LAS 3 RAS 3
A.3 HOKEY
A.3.5 Key delivery
In [Hoeperet al., 2010], the delivery of keys belonging to different levels of the key hierarchy can be performed in a proactive way, e.g. a Home AS can deliver DSRK key to a Foreign AS before it requests. The mechanism uses RADIUS packet form.
EAP Initiate/Re-auth Start
EAP Initiate/Re-auth(SEQ,MAC)
AAA-Response(rMSK, EAP Finish/Re-auth(SEQ, MAC))
MC Authenticator Foreign AS
AAA-Request(Authenticator-ID, EAP Initiate/Re-auth(SEQ, MAC))
EAP Finish/Re-auth(SEQ, MAC)
Figure A.8: HOKEY re-authentication in a foreign network
Appendix B
Time consumption of asymmetric cryptographic primitives
I measured the time consumption of some widely known and analyzed public key based key ex-change, digital signature and encryption algorithms listed below.
Key exchange algorithms
– Diffie-Hellman [Diffie and Hellman, 1976]
– Elliptic Curve Diffie-Hellman [Certicom Research, 2000]
Digital signature algorithms – RSA [Rivestet al., 1978]
– DSA [FIPS PUBS, 1994]
– Elliptic Curve DSA (ECDSA) [Certicom Research, 2000]
Cipher algorithms – RSA
– Elliptic Curve ElGamal (ECELG) [Rabah, 2005]
These cryptographic primitives are already implemented in various crypto libraries. For my measurements, I chose the Open SSL library [OpenSSL, 2010], because of the following reasons:
1) it is a widely used open source library, 2) each crypto primitive is already implemented in it (except for ECElGamal, but general operations over different elliptic curves are supported), 3) it is available in a crosscompiled version for each architecture which is supported by the OpenWRT [OpenWRT, 2010] embedded Linux distribution.
I measured the time consumption of the above listed algorithms with different key sizes or using different elliptic curves. In each case, I considered the average value of 100 measurements.
In the case of Diffie-Hellman key agreement algorithms, I measure the time needed to compute the common key by the two protocol participants. In the case of digital signature algorithms, I mea-sure the time of generating and verifying signatures on a single block of data. The meamea-surements of the encryption algorithms are performed in the same way as in the case of digital signature: I mea-sure the time consumption of the encryption and the decryption, of a single randomly generated data block.
Herein, I define what key parameters were considered in different public key crypto algorithms.
In the case of non-EC algorithms, I measured the time consumption with 256, 384, 512, 1024 and 2048 bit long keys. The generator number of DSA was always 5 and the prime was generated
Table B.1: Test elliptic curve parameters Name Organization Size RSA/DSA Field
secp112r1 SECG 112 512 Fp
secp112r2 SECG 112 512 Fp
secp128r1 SECG 128 704 Fp
secp128r2 SECG 128 704 Fp
secp160k1 SECG 160 1024 Fp
secp160r1 SECG 160 1024 Fp
secp160r2 SECG 160 1024 Fp
sect113r1 SECG 113 512 F2m
sect113r2 SECG 113 512 F2m
sect131r1 SECG 131 704 F2m
sect131r2 SECG 131 704 F2m
sect163k1 SECG 163 1024 F2m
sect163r2 SECG 163 1024 F2m
c2pnb163v1 X9.62 163 1024 F2m
c2pnb163v2 X9.62 163 1024 F2m
wtls1 WAP 113 512 F2m
wtls5 WAP 163 1024 F2m
wtls8 WAP 112 512 Fp
wtls9 WAP 160 1024 Fp
randomly in each run. The exponent of the public key of the RSA algorithm is 65537 both in the case of encryption and digital signature. The elliptic curve based algorithms requires to define an elliptic curve on which the operations can be performed. The OpenSSL implements the elliptic curves proposed and standardized in three different documents issued by three different organiza-tion: SECG [Standards for Efficient Cryptography Group (SECG), 2000], ANSI X9.62 [Accredited Standards Committee X9, 2005], and WAP [Wireless Application Forum, 1999]. In Table B.1, I describe the properties of elliptic curves I considered while measuring the time consumption.
