Crypto++ 8.1 Free C++ class library of cryptographic schemes

integer.h
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1 // integer.h - originally written and placed in the public domain by Wei Dai
2
3 /// \file integer.h
4 /// \brief Multiple precision integer with arithmetic operations
5 /// \details The Integer class can represent positive and negative integers
6 /// with absolute value less than (256**sizeof(word))<sup>(256**sizeof(int))</sup>.
7 /// \details Internally, the library uses a sign magnitude representation, and the class
8 /// has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
9 /// used to hold the representation. The second is a Sign (an enumeration), and it is
10 /// used to track the sign of the Integer.
11 /// \details For details on how the Integer class initializes its function pointers using
12 /// InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
13 /// Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
14 /// \since Crypto++ 1.0
15
16 #ifndef CRYPTOPP_INTEGER_H
17 #define CRYPTOPP_INTEGER_H
18
19 #include "cryptlib.h"
20 #include "secblock.h"
21 #include "stdcpp.h"
22
23 #include <iosfwd>
24
25 NAMESPACE_BEGIN(CryptoPP)
26
27 /// \struct InitializeInteger
28 /// \brief Performs static initialization of the Integer class
29 struct InitializeInteger
30 {
31 InitializeInteger();
32 };
33
34 // Always align, http://github.com/weidai11/cryptopp/issues/256
35 typedef SecBlock<word, AllocatorWithCleanup<word, true> > IntegerSecBlock;
36
37 /// \brief Multiple precision integer with arithmetic operations
38 /// \details The Integer class can represent positive and negative integers
39 /// with absolute value less than (256**sizeof(word))<sup>(256**sizeof(int))</sup>.
40 /// \details Internally, the library uses a sign magnitude representation, and the class
41 /// has two data members. The first is a IntegerSecBlock (a SecBlock<word>) and it is
42 /// used to hold the representation. The second is a Sign (an enumeration), and it is
43 /// used to track the sign of the Integer.
44 /// \details For details on how the Integer class initializes its function pointers using
45 /// InitializeInteger and how it creates Integer::Zero(), Integer::One(), and
46 /// Integer::Two(), then see the comments at the top of <tt>integer.cpp</tt>.
47 /// \since Crypto++ 1.0
48 /// \nosubgrouping
49 class CRYPTOPP_DLL Integer : private InitializeInteger, public ASN1Object
50 {
51 public:
52 /// \name ENUMS, EXCEPTIONS, and TYPEDEFS
53 //@{
54 /// \brief Exception thrown when division by 0 is encountered
55 class DivideByZero : public Exception
56 {
57 public:
58 DivideByZero() : Exception(OTHER_ERROR, "Integer: division by zero") {}
59 };
60
61 /// \brief Exception thrown when a random number cannot be found that
62 /// satisfies the condition
63 class RandomNumberNotFound : public Exception
64 {
65 public:
66 RandomNumberNotFound() : Exception(OTHER_ERROR, "Integer: no integer satisfies the given parameters") {}
67 };
68
69 /// \enum Sign
70 /// \brief Used internally to represent the integer
71 /// \details Sign is used internally to represent the integer. It is also used in a few API functions.
72 /// \sa SetPositive(), SetNegative(), Signedness
73 enum Sign {
74 /// \brief the value is positive or 0
75 POSITIVE=0,
76 /// \brief the value is negative
77 NEGATIVE=1};
78
79 /// \enum Signedness
80 /// \brief Used when importing and exporting integers
81 /// \details Signedness is usually used in API functions.
82 /// \sa Sign
83 enum Signedness {
84 /// \brief an unsigned value
85 UNSIGNED,
86 /// \brief a signed value
87 SIGNED};
88
89 /// \enum RandomNumberType
90 /// \brief Properties of a random integer
91 enum RandomNumberType {
92 /// \brief a number with no special properties
93 ANY,
94 /// \brief a number which is probabilistically prime
95 PRIME};
96 //@}
97
98 /// \name CREATORS
99 //@{
100 /// \brief Creates the zero integer
101 Integer();
102
103 /// copy constructor
104 Integer(const Integer& t);
105
106 /// \brief Convert from signed long
107 Integer(signed long value);
108
109 /// \brief Convert from lword
110 /// \param sign enumeration indicating Sign
111 /// \param value the long word
112 Integer(Sign sign, lword value);
113
114 /// \brief Convert from two words
115 /// \param sign enumeration indicating Sign
116 /// \param highWord the high word
117 /// \param lowWord the low word
118 Integer(Sign sign, word highWord, word lowWord);
119
120 /// \brief Convert from a C-string
121 /// \param str C-string value
122 /// \param order the ByteOrder of the string to be processed
123 /// \details \p str can be in base 2, 8, 10, or 16. Base is determined by a case
124 /// insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
125 /// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
126 /// integers with curve25519, Poly1305 and Microsoft CAPI.
