HElib 1.0 Implementing Homomorphic Encryption

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NumbTh.h File Reference

Miscellaneous utility functions. More...

`#include <vector>`
`#include <cmath>`
`#include <istream>`
`#include <NTL/ZZ.h>`
`#include <NTL/ZZ_p.h>`
`#include <NTL/ZZX.h>`
`#include <NTL/GF2X.h>`
`#include <NTL/vec_ZZ.h>`
`#include <NTL/xdouble.h>`
`#include <NTL/mat_lzz_pE.h>`
`#include <NTL/mat_GF2E.h>`
`#include <NTL/lzz_pXFactoring.h>`
`#include <NTL/GF2XFactoring.h>`
`#include <tr1/unordered_map>`
`#include <string>`

Go to the source code of this file.

## Classes
class | RandomState
| Facility for "restoring" the NTL PRG state. More...

## Typedefs
typedef tr1::unordered_map < string, const char * > | argmap_t

## Functions
bool | parseArgs (int argc, char *argv[], argmap_t &argmap)
| Code for parsing command line arguments. More...
long | multOrd (long p, long m)
| Return multiplicative order of p modulo m, or 0 if GCD(p, m) != 1.
void | ppsolve (vec_zz_pE &x, const mat_zz_pE &A, const vec_zz_pE &b, long p, long r)
| Prime power solver. More...
void | ppsolve (vec_GF2E &x, const mat_GF2E &A, const vec_GF2E &b, long p, long r)
| A version for GF2: must have p == 2 and r == 1.
void | buildLinPolyCoeffs (vec_zz_pE &C, const vec_zz_pE &L, long p, long r)
| Combination of buildLinPolyMatrix and ppsolve. More...
void | buildLinPolyCoeffs (vec_GF2E &C, const vec_GF2E &L, long p, long r)
| A version for GF2: must be called with p == 2 and r == 1.
void | applyLinPoly (zz_pE &beta, const vec_zz_pE &C, const zz_pE &alpha, long p)
| Apply a linearized polynomial with coefficient vector C. More...
void | applyLinPoly (GF2E &beta, const vec_GF2E &C, const GF2E &alpha, long p)
| A version for GF2: must be called with p == 2 and r == 1.
double | log2 (const xdouble &x)
| Base-2 logarithm.
double | log2 (const double x)
void | factorize (vector< long > &factors, long N)
| Factoring by trial division, only works for N<2^{60}, only the primes are recorded, not their multiplicity.
void | factorize (vector< ZZ > &factors, const ZZ &N)
void | phiN (long &phiN, vector< long > &facts, long N)
| Compute Phi(N) and also factorize N.
void | phiN (ZZ &phiN, vector< ZZ > &facts, const ZZ &N)
int | phi_N (int N)
| Compute Phi(N).
void | FindPrimitiveRoot (zz_p &r, unsigned e)
| Find e-th root of unity modulo the current modulus.
void | FindPrimitiveRoot (ZZ_p &r, unsigned e)
int | mobius (int n)
| Compute mobius function (naive method as n is small).
ZZX | Cyclotomic (int N)
| Compute cyclotomic polynomial.
int | primroot (int N, int phiN)
| Find a primitive root modulo N.
int | ord (int N, int p)
| Compute the highest power of p that divides N.
ZZX | RandPoly (int n, const ZZ &p)
void | MulMod (ZZX &out, const ZZX &f, long a, long q, bool abs=true)
| Multiply the polynomial f by the integer a modulo q.
ZZX | MulMod (const ZZX &f, long a, long q, bool abs=true)
template<class T1 , class T2 >
void | convert (T1 &x1, const T2 &x2)
| A generic template that resolves to NTL's conv routine.
template<class T1 , class T2 >
void | convert (vector< T1 > &v1, const vector< T2 > &v2)
| A generic vector conversion routine.
void | mul (vector< ZZX > &x, const vector< ZZX > &a, long b)
void | div (vector< ZZX > &x, const vector< ZZX > &a, long b)
void | add (vector< ZZX > &x, const vector< ZZX > &a, const vector< ZZX > &b)
int | is_in (int x, int *X, int sz)
| Finds whether x is an element of the set X of size sz, Returns -1 it not and the location if true.
template<class zzvec >
bool | intVecCRT (vec_ZZ &vp, const ZZ &p, const zzvec &vq, long q)
| Incremental integer CRT for vectors. More...
template<class T , bool maxFlag>
long | argminmax (vector< T > &v)
| Find the index of the (first) largest/smallest element. More...
template<class T >
long | argmax (vector< T > &v)
template<class T >
long | argmin (vector< T > &v)
void | sampleSmall (ZZX &poly, long n=0)
| Sample polynomials with entries {-1,0,1}. Each coefficient is 0 with probability 1/2 and +-1 with probability 1/4.
void | sampleHWt (ZZX &poly, long Hwt, long n=0)
| Sample polynomials with entries {-1,0,1} with a given HAming weight. More...
void | sampleGaussian (ZZX &poly, long n=0, double stdev=1.0)
| Sample polynomials with Gaussian coefficients.
void | seekPastChar (istream &str, int cc)
| Advance the input stream beyond white spaces and a single instance of the char cc.
template<typename T >
long | lsize (const vector< T > &v)
| Size of STL vector as a long (rather than unsigned long)
template<typename T1 , typename T2 >
bool | sameObject (const T1 *p1, const T2 *p2)
| Testing if two vectors point to the same object.
void | ModComp (ZZX &res, const ZZX &g, const ZZX &h, const ZZX &f)
| Modular composition of polynomials: res = g(h) mod f.
void | PolyRed (ZZX &out, const ZZX &in, int q, bool abs=false)
| Reduce all the coefficients of a polynomial modulo q. More...
void | PolyRed (ZZX &out, const ZZX &in, const ZZ &q, bool abs=false)
void | PolyRed (ZZX &F, int q, bool abs=false)
void | PolyRed (ZZX &F, const ZZ &q, bool abs=false)
Some enhanced conversion routines
void | convert (long &x1, const GF2X &x2)
void | convert (long &x1, const zz_pX &x2)
void | convert (vec_zz_pE &X, const vector< ZZX > &A)
void | convert (mat_zz_pE &X, const vector< vector< ZZX > > &A)
void | convert (vector< ZZX > &X, const vec_zz_pE &A)
void | convert (vector< vector< ZZX > > &X, const mat_zz_pE &A)
The size of the coefficient vector of a polynomial.
ZZ | sumOfCoeffs (const ZZX &f)
ZZ | largestCoeff (const ZZX &f)
xdouble | coeffsL2Norm (const ZZX &f)

