Version 5.0 The LEDA User Manual

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e able to change your message without being detected but everybody can read it. On the other hand, if you use only encryption then nobody can read your message but an attacker could change it. At first sight this does not seem to make much sense because the attacker can only alter ciphertext and he will not be able to predict what the corresponding plaintext will look like. However, this may still cause damage. Imagine for example a satellite that is remote controlled via encrypted but unauthenticated commands. If an attacker manages to make the satellite listen to his commands, he cannot exploit the device but he might be able to make it leave its orbit and crash. Hence, sometimes secrecy and authentication must be used together to achieve the desired security. LEDA makes it easy to combine these different aspects. The example below will illustrate this. The program is similar to the opening example of Chapter 9. It consists of three parts: key generation, encoding and decoding. Each part will be explained below. #include // contains all cryptography classes using namespace leda; void generate_keys(CryptKey& auth_key, CryptKey& cipher_key) { // key generation (two keys) CryptByteString passphrase = CryptKey::read_passphrase("Passphrase: "); CryptByteString salt(1); salt[0] = ’a’; // for authentication auth_key = CryptKey::generate_key(128/8, passphrase, salt); salt[0] = ’c’; // for enciphering/deciphering cipher_key = CryptKey::generate_key(128/8, passphrase, salt); } int main() { string str = "Hello World"; CryptKey auth_key, cipher_key; // encode: MAC -> compress -> encipher typedef CoderPipe3< OMACCoder, PPMIICoder, CBCCoder > CryptCoder; encoding_ofstream out("foo"); generate_keys(auth_key, cipher_key); out.get_coder()->get_coder1()->set_key(auth_key); out.get_coder()->get_coder3()->set_key(cipher_key); out set_key(auth_key);
in.get_coder()->get_coder3()->set_key(cipher_key); str.read_line(in); in.finish(); // read till EOF is reached and then close "in" if (in.fail()) std::cout
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Version 5.0 The LEDA User Manual Al
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4.14 Socket Streambuffer ( socket s
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9.11 Move-To-Front Coder II ( MTF2C
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13.1.2 Handles and Iterators . . .
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16.7 Simplices in 3D-Space ( d3 sim
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License Terms and Availability Any
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7. LEDA is available from Algorithm
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Chapter 2 Basics An extended versio
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XYZ y(x1, ... ,xt); ,tk > and uses
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2.3.1 Linear Orders Many data types
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dictionary D0; // default ordering
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2.3.3 Implementation Parameters Man
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lookup returned the location where
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list::iterator defines the iterator
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• internal (LEDA/incl/internal/)
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string s(const char ∗ p); string
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ool bool bool bool istream& ostream
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string buffer, i.e., all output ope
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andom source& S ≫ char& x random
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int R.set weight(int i, int g) sets
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4.10 Memory Allocator ( leda alloca
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4.11 Error Handling ( error ) LEDA
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4.12 Files and Directories ( file )
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4.13 Sockets ( leda socket ) 1. Def
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ool S.receive string(string& s) rec
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ool sb.failed( ) returns whether a
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4.15 Some Useful Functions ( misc )
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4.16 Timer ( timer ) 1. Definition
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unsigned fibonacci(unsigned n) { st
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unsigned fibonacci(unsigned n) { st
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int Hash(const two tuple& p) hash f
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3. Creation four tuple p; creates a
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4.21 A date interface ( date ) 1. D
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3. Creation date D; creates an inst
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string D.get month name( ) returns
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Now we show an example in which dif
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integer integer a(const char ∗ s)
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5.2 Rational Numbers ( rational ) 1
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5.3 The data type bigfloat ( bigflo
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ounding modes bigfloat :: get round
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ostream& ostream& os ≪ const bigf
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double x.get double error( ) bigflo
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int int real roots(const Polynomial
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√ y v = b 1 c 2 + b 2 c 1 ± sign
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5.5 Interval Arithmetic in LEDA ( i
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void x.set midpoint(VOLATILE I doub
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5.7 The mod kernel of type residual
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int residual :: required primetable
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5.9 A Floating Point Filter ( float
