| D.12.2.1 round | | rounds r to the nearest number in Z |
| D.12.2.2 bubblesort | | sorts elements of the list L |
| D.12.2.3 decimal | | number corresponding to the hexadecimal number s |
| D.12.2.4 eexgcdN | | T with sum_i L[i]*T[i]=T[n+1]=gcd(L[1],...,L[n]) |
| D.12.2.5 lcmN | | compute lcm(a,b) |
| D.12.2.6 powerN | | compute m^d mod n |
| D.12.2.7 chineseRem | | compute x such that x = T[i] mod L[i] |
| D.12.2.8 Jacobi | | the generalized Legendre symbol of a and n |
| D.12.2.9 primList | | the list of all primes <=n |
| D.12.2.10 primL | | first primes p_1,...,p_r such that q<p_1*...*p_r |
| D.12.2.11 intPart | | the integral part of a rational number |
| D.12.2.12 intRoot | | the integral part of the square root of m |
| D.12.2.13 squareRoot | | the square root of a in Z/p, p prime |
| D.12.2.14 solutionsMod2 | | basis solutions of Mx=0 over Z/2 |
| D.12.2.15 powerX | | q-th power of the i-th variable modulo I |
| D.12.2.16 babyGiant | | discrete logarithm x: b^x=y mod p |
| D.12.2.17 rho | | discrete logarithm x: b^x=y mod p |
| D.12.2.18 MillerRabin | | probabilistic primaly-test of Miller-Rabin |
| D.12.2.19 SolowayStrassen | | probabilistic primaly-test of Soloway-Strassen |
| D.12.2.20 PocklingtonLehmer | | primaly-test of Pocklington-Lehmer |
| D.12.2.21 PollardRho | | Pollard's rho factorization |
| D.12.2.22 pFactor | | Pollard's p-factorization |
| D.12.2.23 quadraticSieve | | quadratic sieve factorization |
| D.12.2.24 isOnCurve | | P is on the curve y^2z=x^3+a*xz^2+b*z^3 over Z/N |
| D.12.2.25 ellipticAdd | | P+Q, addition on elliptic curves |
| D.12.2.26 ellipticMult | | k*P on elliptic curves |
| D.12.2.27 ellipticRandomCurve | | generates y^2z=x^3+a*xz^2+b*z^3 over Z/N randomly |
| D.12.2.28 ellipticRandomPoint | | random point on y^2z=x^3+a*xz^2+b*z^3 over Z/N |
| D.12.2.29 countPoints | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.2.30 ellipticAllPoints | | points of y^2=x^3+a*x+b over Z/N |
| D.12.2.31 ShanksMestre | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.2.32 Schoof | | number of points of y^2=x^3+a*x+b over Z/N |
| D.12.2.33 generateG | | m-th division polynomial of y^2=x^3+a*x+b over Z/N |
| D.12.2.34 factorLenstraECM | | Lenstra's factorization |
| D.12.2.35 ECPP | | primaly-test of Goldwasser-Kilian |
| D.12.2.36 calculate_ordering | | Calculates x so that primitive^x == num1 mod mod1 |
| D.12.2.37 is_primitive_root | | Checks if primitive is a primitive root modulo mod1 |
| D.12.2.38 find_first_primitive_root | | Returns the first primitive root modulo mod1, starting with 1 |
| D.12.2.39 binary_add | | Adds a 1 to a binary encoded list |
| D.12.2.40 inverse_modulus | | Finds a t so that t*num = 1 mod mod1 |
| D.12.2.41 is_prime | | Checks if n is prime proc find_biggest_index(a) Returns the index of the biggest element of a |
| D.12.2.42 find_index | | Returns the list index of element e in list a. Returns 0 if e is not in a |
| D.12.2.43 subset_sum01 | | solves the subset-sum-knapsack-problem by calculating all subsets and choosing the right solution |
| D.12.2.44 subset_sum02 | | solves the subset-sum-knapsack-problem with a naive greedy algorithm |
| D.12.2.45 unbounded_knapsack | | solves the unbounded_knapsack-problem, needing a list of knapsack weights, a list of profits and a capacity |
| D.12.2.46 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.12.2.47 naccache_stern_generation | | generates a hard knapsack for the Naccache-Stern Kryptosystem for given key and prime modulus |
| D.12.2.48 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.12.2.49 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.12.2.50 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.12.2.51 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.12.2.52 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.12.2.53 merkle_hellman_encryption | | encrypts a message with the Merkle-Hellman Kryptosystem, using a hard knapsack and a message encoded as binary list |
| D.12.2.54 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.12.2.55 super_increasing_knapsack | | Creates the smallest super-increasing knapsack of given size ksize |
| D.12.2.56 h_increasing_knapsack | | Creates the smallest h-increasing knapsack of given size ksize and h |
| D.12.2.57 injective_knapsack | | Creates all list of all injective knapsacks of given size ksize and maximal element kmaxelement |
| D.12.2.58 calculate_max_sum | | Calculates the maximal sum of a given knapsack a |
| D.12.2.59 set_is_injective | | Checks if knapsack a is injective |
| D.12.2.60 is_h_injective | | Checks if knapsack a is h-injective |
| D.12.2.61 is_fix_injective | | Checks if knapsack a is fix-injective |
| D.12.2.62 three_elements | | Creates the smallest injective knapsack with a given injective_knapsack by using the three-elements-algorithm with a given number of iterations |
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