A method for detecting a speed violation of a vehicle

A Method for Detecting a Speed Violation of a Vehicle

The present invention relates to a method for detecting a speed violation of a vehicle traveling from a first roadside system to a second roadside system, also called “section control”.

The term section control refers to a technical system for the measurement of speeds of vehicles on road segments. Contrary to a standard speed trap, which measures the speed of a bypassing vehicle at a certain point (e.g. by means of a Doppler-radar), a section control system measures the average speed over a certain road-segment It takes notice of the same vehicle passing two geographically distant points within a certain time. The known distance of the measurement devices, hereafter called roadside systems or gantries, in connection with the known travel time permits calculation of the average speed along the section of interest, and subsequent legal actions upon a speed limit violation.

When a section control system is implemented, particular care has to be taken regarding the protection of the identity of an observed vehicle’s driver. In fact, the system must respect the driver’s privacy up to the point when there is evidence of a speed limit violation. In particular, this means that the system should not store or process any personal data for purposes other than detecting a speed limit violation. Identities of drivers that behaved correctly should be protected at all times (i.e. neither be stored or processed any further).

Existing methods for section control (conf. e.g. EP 2 220 634, EP 2 360 647) rely on a comparison of hashed values of vehicle identifiers captured at the first and second roadside systems and, in case of a match, evaluating their clear-text timestamps to calculate travel time and thus the speed of the vehicle between the first and the second roadside systems. When a speed violation is detected, the vehicle identifiers captured at the outset have to be retrieved in the first and second roadside systems on the basis of the hashed values, which requires appropriate look-up tables for the captured evidence data.

All prior art systems are still incomplete regarding data protection and user privacy since the travel time of a vehicle is public, even when there is no speed violation, and since the originally captured evidence data stored in the roadside systems is prone to intruder attacks.

It is therefore an object of the present invention to provide a method for section control with improved security and privacy.

To this end, the invention provides for a method for detecting a speed violation of a vehicle traveling from a first roadside system to a second roadside system, comprising:

setting-up private and public parameters, including a common modulo basis, of an identity based encryption (1BE) scheme in a key generation center and the first and second roadside systems;

capturing at least an identifier of the vehicle and a first timestamp at the first roadside system as first evidence data, using at least the first identifier and first timestamp as a first identity to generate a first 1BE public key, encrypting the first evidence data with a first random session

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-2key, encrypting the first random session key with the first IBE public key, and deleting the first evidence data and the first session key at the first roadside system;

capturing at least an identifier of the vehicle and a second timestamp at the second roadside system as second evidence data, using at least the second identifier and second timestamp as a second identity to generate a second IBE public key, encrypting the second evidence data with a second random session key, encrypting the second random session key with the second IBE public key, and deleting the second evidence data and the second session key at the second roadside system;

calculating a ratio of the first and second public keys, modulo the common modulo basis, and looking-up the ratio in a table of ratios pre-computed for a set of time differences between said first and second timestamps which set represents speed violations, and, when the look-up is successful:

retrieving at least one IBE private key for at least one of said IBE public keys from the key generation center, decrypting at least one of said encrypted session keys with said private key, and decrypting at least one of said encrypted evidence data with said decrypted session key.

By integrating the timestamps of the vehicle passages at the first and second roadside systems into the first and second identities of an IBE encryption scheme, the travel time of a vehicle is completely concealed in cases where there is no speed violation, providing enhanced privacy. The travel time is only obtained for vehicles that were violating the speed limit and not for others.

Comparing the first and second IBE public keys performs a combined vehicle identifier (e.g. license-plate) match and speed limit (timesump difference) violation check in a single blow. This is a remarkable improvement over the prior art two-stage checks which first verify the equality of vehicle identifiers and upon a match compare the timestamps.

Concurrently, using combined vehicle identifier and timestamp identities in an identity based encryption (IBE) scheme completely seals the identities at the roadside systems and, by means of the public keys based thereon, also the underlying evidence data. This dramatically improves security over intruder attacks at the level of the roadside systems. The central key generation center of the IBE scheme can be better protected by cryptographic, technical and organizational measures than the individual roadsides systems which enhance system security. Each roadside can securely encrypt identities and evidence data; only an operator with access to the key generation center can decrypt the data in case of an actually verified speed violation.

