Introduction the CPK

►Ad Hoc Networks Security Mechanism Based on CPK►International Conference on Computational Intelligence and Security Workshops, 15-19 Dec. 2007 Page(s):522 - 525 ►Lei Feng-Yu; Cui Guo-Hua; Liao Xiao-Ding

►A New Key Management and Authentication Method for WSN Based on CPK►08. ISECS International Colloquium on Computing, Communication, Control, and Management, Volume 2, 3-4 Aug. 2008 Page(s):486 - 490 ►Li, Jingjing; Tan, Le; Long, Dongyang

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CPK CPK (Combined Public Key)

A bounded Identity based encryption based on ECC integrates the public key technique with identity-based technique and uses the user’s identity to generate public key.

Patented Publication Number WO/2006/074611 NAN, Xiang-Hao and CHEN, Zhong

Originally described as ECC based system, but equally valid in discrete log.

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CPK Technique based on ECC (1/2) Assuming that an Elliptic Curve over a prime field satisfies the equation E:

y2 = (x3 + ax + b)mod p Parameters T = {a, b, G, n, p} , where a, b F∈ p are the coefficients of the elliptic

curve equation, which satisfies 4a3 + 27b2 ≠ 0 , G= (xG, yG ) is the base point of the Elliptic Curve E(Fp ) , n is the order of G and p is a prime number which is the order of prime field Fp . The private key is an integer r and the corresponding public key is rG , denoted

as (xr , yr ) , which is a point on E(Fp ) .

The matrix size of both SSK (Secret Seed Key Matrix) and PSK (Public Seed Key Matrix) = (m × h). SSK is an integer matrix (rij ) where rij is random chosen integer in Fp. PSK is composed of corresponding points (rijG) = (xij , yij ) on E(Fp ).

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CPK Technique based on ECC (2/2) h(ID) = m1, m2, m3…, mh

m1, m2, m3…, mh as row numbers

SK = (rm11+ rm22

+ …+ rmhh) mod n

PK = ( (xm11, ym11

)+(xm22, ym22

)+…+(xmhh, ymhh

) ) mod p = (rm11+ rm22

+ …+ rmhh)G

Ex: h(ID)= 1325, SK= (rm11+ rm23

+ rm32 + rm45

) mod n, ( (xm11, ym11

)+(xm23, ym23

)+

(xm32, ym32

)+(xm45, ym45

) ) mod p

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Applications CPK can achieve security authentication similarly to PKI but does not need

fixed infrastructure.

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Comments It is a good idea on the situation of mobile computing. The restriction of storage space with the PSK on the mobile node.

How do establish a related PSK? End-users can reconstruct by oneself from a seed.

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Our propose Key pool scheme

Server have a key pool and keep its secret. Client’s secret key is composed with the some sub-key that his ID mapping to the

key pool. ID254 ‘s secret key ga12+a25+a24 mod p

Advances Like the password table but a reduction on the key size.

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