Program Listing for File nbtheory.h
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//==================================================================================
// BSD 2-Clause License
//
// Copyright (c) 2014-2023, NJIT, Duality Technologies Inc. and other contributors
//
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//
// Author TPOC: contact@openfhe.org
//
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// modification, are permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this
// list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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//==================================================================================
/*
* This code provides number theory utilities.
* NBTHEORY is set set of functions that will be used to calculate following:
* - If two numbers are coprime.
* - GCD of two numbers
* - If number i Prime
* - witnesss function to test if number is prime
* - Roots of unit for provided cyclotomic integer
* - Eulers Totient function phin(n)
* - Generator algorithm
*/
#ifndef LBCRYPTO_INC_MATH_NBTHEORY_H
#define LBCRYPTO_INC_MATH_NBTHEORY_H
#include "math/hal/basicint.h"
#include "utils/inttypes.h"
#include "utils/exception.h"
#include <memory>
#include <random>
#include <set>
// #include <string>
#include <vector>
#if defined(HAVE_INT128)
namespace { // to define local (or C-style static) functions here
inline int clz_u128(uint128_t u) {
uint64_t hi(u >> 64), lo(u);
return hi ? __builtin_clzll(hi) : lo ? __builtin_clzll(lo) + 64 : 128;
}
}; // namespace
#endif
namespace lbcrypto {
template <typename IntType>
IntType RootOfUnity(usint m, const IntType& modulo);
template <typename IntType>
std::vector<IntType> RootsOfUnity(usint m, const std::vector<IntType>& moduli);
// precomputed reverse of a byte
inline static unsigned char reverse_byte(unsigned char x) {
static const unsigned char table[] = {
0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0, 0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0, 0x08, 0x88,
0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8, 0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8, 0x04, 0x84, 0x44, 0xc4,
0x24, 0xa4, 0x64, 0xe4, 0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4, 0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac,
0x6c, 0xec, 0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc, 0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2,
0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2, 0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea, 0x1a, 0x9a,
0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa, 0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6, 0x16, 0x96, 0x56, 0xd6,
0x36, 0xb6, 0x76, 0xf6, 0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee, 0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe,
0x7e, 0xfe, 0x01, 0x81, 0x41, 0xc1, 0x21, 0xa1, 0x61, 0xe1, 0x11, 0x91, 0x51, 0xd1, 0x31, 0xb1, 0x71, 0xf1,
0x09, 0x89, 0x49, 0xc9, 0x29, 0xa9, 0x69, 0xe9, 0x19, 0x99, 0x59, 0xd9, 0x39, 0xb9, 0x79, 0xf9, 0x05, 0x85,
0x45, 0xc5, 0x25, 0xa5, 0x65, 0xe5, 0x15, 0x95, 0x55, 0xd5, 0x35, 0xb5, 0x75, 0xf5, 0x0d, 0x8d, 0x4d, 0xcd,
0x2d, 0xad, 0x6d, 0xed, 0x1d, 0x9d, 0x5d, 0xdd, 0x3d, 0xbd, 0x7d, 0xfd, 0x03, 0x83, 0x43, 0xc3, 0x23, 0xa3,
0x63, 0xe3, 0x13, 0x93, 0x53, 0xd3, 0x33, 0xb3, 0x73, 0xf3, 0x0b, 0x8b, 0x4b, 0xcb, 0x2b, 0xab, 0x6b, 0xeb,
0x1b, 0x9b, 0x5b, 0xdb, 0x3b, 0xbb, 0x7b, 0xfb, 0x07, 0x87, 0x47, 0xc7, 0x27, 0xa7, 0x67, 0xe7, 0x17, 0x97,
0x57, 0xd7, 0x37, 0xb7, 0x77, 0xf7, 0x0f, 0x8f, 0x4f, 0xcf, 0x2f, 0xaf, 0x6f, 0xef, 0x1f, 0x9f, 0x5f, 0xdf,
0x3f, 0xbf, 0x7f, 0xff,
};
return table[x];
}
static int shift_trick[] = {0, 7, 6, 5, 4, 3, 2, 1};
/* Function to reverse bits of num */
inline usint ReverseBits(usint num, usint msb) {
usint msbb = (msb >> 3) + (msb & 0x7 ? 1 : 0);
switch (msbb) {
case 1:
return (reverse_byte((num)&0xff) >> shift_trick[msb & 0x7]);
case 2:
return (reverse_byte((num)&0xff) << 8 | reverse_byte((num >> 8) & 0xff)) >> shift_trick[msb & 0x7];
case 3:
return (reverse_byte((num)&0xff) << 16 | reverse_byte((num >> 8) & 0xff) << 8 |