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-3The inventive method has also the following benefits:

) any data collected by a roadside system is only usable in the roadside system for determining whether or not a speed limit violation has happened; there is no semantically meaningful other or further possibility of processing and encrypting this data in a roadside system;

2) evidence data related to a driver’s identity is never stored permanently and can be destroyed immediately and without any traces if no speed limit violation has been discovered. Storage beyond this point in time is only permitted for those vehicles that have provably violated the speed limit;

3) for the period in time in which the vehicle is between two roadside systems, the method ensures that there is no way of extracting the vehicle identifier (e.g. license plate number or any drivers identity) from the data stored in the system;

4) it is impossible to discover that the same vehicle (even without knowing its identifier) has passed several roadside systems, which prevents an adversary from taking travel profiles.

In a preferred embodiment of the invention the IBE scheme is a Boneh-Franklin encryption scheme which is well-studied and has high reliability.

Preferably, the evidence data can be encrypted at the first and/or second roadside system according to a symmetric encryption scheme, in particular according to the advanced encryption standard (AES), ensuring high security.

Security against intruder access and eavesdropping attacks can be further improved when the first and second roadside systems share at least one random or pseudorandom value which is incorporated into the first identity to generate the first IBE public key and into the second identity to generate the second IBE public key. In this way two roadside systems can be “paired”, and the pairing key is a random or pseudorandom value which can optionally be changed routinely. To this end the first and second roadside systems can communicate to synchronously switch from one pseudorandom value to a subsequent pseudorandom value in a series of pseudorandom values.

According to a further preferred embodiment of the invention the first IBE public key is generated in the form

PK:= modp_G with

PKij being the first IBE public key,

LPN, t being the identifier and timestamp of the first evidence data,

Ri being the random or pseudorandom value, g, pc, being public parameters of the IBE scheme,

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-4and the second IBE public key is generated in the form with

PK₂._t being the second IBE public key,

LPN, t being the identifier and timestamp of the second evidence data,

Ri being the random or pseudorandom value, and g, pg being public parameters of the IBE scheme;

and the ratio is preferably calculated in the form

PK_2J PKJ' (modpj

These operations can be implemented efficiently, e.g. by simple bit shifting operations on bit level, and are well-suited for realtime applications.

According to further embodiments of the invention, the first evidence data may comprise a picture of the vehicle taken with a camera at the first roadside system; and/or the second evidence data may comprise a picture of the vehicle taken with a camera at the second roadside system; and/or the first evidence data is cryptographically signed with a signature key of the first roadside system; and/or the second evidence data is cryptographically signed with a signature key of the second roadside system.

In all variants of the invention the first and second IBE public keys, the encrypted first and second session keys and the encrypted first and second evidence data can be optionally deleted after a predetermined period of time. This period can e.g. be set to the maximum travel time it takes for a vehicle with minimum speed-violating travel speed to travel from the first to the second roadside system.

In further embodiments of (he invention the first evidence data may comprise a class of the vehicle captured at the first roadside system. In this case, different tables of IBE public key ratios representative of speed violations can be pre-computed for different classes of vehicles, and the table used for the look-up is chosen according to the captured class of the vehicle.

Alternatively or additionally the first or second evidence data may comprise a weather or road condition captured at the first or second roadside system, different tables of ratios are precomputed for different weather or road conditions, and the table used for the look-up is chosen according to the captured weather or road condition.

The steps of calculating the ratio of the first and second IBE public keys, the subsequent looking-up of the ratio in the pre-computed ratio table and all further steps in case of a speed violation can be performed in either of the first and second roadside systems. To this end, preferably the first IBE public key is sent to the second roadside system, or the second IBE public key is sent to the first roadside system, for calculating the ratio.

