| 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 |