ECRYPT II [FP7 ECRYPT II, 2007] recommendation for 2008 says that the 1024 bit asym-metric keylength and elliptic curves with 160 bit are sufficient for short-term protection (some years). And 816 bit asymmetric keylength and elliptic curves with 128 bit are not sufficient for confidentiality, and offer only very short-term protection for other purposes.
I have measured the time consumption of crypto primitives in two different devices. One device is a regular access point which will be responsible for authenticating the mesh clients in my proposed mechanism. The access point is a Linksys wireless router (WRT54GL v1.1) with 200 MHz MIPS CPU, 16 MB RAM and 4 MB Flash. The other one is a more powerful device as the mesh clients have usually more power than an access point, I used a desktop PC with Core2Duo 6400 CPU and 1 GB RAM.
In FigureB.1, B.2, and B.3, I plotted the results of the measurement of key exchange, digital signature and encryption algorithms, respectively. On thexaxis, I show the delay of the firstly measured operation (i.e., calculation of the common key by the first party, generation of a digital signature, and encryption), while on the y axis, I show the time consumption of the secondly measured operation (i.e., calculation of the common key by the second party, digital signature verification, and decryption). The placing of a point, which is related to a specific algorithm with a specific key parameter, shows the delay of the two operations. The name of the algorithms and the key parameters are indicated in the legend of the figures. Elliptic curves correspond to the abbreviations in TableB.1; the standards and the OpenSSL library use the same or similar names.
For the sake of better readability, I grouped the points into groups and the points are indicated with the same mark in FigureB.1,B.2, andB.3if the points are close to each other.
The DH and ECDH key exchange algorithms are for establishing shared secret between two parties which has no prior knowledge of each other, but the algorithms themselves do not provide
0 50 100 150 200 250 300 0
50 100 150 200 250 300
Time of key generation − node 1 (ms)
Time of key generation − node 2 (ms)
DH−256 bits DH−384 bits ECDH−sect113r1 ECDH−sect113r2 ECDH−wtls1 DH−512 bits ECDH−secp112r1 ECDH−secp112r2 ECDH−secp128r1 ECDH−secp128r2 ECDH−sect131r1 ECDH−sect131r2 ECDH−sect163k1 ECDH−c2pnb163v2 ECDH−wtls5 ECDH−wtls8 ECDH−wtls9 ECDH−secp160k1 ECDH−secp160r1 ECDH−c2pnb163v1 ECDH−secp160r2 ECDH−sect163r2 DH−1024 bits
(a) Access point
0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8
Time of key generation − node 1 (ms)
Time of key generation − node 2 (ms)
DH−256 bits DH−384 bits ECDH−sect113r1 ECDH−sect113r2 ECDH−wtls1 DH−512 bits ECDH−secp112r1 ECDH−secp112r2 ECDH−secp128r1 ECDH−secp128r2 ECDH−sect131r1 ECDH−sect131r2 ECDH−wtls8 ECDH−secp160k1 ECDH−secp160r1 ECDH−secp160r2 ECDH−sect163k1 ECDH−sect163r2 ECDH−c2pnb163v1 ECDH−c2pnb163v2 ECDH−wtls5 ECDH−wtls9 DH−1024 bits
(b) PC
Figure B.1: Time consumption of key exchange algorithms
authenticity. Two things can be drawn from the previous statement: 1) Assuming that the con-nection key is derived from the result of the key exchange algorithm, the key size must be secure enough otherwise an attacker who logged the communication can decrypt it after breaking the key;
2) Beside the key exchange algorithm some other public key algorithms (typically digital signature) should be used to provide authenticity.
In FigureB.1(a)andB.1(b), one can see the time consumption of the key exchange algorithms performed in AP and PC, respectively. As it is expected, the delay of calculating the common key is independent of which private key is used when the common key is calculated.
Considering the time consumption of DH algorithm in AP, I can derive that this mechanism is not promising nowadays, as the delay is much longer for secure key sizes (1024 bit – 300 ms) than a QoS-aware application can tolerate. This is the case for the ECDH in most cases, however some elliptic curves (c2pnb163v2, sect163k1, wtls5 and wtls9) with secure key sizes can be calculated around 50 ms in my representative AP. In any other considered cases, the ECDH algorithm is either slow or insecure.
