 Fourth edition 1991年09月15日.
 [5] Simpson, W., Editor, "PPP LCP Extensions", RFC 1570, 
 Daydreamer, January 1994.
 [6] ANSI X3.4-1977, "American National Standard Code for
 Information Interchange", American National Standards
 Institute, 1977.
 [7] Perez, "Byte-wise CRC Calculations", IEEE Micro, June 1983.
 [8] Morse, G., "Calculating CRC's by Bits and Bytes", Byte,
 September 1986.
 [9] LeVan, J., "A Fast CRC", Byte, November 1987.
 [10] Reynolds, J., and J. Postel, "Assigned Numbers", STD 2, RFC
 1340, USC/Information Sciences Institute, July 1992.
Acknowledgements
 This document is the product of the Point-to-Point Protocol Working
 Group of the Internet Engineering Task Force (IETF). Comments should
 be submitted to the ietf-ppp@merit.edu mailing list.
 This specification is based on previous RFCs, where many
 contributions have been acknowleged.
 The 32-bit FCS example code was provided by Karl Fox (Morning Star
 Technologies).
 Special thanks to Morning Star Technologies for providing computing
 resources and network access support for writing this specification.
Chair's Address
 The working group can be contacted via the current chair:
 Fred Baker
 Advanced Computer Communications
 315 Bollay Drive
 Santa Barbara, California 93117
 fbaker@acc.com
Editor's Address
 Questions about this memo can also be directed to:
 William Allen Simpson
 Daydreamer
 Computer Systems Consulting Services
 1384 Fontaine
 Madison Heights, Michigan 48071
 Bill.Simpson@um.cc.umich.edu
 bsimpson@MorningStar.com