| D.12.3.1 decimal | | number corresponding to the hexadecimal number s |
| D.12.3.2 eexgcdN | | T with sum_i L[i]*T[i]=T[n+1]=gcd(L[1],...,L[n]) |
| D.12.3.3 lcmN | | compute lcm(a,b) |
| D.12.3.4 powerN | | compute m^d mod n |
| D.12.3.5 chineseRem | | compute x such that x = T[i] mod L[i] |
| D.12.3.6 Jacobi | | the generalized Legendre symbol of a and n |
| D.12.3.7 primList | | the list of all primes <=n |
| D.12.3.8 primL | | first primes p_1,...,p_r such that q<p_1*...*p_r |
| D.12.3.9 intPart | | the integral part of a rational number |
| D.12.3.10 intRoot | | the integral part of the square root of m |
| D.12.3.11 squareRoot | | the square root of a in Z/p, p prime |
| D.12.3.12 solutionsMod2 | | basis solutions of Mx=0 over Z/2 |
| D.12.3.13 powerX | | q-th power of the i-th variable modulo I |
| D.12.3.14 babyGiant | | discrete logarithm x: b^x=y mod p |
| D.12.3.15 rho | | discrete logarithm x: b^x=y mod p |
| D.12.3.16 MillerRabin | | probabilistic primaly-test of Miller-Rabin |
| D.12.3.17 SolowayStrassen | | probabilistic primaly-test of Soloway-Strassen |
| D.12.3.18 PocklingtonLehmer | | primaly-test of Pocklington-Lehmer |
| D.12.3.19 PollardRho | | Pollard's rho factorization |
| D.12.3.20 pFactor | | Pollard's p-factorization |
| D.12.3.21 quadraticSieve | | quadratic sieve factorization |
| D.12.3.22 isOnCurve | | P is on the curve y^2z=x^3+a*xz^2+b*z^3 over Z/N |
| D.12.3.23 ellipticAdd | | P+Q, addition on elliptic curves |
| D.12.3.24 ellipticMult | | k*P on elliptic curves |
| D.12.3.25 ellipticRandomCurve | | generates y^2z=x^3+a*xz^2+b*z^3 over Z/N randomly |
| D.12.3.26 ellipticRandomPoint | | random point on y^2z=x^3+a*xz^2+b*z^3 over Z/N |
| D.12.3.27 countPoints | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.3.28 ellipticAllPoints | | points of y^2=x^3+a*x+b over Z/N |
| D.12.3.29 ShanksMestre | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.3.30 Schoof | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.3.31 generateG | | m-th division polynomial of y^2=x^3+a*x+b over Z/N |
| D.12.3.32 factorLenstraECM | | Lenstra's factorization |
| D.12.3.33 ECPP | | primaly-test of Goldwasser-Kilian |
| D.12.3.34 calculate_ordering | | Calculates x so that primitive^x == num1 mod mod1 |
| D.12.3.35 is_primitive_root | | Checks if primitive is a primitive root modulo mod1 |
| D.12.3.36 find_first_primitive_root | | Returns the first primitive root modulo mod1, starting with 1 |
| D.12.3.37 binary_add | | Adds a 1 to a binary encoded list |
| D.12.3.38 inverse_modulus | | Finds a t so that t*num = 1 mod mod1 |
| D.12.3.39 is_prime | | Checks if n is prime proc find_biggest_index(a) Returns the index of the biggest element of a |
| D.12.3.40 find_index | | Returns the list index of element e in list a. Returns 0 if e is not in a |
| D.12.3.41 subset_sum01 | | solves the subset-sum-knapsack-problem by calculating all subsets and choosing the right solution |
| D.12.3.42 subset_sum02 | | solves the subset-sum-knapsack-problem with a naive greedy algorithm |
| D.12.3.43 unbounded_knapsack | | solves the unbounded_knapsack-problem, needing a list of knapsack weights, a list of profits and a capacity |
| D.12.3.44 multidimensional_knapsack | | solves the multidimensional_knapsack-problem by using the PECH algorithm, needing a weight matrix m, a list of capacities and a list of profits |
| D.12.3.45 naccache_stern_generation | | generates a hard knapsack for the Naccache-Stern Kryptosystem for given key and prime modulus |
| D.12.3.46 naccache_stern_encryption | | encrypts a message with the Naccache-Stern Kryptosystem, using a hard knapsack, a message encoded as binary list and a prime modulus |
| D.12.3.47 naccache_stern_decryption | | decrypts a message with the Naccache-Stern Kryptosystem, using the easy knapsack, the key, the prime modulus and the message encoded as integer |
| D.12.3.48 m_merkle_hellman_transformation | | generates a hard knapsack for the multiplicative Merkle-Hellman Kryptosystem for a given easy knapsack and a primitive root for a modulus mod1 |
| D.12.3.49 m_merkle_hellman_encryption | | encrypts a message with the multiplicative Merkle-Hellman Kryptosystem, using a hard knapsack and a message encoded as binary list |
| D.12.3.50 m_merkle_hellman_decryption | | decrypts a message with the multiplicative Merkle-Hellman Kryptosystem, using the easy knapsack, the key given by the primitive root, the modulus mod1 and the message encoded as integer merkle_hellman_transformation(list knapsack, int key, int mod1 generates a hard knapsack for the Merkle-Hellman Kryptosystem for a given easy knapsack , a multiplicator key and a modulus mod1 |
| D.12.3.51 merkle_hellman_encryption | | encrypts a message with the Merkle-Hellman Kryptosystem, using a hard knapsack and a message encoded as binary list |
| D.12.3.52 merkle_hellman_decryption | | decrypts a message with the multiplicative Merkle-Hellman Kryptosystem, using the hard knapsack, the key, the modulus mod1 and the message encoded as integer |
| D.12.3.53 super_increasing_knapsack | | Creates the smallest super-increasing knapsack of given size ksize |
| D.12.3.54 h_increasing_knapsack | | Creates the smallest h-increasing knapsack of given size ksize and h |
| D.12.3.55 injective_knapsack | | Creates all list of all injective knapsacks of given size ksize and maximal element kmaxelement |
| D.12.3.56 calculate_max_sum | | Calculates the maximal sum of a given knapsack a |
| D.12.3.57 set_is_injective | | Checks if knapsack a is injective |
| D.12.3.58 is_h_injective | | Checks if knapsack a is h-injective |
| D.12.3.59 is_fix_injective | | Checks if knapsack a is fix-injective |
| D.12.3.60 three_elements | | Creates the smallest injective knapsack with a given injective_knapsack by using the three-elements-algorithm with a given number of iterations |