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-5Further details, features and advantages of the invention will now become apparent from the following description of preferred embodiments thereof under reference to the accompanying drawings, in which:

Fig. 1 is a block diagram of the high level architecture of the components used in the method 5 of the invention;

Fig. 2 is a flowchart of evidence data preparation and encryption steps in either of the first and second roadside systems within the method of the invention;

Fig. 3 is a sequence diagram of the method of the invention;

Fig. 4 is a sequence diagram of the usage and switching of pseudorandom values of a pseu10 dorandom values series between the first and second roadside systems.

In the example below, we assume the following components and information to be available when describing the system:

• The vehicle class (including single-track and two-track vehicles).

• The current weather and road-conditions, which determine the currently valid speed limit 15 for a specific vehicle class and a given section.

• Synchronized clocks throughout the system with a precision of less than 0.01 sec.

• The roadside systems include roadside cabinets for the electronic equipment, gantries (or any other facilities to affix cameras, e.g. bridges, tunnel portals, poles etc.) which are equipped with cameras that are capable of embedding a time-stamp in the picture. In ad20 dition, we assume the roadside system including a camera to either display via a photo or otherwise provide the following information:

o The face of the driver (insofar legal regulations permit this).

o A unique identification token of the roadside system where the picture has been taken (i.e. a proof of origin of the picture).

o The license-plate number as vehicle identifier.

o The current traffic and weather conditions, including the position and lane of all relevant vehicles.

o A vehicle class detector.

o Other information like the geographical location, roadside system identifier, lane and 30 direction of driving.

• The aforementioned information is available reliably for vehicles passing the roadside system at a speed of up to 250 km/h.

Besides these hypotheses valid for the roadside system, we additionally assume the following:

• All connections between any two entities in the system are SSL-protected, i.e. encrypted 35 and authenticated. State-of-the-art algorithms and key-lengths are employed.

• A central authority, the key-generation center, exists that is protected by cryptographie, technical and organizational measures. In particular, any staff working within this highsecurity domain is trustworthy and any physical access to the respective facilities or data is subject to at least a four-eyes principle.

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-6• Any communication between any two entities in the system uses unique serial numbers to link answers to respective requests (we therefore not explicitly mention the serial number in the subsequent messages and assume it available implicitly).

The high-level architecture (HLA) is displayed in Figure 1. Its main components are the following:

• Roadside systems (RSS): these consist of two roadside system gantries G_h G₂, both of which are equipped with cameras. In each such roadside system gantry, we assume a tamper-proof device (such as a hardware dongle, smartcard, trusted element or cryptoprocessor) available.

• Operator (OP): this is the only entity in the system that gets to see the entire evidence referring to a speed limit violation suspect Its duty is checking the correctness of the suspected violation and - in case of a violation - passing the evidence onwards to the legal authorities.

• Key generation center (KGC): the key generation center’s role is generating the decryption keys for the encrypted evidence upon a signed request from the operator. The necessary hardware and software resides in a high-security domain.

• Legal Authorities: these are not directly part of the technical concept and therefore receive no further discussion in this document

We describe the overall process step-by-step, according to the information flows displayed in Figs. 1 - 3. The process starts when a vehicle passes the first roadside system gantry Gi.

1. The roadside system at gantry G/ notices a vehicle and executes the following steps:

a. Collect all information required for potential legal action. This includes:

• A picture PIC of the vehicle. From the picture, it obtains the license-plate number LPN by means of optical character recognition (OCR). Alternatively, the license-plate number can be replaced or augmented by any identification feature of the vehicle (such as signals from RFID-tokens, color, etc.). Without loss of generality, we shall refer to any unique identification feature of a vehicle as its ‘license-plate number” throughout the remainder of this document, although this means the vehicle identifier in general.

• The vehicle class VC (car, heavy-goods vehicle, etc.).

• A timestamp t (according to the assumptions stated above, we assume synchronized clocks throughout the entire system).

• Additional data AD as required, e.g. the current weather- and road-conditions on the section between Gi and G₂- This respective information is assumed available to both gantries, Gi and G₂.