As Figure B.1(b)shows, a PC is powerful enough to perform such algorithms. Unfortunately, it does not accelerate the key agreement process as the access point and the mesh client has to perform the generation of the common key in parallel.
Note that in FigureB.1(a)andB.1(b), I do not indicate the time consumption of the DH with 2048 bit key size, because it has such a long delay that it would decrease the readability of the figures. In a powerful PC, it needs around 37 ms and in a less powerful AP, it lasts around 1.79 s.
In FigureB.2(a) andB.2(b), the time consumption of the digital signature can be seen in the case of AP and PC, respectively. The three analyzed algorithms show two different properties with the predefined key parameters. The RSA algorithm with small public key exponent is two or three degree quicker when the digital signature is verified compared to the process of signing. The ECDSA and the DSA are the opposite of RSA, the generation is two or three degree quicker than the verification if the operations are performed in the same powerful device. The reason is that in the case of signature generation the most time consuming operations can be performed without the knowledge of the data that has to be signed.
Note that one operation is time consuming considering the analyzed algorithms, and the other one only needs 1-2 ms even if the device has limited capacity. Furthermore, in the case of a powerful device (like PC), only the signature generation of RSA with 2048 bit needs considerable time. In the case of less powerful device (AP), from FigureB.2(a), one can read that an AP is not able to perform the operation which has higher delay (generation of digital signature in the case of RSA and verification in the case of DSA and ECDSA) with secure key sizes within a considerable time.
0 100 200 300 400 500 600 700 0
20 40 60 80 100 120 140 160 180
Time of signing (ms)
Time of verification (ms)
RSA−256 bits RSA−384 bits RSA−512 bits RSA−1024 bits RSA−2048 bits DSA−256 bits DSA−384 bits DSA−512 bits DSA−1024 bits ECDSA−secp112r1 ECDSA−secp112r2 ECDSA−secp128r1 ECDSA−sect113r1 ECDSA−sect113r2 ECDSA−wtls1 ECDSA−wtls8 ECDSA−secp128r2 ECDSA−secp160k1 ECDSA−secp160r1 ECDSA−sect131r1 ECDSA−sect131r2 ECDSA−secp160r2 ECDSA−sect163r2 ECDSA−c2pnb163v1 ECDSA−wtls5 ECDSA−sect163k1 ECDSA−c2pnb163v2 ECDSA−wtls9 DSA−2048 bits
(a) Access point
0 5 10 15
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Time of signing (ms)
Time of verification (ms)
RSA−256 bits RSA−384 bits RSA−512 bits RSA−1024 bits RSA−2048 bits DSA−256 bits DSA−384 bits DSA−512 bits DSA−1024 bits ECDSA−secp112r1 ECDSA−secp112r2 ECDSA−secp128r1 ECDSA−wtls8 ECDSA−secp128r2 ECDSA−sect113r1 ECDSA−sect113r2 ECDSA−wtls1 DSA−2048 bits ECDSA−sect163k1 ECDSA−sect163r2 ECDSA−c2pnb163v1 ECDSA−c2pnb163v2 ECDSA−wtls5 ECDSA−secp160k1 ECDSA−secp160r1 ECDSA−secp160r2 ECDSA−wtls9 ECDSA−sect131r1
(b) PC
Figure B.2: Time consumption of digital signature algorithms
0 50 100 150
0 100 200 300 400 500 600 700
Time of encryption (ms)
Time of decryption (ms)
RSA−256 bits RSA−384 bits RSA−512 bits RSA−1024 bits RSA−2048 bits ECELG−secp112r1 ECELG−sect131r1 ECELG−sect131r2 ECELG−secp112r2 ECELG−secp128r1 ECELG−secp160k1 ECELG−sect163r2 ECELG−secp128r2 ECELG−secp160r1 ECELG−secp160r2 ECELG−c2pnb163v1 ECELG−wtls9 ECELG−c2pnb163v2 ECELG−wtls5 ECELG−wtls8 ECELG−sect113r1 ECELG−sect113r2 ECELG−wtls1 ECELG−sect163k1
(a) Access point
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0
5 10 15
Time of encryption (ms)
Time of decryption (ms)
RSA−256 bits RSA−384 bits RSA−512 bits RSA−1024 bits RSA−2048 bits ECELG−secp112r1 ECELG−secp112r2 ECELG−secp128r1 ECELG−wtls8 ECELG−secp128r2 ECELG−sect113r1 ECELG−sect113r2 ECELG−wtls1 ECELG−secp160k1 ECELG−sect163k1 ECELG−wtls9 ECELG−sect163r2 ECELG−c2pnb163v1 ECELG−c2pnb163v2 ECELG−wtls5 ECELG−secp160r1 ECELG−secp160r2 ECELG−sect131r1 ECELG−sect131r2
