Scalable and Reliable Key Distribution 1/ Ryuzou NISHI † † Institute of Systems & Information Technologies (ISIT)

2/ Introduction Appearance of a large variety of application of an information and telecommunication e.g. Internet, Home automation, Sensor network, and so on In the conventional point-to-point communication, scalability is a issue. Broadcast communication is desired Issues of broadcast security 1. Communication reliability ・ Re-transmission request is a large load to transmitter ・ In a case of failure of receiving keys, it is impossible to decrypt following messages 2. Communication overhead frequent key-update cause communication overhead, and the overhead causes a degradation of communication reliability

Area ： Key distribution for group key update in case of members' joining in or leaving from group in channel of poor quality, e.g. wireless, power line communication. Group key is used to encrypt or decrypt messages and is shared among all the members of a group. Goal ： Reliable group key update where rekey message size is independent of group size, Introduction Our work

Previous Work scalability 4/ □ GKMP : Group Key Management Protocol Key server distributes an updated key to each member through unicast cannel O(N) □ LKH ： Logical Key Hierarchy O(N) → O(log(N)) KdKd KeKe KfKf M1M1 M2M2 M3M3 M4M4 KbKb KaKa KcKc KgKg group key

Previous Work reliability 5/ □ FEC : Forward Error Correction In a sender, redundancy is added into an original data. If data error occur on the way, a receiver corrects the error. method coding gain BCH 2.1 dB Convolution 5.1 dB

Proposal : Basic idea □ Updated key is distributed by using Direct Sequence Spread Spectrum (DS-SS) communication scheme which spreading code are M-sequences (maximal-length sequences) 6/ 1 bit 1 period ｔ ime Updated group key secret key M-sequence secret key ID shift multiplexer Updated group key M-sequence

Proposal : Cyclic shift M-sequence 7/ M-sequences 1 period M-sequences' auto- correlation curve i=j point M-sequences （ u 0,u 1, ・・・,u N- 1 ) Cyclic shift M-sequences U i = （ u i,u i+1, ・・・,u N-1, u 0, ・・・, u i- 1 ) A cross-correlation between U i and U j is maximum N at i=j, and -1 at i≠ ｊ. And a cross-correlation between － U i and U j is maximum -N at i=j, and +1 at i≠ ｊ. u i = +1 or -1 N: sequence's length

Proposal : Setup 8/ 1. The key server sends the secret key to each member in secure channel where secret key is depicted by GK digits and maximum number of each digit is N-1 2. The key server regroup all member into subgroups where the maximum number of members of each subgroup is N 3. The key server sends the M-sequences and ID(1,2,...,GK) Where a different subgroup uses a different M-sequence and each member of a same subgroup uses a different cyclic shift M- sequence generated from a same M-sequence. subgroup #1 subgroup #2 subgroup #Ns ・・・ M-seq.M 1 M-seq.M 2 M-seq.M Ns ID 1 ID 2 ID Ns Key server

9/ Proposal : Basic idea □ Updated key is distributed by using Direct Sequence Spread Spectrum (DS-SS) communication scheme which spreading code are M-sequences (maximal-length sequences) 1 bit 1period ｔ ime Updated group key secret key M-sequence secret key ID shift multiplexer Updated group key M-sequence

Proposal : Secret key → M- sequence In the case that the number of k digit of member M1's secret key is i k, cyclic shift M-sequence （ u ik,u ik+1, ・・・,u N-1, u 0, ・・・, u ik-1 ） is generated by cyclically shifting M-sequence （ u 0,u 1, ・・・,u N-1 ) i k times. About each digit of the secret key, similar process are done. time M-seq. １ period （ u i1,u i1+1, ・・・,u N-1, u 0, ・・・, u i1-1 ） １ -st digit （ u iGK,u iGK+1, ・・・,u N-1, u 0, ・・・, u iGK-1 ） ・・・ GK-th digit M-seq. １ period 10/

11/ Proposal : Basic idea □ Updated key is distributed by using Direct Sequence Spread Spectrum (DS-SS) communication scheme which spreading code are M-sequences (maximal-length sequences) 1 bit 1period ｔ ime Updated group key secret key M-sequence secret key ID shift multiplexer Updated group key M-sequence