From its collected data, it creates the evidence dataset as the record D = (LPN, t, VC, PIC, AD, Sig), where Sig is a digital signature of all evidence data. This can be a standard Rivest-Shamir-Adleman (RSA)-signature, taking the roadside system’s secret signature key SK_G to produce Sig from the data (LPN, t, VC, PIC, AD). It can be verified by the operator who authentically knows the respective public key PKg of the roadside system. This is favourable to avoid attacks which are based on submitting faked evidence data to the operator.

-7b. The roadside system creates a fresh random 128 Bit session key K c {0,1}^,2H and encrypts

D by means of AES (advanced encryption standard) giving the encrypted data ED = AES (D, K). Longer session keys are permissible.

c. The roadside system encrypts the session key K by means of identity-based encryption (IBE). An embodiment of the IBE scheme is the Boneh-Franklin encryption scheme described in D. Boneh and M. Franklin: Identity based encryption from the Weil pairing, SIAM J. of Computing, 2003, 32, pp. 586-615; and L. Martin: Introduction to IdentityBased Encryption, Artech House, 2008. The respective public key PKi,_t of the IBE scheme is created (e.g. within a tamper-proof device) as:

PK„ := modp₍, (1) where || denotes the simple bitstring-concatenation, and θ is the bitwise XOR-operation. The parameter pc, is a prime number that is selected sufficiently large to ensure that the discrete logarithm problem is hard (see Table 6). The remaining inputs and parameters are as follows:

• g is a generating element of the EBE scheme, here the generating element of the finite group Z? (the set of integers modulo the prime pc) with multiplication modulo pgIls bit-length can be chosen as recommended in Table 5.

• pad is any suitable padding string to get the desired bit-length in the exponent. Neither its concrete choice nor its secrecy has an impact on the security of the system. Hence, this value can be chosen fixed throughout the entire system. In particular, all roadside systems can use the same padding.

• t is the UNIX (or POSIX) time-stamp when the vehicle passed the roadside system gantry. This is the number of seconds elapsed since midnight coordinated universal time (UTC) of January 1^st 1970, not counting leap seconds. This value is by default available on any UNIX- or Linux-based computing platform.

• Rt is the currently valid randomizer (pseudorandom bitstring) that each roadside system creates on its own. This value can be set individually and independently random for each pair of roadside systems, and can be changed periodically (see below). The bitwise XOR of Ri with the license-plate number (and padding) thwarts brute-force attacks to disclose the driver’s identity. Its generation and synchronization with its neighboring roadside system is discussed later on.

We explicitly remark that the term randomizer henceforth refers to a pseudorandom value (bitstring), rather to the algorithm that creates it (the latter being referred to as a pseudorandom number generator).

Using PKi,_t, the first roadside system of a section pair encrypts the session key to obtain EK = IBE (K, PK>.i).

d. The session-key K and the evidence data D (it’s plain text) are destroyed immediately and permanently after encrypting it.

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e. The roadside system temporarily stores the encrypted session key EK, the public key PK),, and the encrypted evidence data ED in its storage (e.g. harddisk). Depending on the vehicle class and the speed limit that applies to it under the current weather and road-conditions, this entire record is permanently destroyed after a period of AT time units (e.g. seconds).

The “aging” of public keys does not require an absolute timestamp, but can be implemented with a counter that is decremented periodically and deleted as soon as it reaches zero (similarly to a time-to-live field).

Example (calculation of ΔΤ): Assume that G) and G2 are 5 km apart and that the speed limit is 130 km/h on this section. In this case, a vehicle may not pass G? sooner than

AT=———3600« 138.46s \30km!h after it has passed G,. Otherwise» a speed limit violation must have occurred.

Gantry G/ creates a list of public keys for subsequent look-up requests from gantry G₂ (or vice versa). This list can be cleared from outdated public-keys (temporal storage)» i.e. those which are older than NT. A key can be stored along with the time of its creation, i.e. a record can be e.g. of the form (PKi_ft).