## Detailed Description

Miscellaneous utility functions.

## Function Documentation

void applyLinPoly | ( | zz_pE & | beta,
|  | const vec_zz_pE & | C,
|  | const zz_pE & | alpha,
|  | long | p
| ) |  |

Apply a linearized polynomial with coefficient vector C.

NTL's current smallint modulus, zz_p::modulus(), is assumed to be p^r, for p prime, r >= 1 integer.

template<class T , bool maxFlag>

long argminmax | ( | vector< T > & | v | ) |

Find the index of the (first) largest/smallest element.

These procedures are roughly just simpler variants of std::max_element and std::min_element. argmin/argmax are implemented as a template, so the code must be placed in the header file for the comiler to find it. The class T must have an implementation of operator> and operator< for this template to work.

Template Parameters

  maxFlag | A boolean value: true - argmax, false - argmin

void buildLinPolyCoeffs | ( | vec_zz_pE & | C,
|  | const vec_zz_pE & | L,
|  | long | p,
|  | long | r
| ) |  |

Combination of buildLinPolyMatrix and ppsolve.

Obtain the linearized polynomial coefficients from a vector L representing the action of a linear map on the standard basis for zz_pE over zz_p.

NTL's current smallint modulus, zz_p::modulus(), is assumed to be p^r, for p prime, r >= 1 integer.

template<class zzvec >

bool intVecCRT | ( | vec_ZZ & | vp,
|  | const ZZ & | p,
|  | const zzvec & | vq,
|  | long | q
| ) |  |

Incremental integer CRT for vectors.

Expects co-primes p,q with q odd, and such that all the entries in v1 are in [-p/2,p/2). Returns in v1 the CRT of vp mod p and vq mod q, as integers in [-pq/2, pq/2). Uses the formula:

where [...]_q means reduction to the interval [-q/2,q/2). Notice that if q is odd then this is the same as reducing to [-(q-1)/2,(q-1)/2], which means that [...]_q * p is in [-p(q-1)/2, p(q-1)/2], and since vp is in [-p/2,p/2) then the sum is indeed in [-pq/2,pq/2).

Return true is both vectors are of the same length, false otherwise

bool parseArgs | ( | int | argc,
|  | char * | argv[],
|  | argmap_t & | argmap
| ) |  |

Code for parsing command line arguments.

Tries to parse each argument as arg=val, and returns a correspinding map. It returns false if errors were detected, and true otherwise.

void PolyRed | ( | ZZX & | out,
|  | const ZZX & | in,
|  | int | q,
|  | bool | abs = `false`
| ) |  |

Reduce all the coefficients of a polynomial modulo q.

When abs=false reduce to interval (-q/2,...,q/2), when abs=true reduce to [0,q). When abs=false and q=2, maintains the same sign as the input.

void ppsolve | ( | vec_zz_pE & | x,
|  | const mat_zz_pE & | A,
|  | const vec_zz_pE & | b,
|  | long | p,
|  | long | r
| ) |  |

Prime power solver.

A is an n x n matrix, b is a length n (row) vector, this function finds a solution for the matrix-vector equation x A = b. An error is raised if A is not inverible mod p.

NTL's current smallint modulus, zz_p::modulus(), is assumed to be p^r, for p prime, r >= 1 integer.

void sampleHWt | ( | ZZX & | poly,
|  | long | Hwt,
|  | long | n = `0`
| ) |  |

Sample polynomials with entries {-1,0,1} with a given HAming weight.

Choose min(Hwt,n) coefficients at random in {-1,+1} and the others are set to zero. If n=0 then n=poly.deg()+1 is used.