FULLY HOMOMORPHIC ENCRYPTION: CURRENT STATE OF THE ...
FULLY HOMOMORPHIC ENCRYPTION: CURRENT STATE OF THE ...
FULLY HOMOMORPHIC ENCRYPTION: CURRENT STATE OF THE ...
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“Polly Cracker”: An Early Attempt at SWHE<br />
[Fellows-Koblitz ‘93]<br />
Main Idea<br />
Encryptions of 0 evaluate to 0 at the secret key.<br />
�� KeyGen: Secret = some point s = (s (s1, 1, …,s …,sn) 2 Z n<br />
n) 2 Z n<br />
q .<br />
Public key: Polynomials {ai(x1,…,xn)} s.t. ai(s)=0 mod q.<br />
� Encrypt: From {ai}, generate a random polynomial b(x)<br />
such that b(s) = 0 mod q. For m in {0,1}, ciphertext is:<br />
c(x) = m + b(x) mod q.<br />
� Decrypt: Evaluate ciphertext at secret: c(s)=m mod q.<br />
� ADD and MULT: Output sum or product of ciphertexts.
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