Proposal : ID shift and multiplier □ Sequence （ K id,K id+1, ・・・,K GK-1, K 0, ・・・,K id-1 ） is generated by cyclically shifting updated group key （ K 0,K 1, ・・・,K GK-1 ) id (value of ID) times. □ k-th value GK k (= +1or -1) of the sequence is multiplied with cyclic shift M-sequence （ u ik,u ik+1, ・・・,u N-1, u 0, ・・・,u ik-1 ） 12/ time GK 1 × （ u i1,u i1+1, ・・・,u N-1, u 0, ・・・, u i1-1 ） １ -st digit GK Nr × （ u iNr,u iNr+1, ・・・,u N-1, u 0, ・・・, u iNr-1 ） ・・・ GK-th digit M-seq. １ period

13/ Proposal : Basic idea □ Updated key is distributed by using Direct Sequence Spread Spectrum (DS-SS) communication scheme which spreading code are M-sequences (maximal-length sequences) 1 bit 1period ｔ ime Updated group key secret key M-sequence secret key ID shift multiplexer Updated group key M-sequence

Proposal : Multiplexer □ Multiplier's outputs of all members are multiplexed as follows. For example, multiplexing of two members whose output sequence are U （ u 0,u 1, ・・・,u N- 1 ) and U' （ u' 0,u' 1, ・・・,u' N-1 ) output seq. U （ u 0,u 1, ・・・,u N-1 ) + output seq. U' （ u' 0,u' 1, ・・・,u' N-1 ) multiplexed seq. U+U' （ u 0 +u' 0, u 1 +u' 1, ・・・, u N-1 + u' N-1 ) 14/

Proposal : Decoding of group key 15/ ・・ ・ 2N length shift-register 2N length reference shift-register adder ・・ ・ sampler decoded GK received signal Group key bit can be decoded from the polarity of the adder’s output

Proposal : Decoding of group key 16/ ・・ ・ 2N length shift-register 2N length reference shift-register adder ・・ ・ sampler decoded GK received signal Decoder's output includes the following signals ・ auto-correlation ( this corresponds to sent group key ) ・ closs-correlation between cyclic shift M-sequences which shift times are different, but original M-sequence is same. ・ closs-correlation between different M-sequences

Proposal : Example of decoder's output 17/ Supportable group sizeGK k (+) 1bit quant. (+) 1bit quant.(-) ×2 127 ×3 group key size:128 bits 、 M-sequence size 127bit group size （ number of members ） rekey message size (bit) 3 × × 3 ×127 GKMP 128× 127 proposal 127 GK k (-) 127 ×4 GK k (+) : decoder’s output when polarity of the sent group key is plus(+) GK k ( － ) : decoder’s output when polarity of the sent group key is minus( － ) 1bit quant. (+) : multiplexer’s output is quantized by 1bit when polarity of the sent group key is plus(+) 1bit quant. ( － ) : multiplexer’s output is quantized by 1bit when polarity of the sent group key is plus( － ) The larger decoder‘s output absolute becomes, the stronger the immunity to the noise becomes.

Proposal : Reliability ・ Conventional approach ( approach using FEC without ARQ ) improved SNR ( by coding gain ) 5 dB ( coding ratio : 0.5 、 convolutional coding ) ・ Proposal improved SNR ( by despreading effect ) 16 dB ( = 10 * log(44) ) Criterion : improved SNR for required reliability (error rate) SNR : Signal to Noise Ratio 18/

Proposal : Security 19/ The proposal’s security is based on that member which should be revoked, does not know the number of times of the shift of cyclic shift M-sequences of other members Can an attacker know the number of times of the shift, if he know the original M-sequence and get the receiver? …No. Because the decoder output is multiplexed signal as follows. Only legitimate member who knows the number of times of the shift, can decode group key. Decoder output

Conclusion We propose the scalable and reliable key distribution scheme where rekey message size is indepedent of group size by using DS-SS communication scheme which spreading code is M-sequences including cyclic shift M-sequences. The proposal improves the reliability of key and reduces the rekey message size. 20/