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Scalable and Reliable Key Distribution

Ryuzou NISHI†

† Institute of Systems & Information Technologies (ISIT)

1/

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

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

2/

Our work

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,

□ 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))

group key

Ka

Kc

Kb

Kg

Kd

Ke

Kf

M4

M3

M1

M2

4/

□ 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.

methodcoding gain

BCH2.1 dB

Convolution 5.1 dB

5/

□ Updated key is distributed by using Direct

Sequence Spread Spectrum (DS-SS)

communication scheme which spreading code

are M-sequences (maximal-length sequences)

Updated

group key

ID

shift

Updated

group key

1 bit

multiplexer

ｔime

M-sequence

secret key M-sequence

1 period

ｔime

secret key

6/

Proposal : Cyclic shift M-sequence

M-sequences（u0,u1,・・・,uN-1)

ui = +1 or -1N: sequence\'s length

Cyclic shift M-sequences Ui = （ui,ui+1,・・・,uN-1 , u0,・・・, ui-1)

A cross-correlation between Ui and Uj is maximum N

at i=j, and -1 at i≠ｊ.

And a cross-correlation between －Ui and Uj is maximum -N at i=j, and +1 at i≠ｊ.

i=j point

M-sequences\' auto-correlation curve

M-sequences 1 period

7/

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.

Key server

M-seq.M1

M-seq.MNs

M-seq.M2

ID1

・・・

IDNs

ID2

subgroup #1

subgroup #Ns

subgroup #2

8/

□ Updated key is distributed by using Direct

Sequence Spread Spectrum (DS-SS)

communication scheme which spreading code

are M-sequences (maximal-length sequences)

Updated

group key

ID

shift

Updated

group key

1 bit

multiplexer

ｔime

M-sequence

secret key M-sequence

1period

ｔime

secret key

9/

Proposal : Secret key →M-sequence

In the case that the number of k digit of member M1\'s secret key is ik, cyclic shift M-sequence （uik,uik+1,・・・,uN-1 , u0,・・・,uik-1）is generated by cyclically shifting M-sequence （u0,u1,・・・,uN-1) ik times.

About each digit of the secret key, similar process are done.

１-st digit

GK-th digit

・・・

（ui1,ui1+1,・・・,uN-1 , u0,・・・,ui1-1）

（uiGK,uiGK+1,・・・,uN-1 , u0,・・・,uiGK-1）

time

M-seq.１ period

M-seq.１ period

10/

□ Updated key is distributed by using Direct

Sequence Spread Spectrum (DS-SS)

communication scheme which spreading code

are M-sequences (maximal-length sequences)

Updated

group key

ID

shift

Updated

group key

1 bit

multiplexer

ｔime

M-sequence

secret key M-sequence

1period

ｔime

secret key

11/

Proposal : ID shift and multiplier

□Sequence （Kid,Kid+1,・・・,KGK-1 , K0,・・・,Kid-1）

is generated by cyclically shifting updated

group key（K0,K1,・・・,KGK-1) id (value of ID)

times.

□k-th value GKk(= +1or -1) of the sequence is

multiplied with cyclic shift M-sequence

（uik,uik+1,・・・,uN-1, u0,・・・,uik-1）

GK-th digit

１-st digit

・・・

GK1 ×（ui1,ui1+1,・・・,uN-1 , u0,・・・,ui1-1）

GKNr × （uiNr,uiNr+1,・・・,uN-1 , u0,・・・,uiNr-1）

time

M-seq.１ period

M-seq.１ period

12/

□ Updated key is distributed by using Direct

Sequence Spread Spectrum (DS-SS)

communication scheme which spreading code

are M-sequences (maximal-length sequences)

Updated

group key

ID

shift

Updated

group key

1 bit

multiplexer

ｔime

M-sequence

secret key M-sequence

1period

ｔime

secret key

13/

□Multiplier\'s outputs of all members are

multiplexed as follows.

For example, multiplexing of two members

whose output sequence are U（u0,u1,・・・,uN-1)

and U\'（u\'0,u\'1,・・・,u\'N-1)

output seq. U（u0,u1,・・・,uN-1)

+

output seq. U\'（u\'0,u\'1,・・・,u\'N-1)

multiplexed seq. U+U\'（u0+u\'0, u1+u\'1,・・・, uN-1+ u\'N-1)

14/

Proposal : Decoding of group key

2N length shift-register

received signal

・・・

sampler

decoded GK

adder

・・・

2N length reference shift-register

Group key bit can be decoded from the polarity of the adder’s output

15/

Proposal : Decoding of group key

2N length shift-register

received

signal

・・・

sampler

decoded GK

adder

・・・

2N length reference shift-register

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

16/

Proposal : Example of decoder\'s output

group key size:128 bits、M-sequence size 127bit

1bit

quant. (+)

1bit

quant.(-)

GKk(-)

Supportable group size

GKk(+)

19

-15

127 ×2

126

-126

25

-9

127 ×3

109

-125

127 ×4

44

-188

GKk(+) : decoder’s output when polarity of the sent group key is plus(+)

GKk(－) : 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.

rekey message size (bit)

GKMP

128× 3 ×127

proposal

128× 127

group size （number of members）

127

3 ×127

17/

Criterion : improved SNR for required reliability (error rate)

SNR : Signal to Noise Ratio

・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) )

18/

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

19/

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/

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