Figure 2 displays the details of step I graphically. It is, in general, advisable to perform all cryptographic operations within the security module domain. However, for performance reasons, AES- and IBE-encryption can be done outside the security module (boundary shown as a dashed line in Figure 2), provided that the session key K is destroyed reliably after encrypting the data D and concealing it via IBE.

2. Roadside system gantry G₂ notices a passing vehicle at (a later) time L It performs the same steps as Gt does. In addition, it submits (t,PK₂jf along with additional data (vehicle class, road conditions, weather conditions, etc.) as required, to G/, see message 1 (or vice versa). Alternatively, it is possible to send only the public key along with one additional bit (to indicate which randomizer to use for checking in step 3, see below, within a period of ΔΤafter switching), so as to avoid sending a timestamp (see later on details).

3. At time t' > t, roadside system G/ receives (r, PK₂,_t) from G₂. Roadside system G/ filters its list of public keys and selects a set of n entries, which are relevant for comparison with PK₂j- We denote this (shortened and renamed) list as {ΡΚι,ι. PKi_t2,.... PKt^h The check is performed by calculating

V = PK₂, /^(modpj = gfouw.ipri)®#, )1^4((^^ j (2) for all indices j = 1,2,..., n, and where y has the same bit-length as the timestamps. The products PK^ PK^tmodp_c) can be determined using standard programming libraries for modulo arithmetic and the resulting value V is looked up in a pre-computed table.

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-9The pre-computed lookup-table stores pairs (V, time-difference) of the form displayed in Table 1, where ΔΤ is the time for a travel from G/ to G2 at maximal permitted speed for the slowest vehicle class (e.g. 139 seconds for a 5 km distance at speed 130 km/h). Notice that Table I can be pre-computed and stored as a hash-table (for fast access) in the roadside systems's hardware. Physically impossible values like 0 do not need to be included in the table. Furthermore, for better performance, it is advisable to store more likely timedifferences first and unlikely time-differences last when filling the table initially. Alternatively, the hash-table lookup can be replaced by a binary search within a pre-sorted table (at the cost of getting logarithmic running time for the table-lookup).

<td> V</td><td> Time-Difference</td>

<td> xMODp_f</td><td> 0</td>

<td> /MODp,</td><td> i</td>

<td> ^M0Dp_t</td><td> 2</td>

<td></td><td> •</td>

<td> ?^rM0Dp,</td><td> AT</td>

Table 1 : Pre-computed values for speed limit checking

For efficiency reasons, G2 can send (t, PK2.,'¹) to Gi and have G/ compute and look-up PKzi‘ · PKtj in its table (or vice versa). The contents of Table 1 have to be altered accordingly.

• If the table-lookup comes back negative, i.e. the value V = PK_2t PK;} has not been found, then xly > ΔΤ. This indicates that either x # 0, so that LPN2 Ψ LPNj, i.e. the license-platc numbers are different, or otherwise x = 0 (meaning identical licenseplates) and y = t - tj> ΔΤ, so that no speed limit violation has happened. In either case, we have no suspect of a violation. In particular, this means that the comparison can practically never yield false-negative alarms.

• If the table-lookup came back positive, then the value V = g' (x|y) has been found, and the value xly can be obtained from the table-lookup (“Time-Difference”-column). Observe that the table may only store records for time-differences up to ΔΤ. Notice that the randomizers within PK₂ and PK|j can be assumed identical by virtue of synchronization (cf. below).

We approximate the likelihood of a false-positive as follows: Let N be the number of entries in Table 1. This value depends on ΔΤ (e.g. for ΔΤ = 139 seconds and a timemeasurement with an accuracy of 0.01 seconds, we get N -13900 entries in the table). The probability for a false-positive is roughly

N N &lt;4

Of 11) ₂bitlength(p_c) 2¹⁶⁰ and thus negligible. So upon a positive table-lookup, we have overwhelmingly strong evidence that the same vehicle has passed both roadside systems within a time shorter than ΔΤ. This indicates a speed limit violation, which can be passed on to an operator

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- 10for a manual second check. As far as it regards the automatic checking via the tablelookup, there are practically no false-positive alarms.