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5.10 Double-Valued Vectors ( vector
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double v.zcoord( ) returns the seco
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matrix matrix matrix vector M + con
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5.12 Vectors with Integer Entries (
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5.13 Matrices with Integer Entries
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integer matrix inverse(const intege
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distinct representatives and linear
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at vector v(const array& A); introd
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int compare by angle(const rat vect
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5.15 Real-Valued Vectors ( real vec
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int compare by angle(const real vec
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eal matrix M + const real matrix& M
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5.17.2 Integration double integrate
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array A(int low, const E& x, const
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int A.binary locate(int (∗cmp)(co
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6.3 Stacks ( stack ) 1. Definition
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6.5 Bounded Stacks ( b stack ) 1. D
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6.7 Linear Lists ( list ) 1. Defini
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const E& L.pop front( ) same as L.p
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Sorting and Searching void L.sort(i
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Input and Output void L.read(istrea
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6.8 Singly Linked Lists ( slist ) 1
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6.9 Sets ( set ) 1. Definition An i
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4. Implementation Sets are implemen
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int set S | const int set& T return
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d int set S − const d int set& T
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6.12 Partitions ( partition ) 1. De
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6.13 Parameterized Partitions ( Par
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void D.evert(vertex v) makes v the
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4. Implementation Dynamic collectio
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dictionary D(int (∗cmp)(const K&
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7.2 Dictionary Arrays ( d array ) 1
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{ d_array dic; dic["hello"] = "hall
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ool A.empty( ) returns true if A is
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Note that it is not possible to ite
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void M.clear( ) clears M by making
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p dictionary D.change inf(p dic ite
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void D.del(const K& k) deletes the
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3. Creation sortseq S; creates an i
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seq item S.max item( ) returns the
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Iteration forall items(it, S) { “
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Chapter 8 Priority Queues 8.1 Prior
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6. Example Dijkstra’s Algorithm (
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int Q.size( ) returns the size of Q
Page 194 and 195: Assume that you want to send the fi
Page 196 and 197: 9.1 Adaptive Arithmetic Coder ( A0C
Page 198 and 199: uint32 C.get scale threshold( ) uin
Page 200 and 201: uint32 C.decode memory chunk(const
Page 202 and 203: 3. Creation PPMIICoder C(streambuf
Page 204 and 205: 9.4 Deflation/Inflation Coder ( Def
Page 206 and 207: void C.set compression level(int le
Page 208 and 209: void void C.set src stream(streambu
Page 210 and 211: streambuf ∗ C.get src stream( ) r
Page 212 and 213: streambuf ∗ C.get src stream( ) r
Page 214 and 215: uint32 C.decode memory chunk(const
Page 216 and 217: uint32 C.encode memory chunk(const
Page 218 and 219: 9.10 Move-To-Front Coder ( MTFCoder
Page 220 and 221: 9.11 Move-To-Front Coder II ( MTF2C
Page 222 and 223: 9.12 RLE for Runs of Zero ( RLE0Cod
Page 224 and 225: 9.13 Checksummers ( checksummer bas
Page 226 and 227: ool C.checksum is valid( ) returns
Page 228 and 229: 9.19 Encoding Output Stream ( encod
Page 230 and 231: ostream& os.seekp(streamoff off , i
Page 232 and 233: 9.23 Coder Pipes ( CoderPipe2 ) 1.
Page 234 and 235: void C.set coder1(Coder1 ∗ c1 , b
Page 236 and 237: void void C.set src stream(streambu
Page 238 and 239: 3. Operations Standard Operations v
Page 240 and 241: string out_file1 = tmp_file_name(),
Page 242 and 243: void mb.truncate(streamsize n) also
Page 246 and 247: Then you can use the CryptAutoDecod
Page 248 and 249: 10.1 Secure Byte String ( CryptByte
Page 250 and 251: CryptKey k(const byte ∗ bytes, ui
Page 252 and 253: 10.3 Encryption and Decryption with
Page 254 and 255: 10.4 Example for a Stream-Cipher (
Page 256 and 257: uint16 void C.get accepted key size
Page 258 and 259: 3. Operations Standard Operations v
Page 260 and 261: 10.6 Automatic Decoder supporting C
Page 262 and 263: void C.add keys in file(const char
Page 264 and 265: secure socket streambuf sb(leda soc
Page 267 and 268: Chapter 11 Graphs and Related Data
Page 269 and 270: 2. Creation graph G; creates an obj
Page 271 and 272: edge G.first in edge(node v) return
Page 273 and 274: void G.hide node(node v) removes no
Page 275 and 276: void G.bucket sort nodes(int l, int
Page 277 and 278: edge G.new map edge(edge e1 , edge
Page 279 and 280: edge edge edge G.new edge(node v, e
Page 281 and 282: void void G.print(string s, ostream
Page 283 and 284: graph algorithms, i.e., algorithms
Page 285 and 286: void void G.sort nodes(const list&
Page 287 and 288: • Opposite Graphs (opposite graph
Page 289 and 290: 4. Operations The interface consist
Page 291 and 292: int main () { static_graph G; array
Page 293 and 294: 3. Implementation see section 11.2.
