a590003

5.1 Homomorphic Operations over GF (2 8 )
/*** Determine the parameters (cf. [5, Appendix C]) ***/
long ptxtSpace = 2;
long nDigits = 2; // # of digits/# of columns in key-switching matrices
long k = 80; // security parameter
long weight = 64; // Hamming weight of secret keys
long lvls = 3; // number of ciphertext-primes in the modulus chain
long m = 11441; // the parameter m, defining Zm^* and Phi_m(X)
/*** Setup the various tables, and choose the keys ***/
FHEcontext context(m); // initialize a new context for the parameter m
buildModChain(context, lvls, nDigits); // build the modulus chain
FHESecKey secretKey(context);
const FHEPubKey& publicKey = secretKey;
secretKey.GenSecKey(weight,ptxtSpace);
// initialize a secret-key object
// use the same object as a public-key
// draw a random secret key
addSome1DMatrices(secretKey);
// compute some key-switching matrices
// We could also use add1DMatrices instead of addSome1DMatrices
GF2X G; // G is the AES polynomial, G(X)= X^8 +X^4 +X^3 +X +1
SetCoeff(G,8); SetCoeff(G,4); SetCoeff(G,3); SetCoeff(G,1); SetCoeff(G,0);
EncryptedArray ea(context, G); // An EncryptedArray object, encoding wrt G
long nslots = ea.size(); // number of plaintext slots
/*** Encrypt random arrays over GF(2^8) ***/
vector p0, p1, p2, p3;
ea.random(p0);
ea.random(p1);
ea.random(p2);
ea.random(p3);
vector const1, const2;
ea.random(const1);
ea.random(const2);
// Choose random arrays
// two more random "constants"
ZZX const1_poly, const2_poly; // encode constants as polynomials
ea.encode(const1_poly, const1);
ea.encode(const2_poly, const2);
// Encrypt the random arrays
Ctxt c0(publicKey), c1(publicKey), c2(publicKey), c3(publicKey);
ea.encrypt(c0, publicKey, p0);
ea.encrypt(c1, publicKey, p1);
ea.encrypt(c2, publicKey, p2);
ea.encrypt(c3, publicKey, p3);
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16. Design and Implementation of a Homomorphic-Encryption Library