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DoubleCRT& operator-=(const ZZ &num);
DoubleCRT& operator-=(long num);
// These are the prefix versions, ++dcrt and --dcrt.
DoubleCRT& operator++();
DoubleCRT& operator--();
// Postfix versions (return type is void, it is offered just for style)
void operator++(int);
void operator--(int);
DoubleCRT& operator*=(const DoubleCRT &other); // Multiplication
DoubleCRT& operator*=(const ZZX &poly); // expensive
DoubleCRT& operator*=(const ZZ &num);
DoubleCRT& operator*=(long num);
// Procedural equivalents, providing also the matchIndexSets flag
void Add(const DoubleCRT &other, bool matchIndexSets=true);
void Sub(const DoubleCRT &other, bool matchIndexSets=true);
void Mul(const DoubleCRT &other, bool matchIndexSets=true);
DoubleCRT& operator/=(const ZZ &num);
DoubleCRT& operator/=(long num);
// Division by constant
void Exp(long k);
// Small-exponent polynomial exponentiation
// Automorphism F(X) --> F(X^k) (with gcd(k,m)==1)
void automorph(long k);
DoubleCRT& operator>>=(long k);
We also provide methods for choosing at random polynomials in DoubleCRT format, as follows:
void randomize(const ZZ* seed=NULL);
Fills each row i ∈ getIndexSet() with random integers modulo p i . This procedure uses the
NTL PRG, setting the seed to the seed argument if it is non-NULL, and using the current
PRG state of NTL otherwise.
void sampleSmall();
Draws a random polynomial with coefficients −1, 0, 1, and converts it to DoubleCRT format.
Each coefficient is chosen as 0 with probability 1/2, and as ±1 with probability 1/4 each.
void sampleHWt(long weight);
Draws a random polynomial with coefficients −1, 0, 1, and converts it to DoubleCRT format.
The polynomial is chosen at random subject to the condition that all but weight of its
coefficients are zero, and the non-zero coefficients are random in ±1.
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16. Design and Implementation of a Homomorphic-Encryption Library