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list M.triangulate( ) triangulates
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void M.assign(face f, const ftype&
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void A.init(const graph t& G, int n
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ool M.use node data(const graph t&
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ool M.use edge data(const graph t&
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E& M[face f] returns the variable M
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4. Implementation Node matrices for
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4. Implementation Node maps are imp
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11.17 Sets of Edges ( edge set ) 1.
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node L.cyclic pred(node v) returns
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11.20 Node Priority Queues ( node p
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11.21 Bounded Node Priority Queues
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11.22 Graph Generators ( graph gen
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uedges. For n > 3, a random maximal
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void random planar graph(graph& G,
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ool Is Bidirected(const graph& G) r
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list Delete Loops(graph& G) returns
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11.25 Dynamic Markov Chains ( dynam
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has a source and a target. These ar
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void parser.append(const char ∗ k
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11.27 The LEDA graph input/output f
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arithmetic demand for each function
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GRAPH TRANSITIVE CLOSURE(const gra
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template bool SHORTEST PATH T(cons
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template bool ALL PAIRS SHORTEST P
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The algorithms have the following a
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inline NT MAX FLOW GRH T(const grap
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12.5 Minimum Cut ( min cut ) A cut
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that the bipartition (A, B) is give
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The pre-instantiations for number t
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template bool CHECK MIN WEIGHT ASS
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in general graph. You may skip the
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Worst-Case Running Time: All functi
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list MIN WEIGHT PERFECT MATCHING T(
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12.10 Stable Matching ( stable matc
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12.11 Minimum Spanning Trees ( min
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12.13 Algorithms for Planar Graphs
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ool bool Is CCW Ordered(const graph
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ool void void void TUTTE EMBEDDING(
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Chapter 13 Graphs and Iterators 13.
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The purpose of each iterator is the
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template void set_and_check (graph
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In addition to the algorithm mentio
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13.3 Edge Iterators ( EdgeIt ) 1. D
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#include < LEDA/graph/graph iterato
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OutAdjIt OutAdjIt OutAdjIt it(const
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OutAdjIt& −−it performs one ste
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ool it.eol( ) returns !it.valid( )
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void it.del( ) deletes the marked l
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3. Operations void fc.init(const le
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We would have to write something li
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Equal is a class that compares two
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used only as a “Trojan horse,”
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typename DataAccessor :: value type
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13.14 Constant Accessors ( constant
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13.16 Node Attribute Accessors ( no
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GIT BFS< OutAdjIt, Queuetype, Mark
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3. dfs grow depth: a new adjacency
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• indegree stores for every node
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• Mark is a data accessor that ha
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OutAdjIt algorithm.curr adj( ) retu
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14.1 Points ( point ) 1. Definition
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point p.reflect(const point& q, con
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ool contained in simplex(const arra
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4. Operations point s.start( ) retu
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segment s.rotate90(const point& q,
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double r.direction( ) returns the d
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14.4 Straight Lines ( line ) 1. Def
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line l.translate(const vector& v) r
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14.5 Circles ( circle ) 1. Definiti
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circle C + const vector& v returns
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14.6 Polygons ( POLYGON ) 1. Defini
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const list& P.segments( ) returns t
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ool P.inside(const POINT & p) bool
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14.7 Generalized Polygons ( GEN POL
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GEN POLYGON GEN POLYGON :: make wea
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int P.side of(const POINT & p) regi
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14.8 Triangles ( triangle ) 1. Defi
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triangle t.rotate90(const point& q,
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double r.height( ) returns the heig
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14.10 Rational Points ( rat point )
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at point p.reflect(const rat point&
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int side of halfspace(const rat poi
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at segment s(const segment& s1 , in
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ational s.y abs( ) returns the y-ab
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14.12 Rational Rays ( rat ray ) 1.