4. If a speed limit violation is detected in this way, then Gi responds to Gj accordingly, see message 2 in Figure I (or vice versa, if the table look-up had been made at Gj), and both send their encrypted evidence data ED/, ED₂, public keys ΡΚι. PK2, encrypted session keys ΕΚ/, EK2 and the respective roadside system gantry-IDs G/Di, G/D₂ to the operator. Messages 3 in Figure I (3a and 3b in Figure 3) are sent from Gi to the operator, and are for i = 1. 2 - of the form (PKi,EKi,EDi,GlDi.H(PKilPK2)),whas the last entry Η(ΡΚιϊΡΚ₂) establishes an optional link between the two messages from both roadside systems. The function // is a cryptographically secure hash-function. The operator can acknowledge both messages by sending a short notification to the roadside systems (to prevent an adversary from blocking this conversation in order to hide a speed limit violation).

The correct response from Gi to G₂, message 2 (or vice versa) is formed by sending (PK₂> response) with response c {yes.no} to G2, which assures that G₂ can correctly relate the response to a former query (or vice versa).

5. The operator transmits (PK/ PK₂) to the key generation center and digitally signs his entire request with his secret signature key SK_siiJV (message 4).

6. Upon successful signature verification, the key generation center calculates the decryption keys SK). SK₂ referring to PK), PK₂. Observe that these decryption keys do neither exist elsewhere in the system nor prior to a suspected speed limit violation. The key generation center encrypts the record (SKt, SK2) with the operator's public key PK_op and sends an RSA-ciphertext C = RSA ((SKhSKt),PK_v) back to the operator (message 5).

7. The operator decrypts C with his secret key SK_ap and extracts SK/. SK₂. These are required to decrypt the session keys EK,, EK₂ to obtain the AES-keys K_h K2, which are used to decrypt the evidence data D_t, D₂. After a manual check for a correctly indicated speed limit violation the evidence data can be forwarded to the legal authorities (message 6).

Figure 3 displays the whole process as a sequence diagram.

The process described so far refers to a single vehicle class and optimal road conditions. Depending on the weather conditions and vehicle class, different speed limits may apply. This amounts to using a different parameter ΔΤ when doing the table-lookup upon a request from G2 (or G/). There are two basic ways to implement this:

I. Pre-compute Table I up to the maximum ΔΤ of all vehicle classes, and do the look-up to get the actual travel time (or get a “not found’’ if the travel time was longer than implied by the lowest speed limit on this section). For instance, if a heavy-goods vehicle is limited to 60 km/h (giving SThgs = 300 s) and a car may drive at up to 130 km/h (giving ΔΤ _car = /38 s), then the table is computed up to values g^àr with ΔΤ = max/ ΔΤ hgs> ST _car} = 300 s. This determines the size of the table, and the vehicle class (transmitted as additional data in the query) can be used to decide later, whether the speed limit violation has actually occurred, if the look-up came back positive.

2. Alternatively, a different look-up table (Table 1) can be computed specifically for each vehicle class and speed limit. In that case, the transmitted vehicle class determines which table is used for the look-up by RSS. This avoids the additional check

CA 02Θ03Θ40 2013-01-23 required by the single-table approach and is faster because fewer entries have to be searched for each query. Moreover, this hides travel times of vehicles that have been found in the table, but have not committed a speed-limit violation with respect to their specific vehicle class.

During the system set-up phase, each pair of roadside systems (gantries) can optionally receive a shared randomizer i.e. a random or pseudorandom value. For security, a particular randomizer Ro should not be shared by more than two roadside systems.

Particular care has to be taken when changing the randomizer. Let us call the initial randomizer Ro within both roadside system gantries G/, G2 (established during the system initialization). Within e.g. a tamper-proof device (such as a hardware dongle, smartcard, trusted element, cryptoprocessor et cet.), we generate the next randomizer by hashing the last one, i.e. Rm =

The randomizer should not leave the tamper-proof device nor be accessible in any way from outside, hence equation (I) should be evaluated within the tamper-proof device. Storing the randomizer externally - if needed - should be done in an encrypted fashion.

