Challenge-response identification (strong authentication)

The idea of cryptographic challenge-response protocols is that one entity (the claimant) “proves” its identity to another entity (the verifier) by demonstrating knowledge of a secret known to be associated with that entity, without revealing the secret itself to the verifier during the protocol.3 This is done by providing a response to a time-variant challenge, where the response depends on both the entity’s secret and the challenge. The challenge is typically a number chosen by one entity (randomly and secretly) at the outset of the protocol. If the communications line is monitored, the response from one execution of the identification protocol should not provide an adversary with useful information for a subsequent identification, as subsequent challenges will differ.

Before considering challenge-response identification protocols based on symmetric- key techniques (§10.3.2), public-key techniques (§10.3.3), and zero-knowledge concepts (§10.4), background on time-variant parameters is first provided.

Background on time-variant parameters

Time-variant parameters may be used in identification protocols to counteract replay and interleaving attacks (see § 10.5), to provide uniqueness or timeliness guarantees, and to prevent certain chosen-text attacks. They may similarly be used in authenticated key establishment protocols (Chapter 12), and to provide uniqueness guarantees in conjunction with message authentication (Chapter 9).

Time-variant parameters which serve to distinguish one protocol instance from another are sometimes called nonces, unique numbers, or non-repeating values-, definitions of these terms have traditionally been loose, as the specific properties required depend on the actual usage and protocol.

10.9 Definition A nonce is a value used no more than once for the same purpose. It typically serves to prevent (undetectable) replay. [1]

The term notice is most often used to refer to a “random” number in a challenge-response protocol, but the required randomness properties vary. Three mam classes of time-variant parameters are discussed in turn below: random numbers, sequence numbers, and time- stamps. Often, to ensure protocol security, the integrity of such parameters must be guaranteed (e.g., by cryptographically binding them with other data in a challenge-response sequence). This is particularly true of protocols in which the only requirement of a time- variant parameter is uniqueness, e.g., as provided by a never-repeated sequential counter.[2]

Following are some miscellaneous points about time-variant parameters.

  • 1. Verifiable timeliness may be provided through use of random numbers in challenge- response mechanisms, timestamps in conjunction with distributed timeclocks, or sequence numbers in conjunction with the maintenance of pairwise (claimant, verifier) state information.
  • 2. To provide timeliness or uniqueness guarantees, the verifier in the protocol controls the time-variant parameter, either directly (through choice of a random number) or indirectly (through information maintained regarding a shared sequence, or logically through a common time clock).
  • 3. To uniquely identify a message or sequence of messages (protocol instance), nonces drawn from a monotonically increasing sequence may be used (e.g., sequence or serial numbers, and timestamps, if guaranteed to be increasing and unique), or random numbers of sufficient size. Uniqueness is often required only within a given key lifetime or time wmdow.
  • 4. Combinations of time-variant parameters may be used, e.g., random numbers concatenated to timestamps or sequence numbers. This may guarantee that a pseudorandom number is not duplicated.
  • (i) Random numbers

Random numbers may be used in challenge-response mechanisms, to provide uniqueness and timeliness assurances, and to preclude certain replay and interleaving attacks (see § 10.5, including Remark 10.42). Random numbers may also serve to provide unpredictability, for example, to preclude chosen-text attacks.

The term random numbers, when used in the context of identification and authentication protocols, includes pseudorandom numbers which are unpredictable to an adversary (see Remark 10.11); this differs from randomness in the traditional statistical sense. In protocol descriptions, “choose a random number” is usually intended to mean “pick a number with uniform distribution from a specified sample space” or “select from a uniform distribution”.

Random numbers are used in challenge-response protocols as follows. One entity includes a (new) random number in an outgoing message. An incoming message subsequently received (e.g., the next protocol message of the same protocol instance), whose construction required knowledge of this nonce and to which this nonce is inseparably bound, is then deemed to be fresh (Remark 10.10) based on the reasoning that the random number links the two messages. The non-tamperable binding is required to prevent appending a nonce to an old message.

Random numbers used in this manner serve to fix a relative point in time for the parties involved, analogous to a shared timeclock. The maximum allowable time between protocol messages is typically constrained by a timeout period, enforced using local, independent countdown timers.