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ool r.contains(const rat segment& s
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void l.normalize( ) simplifies the
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at line p bisector(const rat point&
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at circle C(const circle& c, int pr
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14.15 Rational Triangles ( rat tria
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at triangle t − const rat vector&
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list r.vertices( ) returns the vert
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list r.intersection(const rat recta
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int p.orientation(const real point&
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eal area(const real point& a, const
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14.18 Real Segments ( real segment
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ool s.intersection(const real segme
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14.19 Real Rays ( real ray ) 1. Def
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Non-Member Functions int orientatio
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4. Operations real point l.point1(
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int cmp slopes(const real line& l1
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eal circle C(const circle& c, int p
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ool radical axis(const real circle&
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eal point t.point3( ) returns the t
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14.23 Iso-oriented Real Rectangles
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eal rectangle r.translate(real dx,
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14.24 Geometry Algorithms ( geo alg
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edge TRIANGULATE PLANE MAP(GRAPH &
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gen polygon MINKOWSKI SUM(const pol
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ool MIN WIDTH ANNULUS(const list& L
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double CLOSEST PAIR(list& L, point&
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14.25 Transformation ( TRANSFORM )
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TRANSFORM reflection(const POINT& q
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void random points in unit cube(int
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void random points on unit circle(i
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const rat point& p.to rat point( )
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circle segment cs(const rat circle&
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list cs.intersection(const r circle
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14.29 Polygons with circular edges
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CHECK TYPE P.check simplicity( ) ch
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ool P.inside(const r circle point&
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circle gen polygon P (KIND k); crea
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list P.intersection(const rat line&
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double P.approximate area( ) approx
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const I& D.inf(dic2 item it) return
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15.2 Point Sets and Delaunay Triang
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ool T.is hull edge(edge e) as above
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list T.range search(node v, const P
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15.3 Sets of Intervals ( interval s
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15.4 Sets of Parallel Segments ( se
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15.5 Sets of Parallel Rational Segm
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15.6 Planar Subdivisions ( subdivis
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16.1 Points in 3D-Space ( d3 point
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d3 point midpoint(const d3 point& a
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ool outside sphere(const d3 point&
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ool bool r.project xz(ray& m) if th
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segment s.project xy( ) returns the
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ool l.project(const d3 point& p, co
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double p.sqr dist(const d3 point& q
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16.6 Spheres in 3D-Space ( d3 spher
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16.7 Simplices in 3D-Space ( d3 sim
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16.8 Rational Points in 3D-Space (
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d3 rat point p.translate(const rat
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ool coplanar(const d3 rat point& a,
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d3 rat point random d3 rat point in
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void random d3 rat points on segmen
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ool r.project xy(rat ray& m) bool r
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ool l.project yz(rat line& m) if th
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16.11 Rational Segments in 3D-Space
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d3 rat segment s + const rat vector
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d3 plane p.to float( ) returns a fl
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16.13 Rational Spheres ( d3 rat sph
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16.14 Rational Simplices ( d3 rat s
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16.15 3D Convex Hull Algorithms ( d
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Chapter 17 Graphics This section de
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17.2 Windows ( window ) 1. Definiti
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18. The buttons per line parameter
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void W.display(window& W 0 , int x,
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void W.set show coord object(const
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int W.menu bar height( ) returns th
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void W.draw ray(point p, point q, l
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void W.draw filled ellipse(double x
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void void void void void W.draw rou
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void void void W.draw edge(double x
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void W.screenshot(string fname, boo
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int W.read mouse seg(const point& p
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int W.read event(int& val, double&
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window& W ≫ segment& s reads a se
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panel item W.bool item(string s, bo
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panel item W.int item(string s, int
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int W.button(string s, const char
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int W.button(string s, window& M, c
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void void void W.redraw panel(panel
Page 651 and 652:
17.4 Menues ( menu ) 1. Definition
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17.5 Postscript Files ( ps file ) 1
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shape: the shape of the node (type
Page 657 and 658:
void gw.display(int x, int y) displ
Page 659 and 660:
param type gw.set param(node v, par
Page 661 and 662:
string gw.set edge index format(str
Page 663 and 664:
void void gw.transform layout(node
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int bool bool gw.load layout(istrea
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void void gw.set edge slider handle
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int bool bool bool bool bool bool g
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void gw.restore all attributes( ) .