Table 2 in connection with Figure 4 explains which randomizers are used by Gi. G2 for creating the public keys (“encrypt”) and which randomizer is used by Gi (or G2) when searching its look-up table upon a request from G? (or G/) (“check”).

<td rowspan="2"> Arrival time at RSS gantry G,</td><td colspan="2"> Arrival time at RSS gantry G;</td>

<td> Before</td><td> After</td>

<td> Before Imuci, ΔΤ</td><td> Cassia) encrypt GpR, encrypt G₂:R check: R</td><td> Case (b) encrypt GpR, encrypt G₂:R' check: Gi would check with R' but has deleted the respective public-key by that time, so no speed limit violation has occurred (travel time &gt; AT)</td>

<td> Between - AT and tswitch</td><td> Case (c) encrypt G,:R and R\ encrypt GgR' check: R</td><td> Case(d) encrypt G_hR and R\ encrypt G₂:R' check: R'</td>

<td> After t_nvch</td><td> impossible</td><td> Case(e) encrypt Gr.R\ encrypt GgR' check: R'</td>

Table 2: Randomizer Usage for Public-Key Creation and Checking

Switching the randomizers is preferably done periodically, provided that the validity period of a randomizer is greater than ST in order to avoid synchronization problems. During startup or after a power-failure, G/ and G; could use an authenticated SSL connection to secretly agree on a fresh initial randomizer Ro and start the hash-chain all over again. This can be done using the standard Station-to-Station protocol such as the Diffie-Hellman Key-exchange. However,

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- 12this synchronization “from scratch” might only be needed once in a while, e.g. after a powerfailure, and is not required to happen very frequently. Alternatively, a manual key-exchange (storage of the new R_o on a smartcard and copy it from the smartcard into both RSSs) after a power-failure is as well possible. This avoids the need to store designated cryptographic keys for synchronization in each roadside system.

All traffic from the operator to the KGC can be digitally signed. Notice that it is not required to digitally sign messages 3 from the gantries to the operator, since each roadside system has signed its enciypted evidence data in first instance. This means that no faked evidence data will be accepted for processing by the operator. The respective signature key can be stored in a tamper-proof device. The operator’s secret key is protected by a PiN-code to prevent the adversary having compromised the operator’s hardware from accessing the key, since the operator's signature key is inaccessible without the PIN.

The management of SSL-related keys is up to the particular SSL protocol stack implementation. State-of-the-art key-lengths and algorithms can be employed to this end.

For each component of the system, Table 3 lists the key that it stores, along with the recommended protection for the particular key. The 1BE system parameters are assumed authentically known to each component.

<td> Component</td><td> Key / Data Item</td><td> (Cryptographic) Protection</td>

<td> Roadside System</td><td> Secret signature key SK_G</td><td> Confidential (inside a tamper-proof device)</td>

<td rowspan="3"> Operator</td><td> Roadside system's public key(s) PK_C</td><td> Authentic (certified)</td>

<td> Secret signature key</td><td> Confidential (inside a tamper-proof device, access is PIN-protected</td>

<td> Secret decryption key SK„_P</td><td> Confidential (same as</td>

<td rowspan="2"> Key-Generation Center</td><td> Operator’s public encryption key PK_M</td><td> Authentic (certified)</td>

<td> Operators public signature verification key</td><td> Authentic (certified)</td>

Table 3: Overview of cryptographic keys

Table 4 gives a list of system parameters, respective descriptions, owners and visibility of each parameter. For conciseness, we refrain from explicitly listing the specific parameters for each cryptosystem in charge. We propose using RSA and AES to encrypt channels and to use Digital secure standard (DSS) to create digital signatures, although other encryption and authentication standards known in the art could be used. The respective parameters are implicitly listed in Table 4 through the presence of the respective public and secret keys. All parameters, regardless of their visibility, should be authentic at best in order to thwart attacks based on parameter manipulation.