  • 10.10 Remark (freshness) In the context of challenge-response protocols, fresh typically means recent, in the sense of having originated subsequent to the beginning of the current protocol instance. Note that such freshness alone does not rule out interleaving attacks using parallel sessions (see §10.5).
  • 10.11 Remark (birthday repetitions in random numbers) In generating pseudorandom numbers for use as time-variant parameters, it suffices if the probability of a repeated number is acceptably low and if numbers are not intentionally reused. This may be achieved by selecting the random value from a sufficiently large sample space, taking into account coincidences arising from the birthday paradox. The latter may be addressed by either using a larger sample space, or by using a generation process guaranteed to avoid repetition (e.g., a bijection), such as using the counter or OFB mode of a block cipher (§7.2.2).
  • 10.12 Remark (disadvantages of random numbers) Many protocols involving random numbers require the generation of cryptographically secure (i.e., unpredictable) random numbers. If pseudorandom number generators are used, an initial seed with sufficient entropy is required. When random numbers are used in challenge-response mechanisms in place of timestamps, typically the protocol involves one additional message, and the challenger must temporarily maintain state information, but only until the response is verified.
  • (ii) Sequence numbers

A sequence number (serial number, or counter value) serves as a unique number identifying a message, and is typically used to detect message replay. For stored files, sequence numbers may serve as version numbers for the file in question. Sequence numbers are specific to a particular pair of entities, and must explicitly or implicitly be associated with both the originator and recipient of a message; distinct sequences are customarily necessary for messages from A to В and from В to A.

Parties follow a pre-defined policy for message numbering. A message is accepted only if the sequence number therein has not been used previously (or not used previously within a specified tune period), and satisfies the agreed policy. The simplest policy is that a sequence number starts at zero, is incremented sequentially, and each successive message has a number one greater than the previous one received. A less restrictive policy is that sequence numbers need (only) be monotonically increasing; this allows for lost messages due to non-malicious communications errors, but precludes detection of messages lost due to adversarial intervention.

10.13 Remark (disadvantages of sequence numbers) Use of sequence numbers requires an overhead as follows: each claimant must record and maintain long-term pairwise state information for each possible verifier, sufficient to determine previously used and/or still valid sequence numbers. Special procedures (e.g., for resetting sequence numbers) may be necessary following circumstances disrupting normal sequencing (e.g., system failures). Forced delays are not detectable in general. As a consequence of the overhead and synchronization necessary, sequence numbers are most appropriate for smaller, closed groups. [3]

Timestamps function as follows. The party originating a message obtains a timestamp from its local (host) clock, and cryptographically binds it to a message. Upon receiving a time-stamped message, the second party obtains the current time from its own (host) clock, and subtracts the timestamp received. The received message is valid provided:

  • 1. the timestamp difference is within the acceptance window (a fixed-size time interval, e.g., 10 milliseconds or 20 seconds, selected to account for the maximum message transit and processing time, plus clock skew); and
  • 2. (optionally) no message with an identical timestamp has been previously received from the same originator. This check may be made by the verifier maintaining a list of all timestamps received from each source entity within the current acceptance window. Another method is to record the latest (valid) timestamp used by each source (in this case the verifier accepts only strictly increasing time values).

The security of timestamp-based verification relies on use of a common time reference. This requires that host clocks be available and both “loosely synchronized'' and secured from modification. Synchronization is necessary to counter clock drift, and must be appropriate to accommodate the acceptance window used. The degree of clock skew allowed, and the acceptance window, must be appropriately small to preclude message replay if the above optional check is omitted. The timeclock must be secure to prevent adversarial resetting of a clock backwards so as to restore the validity of old messages, or setting a clock forward to prepare a message for some future point in time (cf. Note 10.7).

  • 10.14 Remark (disadvantages of timestamps) Timestamp-based protocols require that time- clocks be both synchronized and secured. The preclusion of adversarial modification of local timeclocks is difficult to guarantee in many distributed environments; in this case, the security provided must be carefully re-evaluated. Maintaining lists of used timestamps within the current window has the drawback of a potentially large storage requirement, and corresponding verification overhead. While technical solutions exist for synchronizing distributed clocks, if synchronization is accomplished via network protocols, such protocols themselves must be secure, which typically requires authentication; this leads to a circular security argument if such authentication is itself timestamp-based.
  • 10.15 Remark (comparison of time-variant parameters) Timestamps in protocols offer the advantage of fewer messages (typically by one), and no requirement to maintain pan-wise long-term state information (cf. sequence numbers) or per-connection short-term state information (cf. random numbers). Minimizing state information is particularly important for servers in client-server applications. The main drawback of timestamps is the requirement of maintaining secure, synchronized distributed timeclocks. Timestamps in protocols may typically be replaced by a random number challenge plus a return message.

  • [1] In some mechanisms, the secret is known to die verifier, and is used to verify die response; in odiers, die secretneed not actually be known by the verifier.
  • [2] Such predictable parameters differ from sequence numbers in that they might not be bound to any stored state.Without appropriate cryptographic binding, a potential concern then is a pre-play attack wherein an adversaryobtains the response before the time-variant parameter is legitnnately sent (see Note 10.7).
  • [3] Timestamps Timestamps may be used to provide timeliness and uniqueness guarantees, to detect message replay. They may also be used to implement time-limited access privileges, and todetect forced delays.
 
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