reverse_byte((num >> 16) & 0xff)) >>
shift_trick[msb & 0x7];
case 4:
return (reverse_byte((num)&0xff) << 24 | reverse_byte((num >> 8) & 0xff) << 16 |
reverse_byte((num >> 16) & 0xff) << 8 | reverse_byte((num >> 24) & 0xff)) >>
shift_trick[msb & 0x7];
default:
return -1;
// OPENFHE_THROW("msbb value not handled:" +
// std::to_string(msbb));
}
}
template <
typename T,
std::enable_if_t<std::is_integral_v<T> || std::is_same_v<T, int128_t> || std::is_same_v<T, uint128_t>, bool> = true>
inline constexpr usint GetMSB(T x) {
if constexpr (sizeof(T) <= 8) {
if (x == 0)
return 0;
#if defined(_MSC_VER)
unsigned long msb; // NOLINT
_BitScanReverse64(&msb, uint64_t(x));
return msb + 1;
#else
// a wrapper for GCC
return 64 -
(sizeof(unsigned long) == 8 ? __builtin_clzl(uint64_t(x)) : __builtin_clzll(uint64_t(x))); // NOLINT
#endif
}
#if defined(HAVE_INT128)
else if constexpr (sizeof(T) == 16) {
#if defined(_MSC_VER)
static_assert(false, "MSVC doesn't support 128-bit integers");
#endif
return 128 - clz_u128(uint128_t(x));
}
#endif
else {
OPENFHE_THROW("Unsupported int type (GetMSB() supports 32-, 64- and 128-bit integers only)");
return 0;
}
}
inline constexpr usint GetMSB64(uint64_t x) {
return GetMSB(x);
}
template <typename IntType>
std::shared_ptr<std::vector<int64_t>> GetDigits(const IntType& u, uint64_t base, uint32_t k) {
auto u_vec = std::make_shared<std::vector<int64_t>>(k);
size_t baseDigits = (uint32_t)(std::round(log2(base))); // ?
// if (!(base & (base - 1)))
IntType uu = u;
IntType uTemp;
for (size_t i = 0; i < k; i++) { // ****************4/1/2018 This loop is correct.
uTemp = uu >> baseDigits;
(*u_vec)[i] = (uu - (uTemp << baseDigits)).ConvertToInt();
uu = uTemp;
}
return u_vec;
}
template <typename IntType>
IntType GreatestCommonDivisor(const IntType& a, const IntType& b);
template <typename IntType>
bool MillerRabinPrimalityTest(const IntType& p, const usint niter = 100);
template <typename IntType>
const IntType PollardRhoFactorization(const IntType& n);
template <typename IntType>
void PrimeFactorize(IntType n, std::set<IntType>& primeFactors);
template <typename IntType>
IntType FirstPrime(uint32_t nBits, uint32_t m);
template <typename IntType>
IntType LastPrime(uint32_t nBits, uint32_t m);
template <typename IntType>
IntType NextPrime(const IntType& q, uint32_t m);
template <typename IntType>
IntType PreviousPrime(const IntType& q, uint32_t m);
usint ModInverse(usint a, usint b);
template <typename IntType>
IntType NextPowerOfTwo(IntType n);
uint64_t GetTotient(const uint64_t n);
template <typename IntType>
std::vector<IntType> GetTotientList(const IntType& n);
template <typename IntVector>
IntVector PolyMod(const IntVector& dividend, const IntVector& divisor, const typename IntVector::Integer& modulus);
template <typename IntVector>
IntVector PolynomialMultiplication(const IntVector& a, const IntVector& b);
template <typename IntVector>
IntVector GetCyclotomicPolynomial(usint m, const typename IntVector::Integer& modulus);
std::vector<int> GetCyclotomicPolynomialRecursive(usint m);
template <typename IntVector>
typename IntVector::Integer SyntheticRemainder(const IntVector& dividend, const typename IntVector::Integer& a,
const typename IntVector::Integer& modulus);
template <typename IntVector>
IntVector SyntheticPolyRemainder(const IntVector& dividend, const IntVector& aList,
const typename IntVector::Integer& modulus);
template <typename IntVector>
IntVector PolynomialPower(const IntVector& input, usint power);
template <typename IntVector>
IntVector SyntheticPolynomialDivision(const IntVector& dividend, const typename IntVector::Integer& a,
const typename IntVector::Integer& modulus);
template <typename IntType>
bool IsGenerator(const IntType& g, const IntType& q);
template <typename IntType>
IntType FindGeneratorCyclic(const IntType& q);
uint32_t FindAutomorphismIndex2n(int32_t i, uint32_t m);
uint32_t FindAutomorphismIndex2nComplex(int32_t i, uint32_t m);
uint32_t FindAutomorphismIndexCyclic(int32_t i, uint32_t m, uint32_t g);
void PrecomputeAutoMap(uint32_t n, uint32_t k, std::vector<uint32_t>* precomp);
} // namespace lbcrypto
#endif