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6. edge index format format This li
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of GraphWin) are 0 (central pos) 1
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17.7.1 A complete example LEDA.GRAP
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17.8 Geometry Windows ( GeoWin ) 1.
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0 will be drawn on top in the order
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geowin new scene and geowin get obj
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e inserted in the result scene. In
Page 687 and 688:
geo_scene sc_points = gw.new_scene(
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} }; int main() { GeoWin gw; list L
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virtual bool is_running(const GeoWi
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geo scene void int GW.get scene wit
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color GW.get fill color(geo scene s
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void∗ GW.set client data(geo scen
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color GW.set obj color(GeoBaseScene
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template string GW.set obj label(G
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string string GW.get bg pixmap( ) r
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• A DRAG (button not released)
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template bool GW.set post del hand
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geowin_gui_rat_transform geowin_gui
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ool GW.del(geo scenegroup GS , geo
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void GW.set d3 fcn(geo scene sc, vo
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17.9 Windows for 3d visualization (
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int D.move( ) animates the contents
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Chapter 18 Implementations 18.1 Lis
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void clear(); int size() const; };
Page 723:
18.2.3 Sorted Sequences Any class s
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libGeoW is the LEDA library providi
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(b) Type VCVARS32 (VSVARS32). 2. Go
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LEDA MEMORY STD: If this is set, th
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When using graphics on Solaris syst
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(7) Double click on prog.cpp If you
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• extend LIB by Otherwise add ne
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and at least one of the following d
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• Copy leda .dll to the bin\ subd
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Preparations To install LEDA you on
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• libg .lib libl .lib for program
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cl -TP prog.c Programs using grap
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Automatic Setting Include header fi
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The default value is ”/MLd”, al
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2. Windows 95/98: (a) Add the line
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Preparations To install LEDA you on
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A.16 Platforms When this manual was
Page 758 and 759:
(b) For objects x and y of an indep
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A and B are different objects: A ==
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if (p.y > q.y) return 1; return 0;
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partypes={no, yes} Determines how p
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Stacks ( stack ) 1. Definition An i
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Bibliography [1] H. Alt, N. Blum, K
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[31] I. Fary: “On Straight Line R
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[67] M. Mignotte: Mathematics for C
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Index Symbols L A TEX . . . . . . .
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adj nodes(...) graph . . . . . . .
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circle gen polygon . . . . . . . .
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at ray . . . . . . . . . . . . . .
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CBCCoder< BlkCipher > . . . . . . .
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disconnect() leda socket . . . . .
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edges() GEN POLYGON . . . . . . . .
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finger locate pre...(...) sortseq .
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checksummer base . . . . . . . . .
Page 793 and 794:
OMACCoder< BlkCipher > . . . . . .
Page 795 and 796:
get stack() GIT DFS . . . . . . . .
Page 797 and 798:
in pred(...) graph . . . . . . . .
Page 799 and 800:
eal triangle . . . . . . . . . . .
Page 801 and 802:
at segment . . . . . . . . . . . .
Page 803 and 804:
eal rectangle . . . . . . . . . . .
Page 805 and 806:
mw matching . . . . . . . . . . . .
Page 807 and 808:
outdeg(...) graph . . . . . . . . .
Page 809 and 810:
pos(...) POINT SET . . . . . . . .
Page 811 and 812:
eal matrix . . . . . . . . . . . .
Page 813 and 814:
FaceIt . . . . . . . . . . . . . .
Page 815 and 816:
save gw(...) GraphWin . . . . . . .
Page 817 and 818:
set edge index fo...(...) GraphWin
Page 819 and 820:
GeoWin . . . . . . . . . . . . . .
Page 821 and 822:
DeflateCoder . . . . . . . . . . .
Page 823 and 824:
planar map . . . . . . . . . . . .
Page 825 and 826:
d3 rat point . . . . . . . . . . .
Page 827 and 828:
GraphWin . . . . . . . . . . . . .
Page 829 and 830:
at segment . . . . . . . . . . . .
show all

Version 5.0 The LEDA User Manual

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