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<td> Parameter</td><td> Semantics and Description</td><td> Owner</td><td> Visibility</td>

<td> PKg</td><td> Public signature key of each roadside system. Needed to authenticate data submitted to the operator for verification</td><td> Roadside system (specific for each gantry)</td><td> Public</td>

<td> SK_o</td><td> Secret signature creation key of a roadside system. Needed to digitally sign any pay load handed over to the operator.</td><td> Roadside system (specific for each gantry)</td><td> Secret</td>

<td> pk._t</td><td> Public encryption key of the operator. Used by the KGC to secretly deliver a secret key upon a request.</td><td> Operator</td><td> Public</td>

<td> SK.^</td><td> Secret decryption key of the operator. Used to decipher the encrypted secret key for IBE.</td><td> Operator</td><td> Secret</td>

<td></td><td> Public signature key of the operator. Used to verify the authenticity of queries to the KGC.</td><td> KGC</td><td> Public</td>

<td></td><td> Secret signature key of the operator to authenticate queries to the KGC.</td><td> Operator</td><td> Secret</td>

<td> Pg</td><td> A prime number to create encryption keys within a roadside system</td><td> Roadside system (same for all cooperating gantries)</td><td> Public</td>

<td> 8</td><td> Generating element of the finite group Z*_c with modulo multiplication.</td><td> Every (cooperating) component in the system</td><td> Public</td>

<td> IBE System parameters</td><td> See D. Boneh and M. Franklin, Lc.</td><td> Roadside system (same for all cooperating gantries) and the keygeneration center</td><td> Public, except for the KGC master-key.</td>

Table 4: System Parameters

We recommend the following key-sizes and parameter constraints of Table 5. although not mandatory (in general, we say that a number n has bit-length t if 2¹⁴ &lt;n&lt; 2').

<td> Cryptosystem</td><td> Parameter constraints</td>

<td> RSA encryption</td><td> Primes p, q of minimum bit-length t = 2048 Bit (NIST recommendation)</td>

<td> DSA Digital Signatures</td><td> Primes p, q where p has minimal bit-length t = 1024 Bit and q has minimal bit-length t = 160 Bit</td>

<td> Identity Based Encryption</td><td> Prime &lt;7 with bit-length at least t = 160 Bit</td>

<td> Finite group Z*_c</td><td> Prime p_c with bit-length at least t = 160 Bit</td>

Table 5: Recommended Key Sizes (Security parameter 0

CA 02803840 2013-01-23

- 14As far as identity based encryption (IBE) is concerned, apart from the above recommended key-sizes no other constraints on the curves (such as minimal class number or others) used for digital signatures apply since we deal with encryption and not with signatures of the BonehFranklin scheme. Nevertheless, we recommend the key-sizes used for signatures to be used as 5 well for IBE.

In general, it is advisable to ensure that the discrete logarithm or factorization problem in the group that we are using is hard. The bit-strength b measures the efforts of factorizing an integer or finding a discrete logarithm, compared to a brute-force search over a set of 2^b values. Hence, an example interpretation of Table 6 is the following: The last row in the table tells 10 that finding a discrete logarithm modulo a prime of at least 256 Bit size (using Pollard's rhoalgorithm, cf. A. Menezes, P.C. van Oorschot and S. Vanstone: Handbook of applied Cryptography, CRC Press LLC, 1997) is equally difficult as brute-force breaking trying all 2¹²⁸keys to a symmetric cipher, or equivalently hard as factoring an integer with 3072 Bit. Comparing the values in Table 5 to the recommendations given by Table 6, we recommend the 15 latter sizes for security, since these agree with standardized recommendations, yet provide better long-term security:

<td> Bit-strength</td><td> Size of group (prime)</td><td> Size of Integer or Finite Field</td>

<td> 80</td><td> 160</td><td> 1024</td>

<td> 112</td><td> 224</td><td> 2048</td>

<td> 128</td><td> 256</td><td> 3072</td>

<td> 192</td><td> 384</td><td> 7168</td>

<td> 256</td><td> 512</td><td> 15360</td>

Table 6: Equivalent cryptographic strength provided by different algorithms