(b) PC
Figure B.3: Time consumption of encryption algorithms
In Figure B.3(a) and B.3(b), the time consumption of the encryption algorithms can be seen in the case of AP and PC, respectively. Again, I can observe that the public key operation of the RSA, i.e. herein the encryption, is two or three orders of magnitude quicker than the decryption and does not cause more than 1-2 ms delay either in a limited device. The decryption process of the RSA with secure key sizes in AP needs more time than a QoS-aware application can tolerate. Considering the ECELG algorithm, the decryption is quicker than the encryption, but approximately two times, only. While, the quickest decryption with sufficiently large key size lasts more than 50 ms on average. Thus, the decryption can not be performed in limited device in any case during the handover. A more powerful device (PC) is able to encrypt and decrypt within the considered time with any kind of considered algorithms and with any kind of considered key parameter, except for the RSA decryption with 2048 bits (lasts 15 ms on average).
The conclusion is that using asymmetric key crypto in a powerful device does not preclude the possibility of seamless handover. While on a limited device, such as an AP, some crypto primitives cause too long delays. Here, I collect those from the set of considered algorithms and key parameters which can be performed with a sufficiently short delay:
Digital signature generation with any key size using DSA or ECDSA
Digital signature verification with any key size using RSA
Any digital signature operation with a weak key
Encryption with any key size using RSA
Thus, if the mesh client is as constraint as the considered access point, then they are not able to generate a shared secret securely within a considerable time. Furthermore, they are not able to generate and verify digital signatures using securely large keys. The main consequence is that two computationally constraint devices are not able to authenticate each other and to perform a DH key agreement protocol within the time that a seamless handover requires.
AP Access point
ARM Advanced RISC Machine or Acorn RISC Machine BIONETS BIOlogically inspired NETwork and Services
BWM Blake-Wilson and Menezes Provably Secure Key Transport Protocol CAPWAP Control And Provisioning of Wireless Access Points
CAT Category identifier
CCTV Closed-circuit television
CA Certificate Authority
CRL Certificate Revocation List DoS Denial-of-Service
DTN Delay Tolerant Network
EAP Extensible Authentication Protocol
EAPOL EAP over LAN
EU European Union
FP Framework Programme
GSM Global System for Mobile Communications
GW Gateway
HLS Hide-and-Lie Strategy HOKEY Handover Keying
IAPP Inter Access Point Protocol
ID Identity
IEEE Institute of Electrical and Electronics Engineers IETF Internet Engineering Task Force
IP Interest Profile
IPsec Internet Protocol Security ISP Internet Service Provider
LAN Local Area Network
LAS Local Authentication Server MAC Message Authentication Code MAC address Media Access Control address MANET Mobile Ad Hoc Network
MC Mesh client
MR Mesh router
MSK Master Session Key
Multi-WMN Multi-operator maintained WMN using multiple channels
NTV Node Trust Value
OP Operator
PANA Protocol for carrying Authentication for Network Access
PMK Pairwise Master Key PTK Pairwise Transient Key QoS Quality of Services
RADIUS Remote Authentication Dial In User Service RAS Remote Authentication Server
RRW Restricted Random Waypoint mobility model
RW Random Walk mobility model
SEQ Sequence number
SUMO Simulation of Urban MObility TLS Transport Layer Security
UP User Profile
VANET Vehicular Ad-hoc Network
VoIP Voice over IP
WMN Wireless Mesh Network
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