Homomorphic encryption

Duohui Tian201469772

abstact 1 definition

2 type

3 algorithm

4 application

definition Homomorphic encryption is a form of

encryption, it allows people to get specific algebraic operations on the ciphertext is still encrypted with the same operation results, then the results of the plaintext encryption. [4]

Group Homomorphism [1]

types

1  fully homomorphic cryptosystems

2  somewhat homomorphic cryptosystems

somewhat homomorphic cryptosystems Somewhat Homomorphic Encryption

(SHE) schemes are encryption schemes that have some homomorphic properties but are not fully homomorphic[4]

fully homomorphic cryptosystems using lattice-based cryptography,

described the first plausible construction for a fully homomorphic encryption scheme. Gentry's scheme supports both addition and multiplication operations on ciphertexts, from which it is possible to construct circuits for performing arbitrary computation.[4]

algorithm

FHE Scheme Structure and Flow[2]

integer-based somewhat scheme 1 Key Generation, select key(p) is odd 2 Encryption, C = pq + 2r + m The q and r is also an random integer 3 Decryption M =( c(mod p))(mod 2) [1]

Fully Homomorphic Property c1 + c2 = (q1+q2)p+2(r1+r2)+

(m1+m2)

c1*c2=(p*q1*q2+2*q1*r2+2*q2*r1+m1*q2+m2*q2)*p+2(2*r1*r2+m1*r2+m2*r1)+m1*m2 [1]

So

( (c1+c2)(mod p))(mod 2) = m1+m2 ( (c1*c2)(mod p))(mod 2) = m1*m2

[1]

example Set p=17, m1 =0, and m2 =1

q1=1,r1=1,q2=2,r2=2the ciphertexts is below

c1 = 17*1 + 2*1 +0 =19 c2 = 17*2+2*2 + 1 = 39 ( (c1+c2)(mod p))(mod 2) = (58( mod

17)) (mod 2) = 7(mod 2) =1 = m1 + m2

( (c1*c2)(mod p))(mod 2) = (741( mod 17)) (mod 2)

= 10(mod 2) =0 = m1 * m2 [1]

application

1 image Signal Processing Using Fully Homomorphic Encryption

2 secure cloud computing and client computing

3 remote file storage

4 the cipher text retrieval

image Signal Processing Using Fully Homomorphic Encryption [2]

The problems of FHE

1 initial phase in cloud compution

2 eliminate the extra noise algorithm

reference [1]Yi, X., Paulet, R., & Bertino, E. (n.d.). Homomorphic

encryption and applications. [2]Advanced Concepts for Intelligent Vision Systems 16th

International Conference, Acivs 2015, Proceedings. (2015). Springer-Verlag New York.

[3]Zhu, P., & Xiang, G. (2011). The Protection Methods for Mobile Code Based on Homomorphic Encryption and Data Confusion. Management of E-Commerce and E-Government (ICMeCG), 2011 Fifth International Conference on, 256-260.

[4] Lin ming, Gong & shun dong, Li (2016) The Development and Applications of Homomorphic Encryption, School of Computer Science, Shanxi Normal University

[5] (n.d.). Retrieved March 28, 2016, from https://en.wikipedia.org/wiki/Homomorphic_encryption

Thank you !