127 explicit Integer(const char *str, ByteOrder order = BIG_ENDIAN_ORDER);
128
129 /// \brief Convert from a wide C-string
130 /// \param str wide C-string value
131 /// \param order the ByteOrder of the string to be processed
132 /// \details \p str can be in base 2, 8, 10, or 16. Base is determined by a case
133 /// insensitive suffix of 'h', 'o', or 'b'. No suffix means base 10.
134 /// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
135 /// integers with curve25519, Poly1305 and Microsoft CAPI.
136 explicit Integer(const wchar_t *str, ByteOrder order = BIG_ENDIAN_ORDER);
137
138 /// \brief Convert from a big-endian byte array
139 /// \param encodedInteger big-endian byte array
140 /// \param byteCount length of the byte array
141 /// \param sign enumeration indicating Signedness
142 /// \param order the ByteOrder of the array to be processed
143 /// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
144 /// integers with curve25519, Poly1305 and Microsoft CAPI.
145 Integer(const byte *encodedInteger, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER);
146
147 /// \brief Convert from a big-endian array
148 /// \param bt BufferedTransformation object with big-endian byte array
149 /// \param byteCount length of the byte array
150 /// \param sign enumeration indicating Signedness
151 /// \param order the ByteOrder of the data to be processed
152 /// \details Byte order was added at Crypto++ 5.7 to allow use of little-endian
153 /// integers with curve25519, Poly1305 and Microsoft CAPI.
154 Integer(BufferedTransformation &bt, size_t byteCount, Signedness sign=UNSIGNED, ByteOrder order = BIG_ENDIAN_ORDER);
155
156 /// \brief Convert from a BER encoded byte array
157 /// \param bt BufferedTransformation object with BER encoded byte array
158 explicit Integer(BufferedTransformation &bt);
159
160 /// \brief Create a random integer
161 /// \param rng RandomNumberGenerator used to generate material
162 /// \param bitCount the number of bits in the resulting integer
163 /// \details The random integer created is uniformly distributed over <tt>[0, 2<sup>bitCount</sup>]</tt>.
164 Integer(RandomNumberGenerator &rng, size_t bitCount);
165
166 /// \brief Integer representing 0
167 /// \returns an Integer representing 0
168 /// \details Zero() avoids calling constructors for frequently used integers
169 static const Integer & CRYPTOPP_API Zero();
170 /// \brief Integer representing 1
171 /// \returns an Integer representing 1
172 /// \details One() avoids calling constructors for frequently used integers
173 static const Integer & CRYPTOPP_API One();
174 /// \brief Integer representing 2
175 /// \returns an Integer representing 2
176 /// \details Two() avoids calling constructors for frequently used integers
177 static const Integer & CRYPTOPP_API Two();
178
179 /// \brief Create a random integer of special form
180 /// \param rng RandomNumberGenerator used to generate material
181 /// \param min the minimum value
182 /// \param max the maximum value
183 /// \param rnType RandomNumberType to specify the type
184 /// \param equiv the equivalence class based on the parameter \p mod
185 /// \param mod the modulus used to reduce the equivalence class
186 /// \throw RandomNumberNotFound if the set is empty.
187 /// \details Ideally, the random integer created should be uniformly distributed
188 /// over <tt>{x | min <= x <= max</tt> and \p x is of rnType and <tt>x \% mod == equiv}</tt>.
189 /// However the actual distribution may not be uniform because sequential
190 /// search is used to find an appropriate number from a random starting
191 /// point.
192 /// \details May return (with very small probability) a pseudoprime when a prime
193 /// is requested and <tt>max > lastSmallPrime*lastSmallPrime</tt>. \p lastSmallPrime
194 /// is declared in nbtheory.h.
195 Integer(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType=ANY, const Integer &equiv=Zero(), const Integer &mod=One());
196
197 /// \brief Exponentiates to a power of 2
198 /// \returns the Integer 2<sup>e</sup>
199 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
200 static Integer CRYPTOPP_API Power2(size_t e);
201 //@}
202
203 /// \name ENCODE/DECODE
204 //@{
205 /// \brief Minimum number of bytes to encode this integer
206 /// \param sign enumeration indicating Signedness
207 /// \note The MinEncodedSize() of 0 is 1.
208 size_t MinEncodedSize(Signedness sign=UNSIGNED) const;
209
210 /// \brief Encode in big-endian format
211 /// \param output big-endian byte array
212 /// \param outputLen length of the byte array
213 /// \param sign enumeration indicating Signedness
214 /// \details Unsigned means encode absolute value, signed means encode two's complement if negative.
215 /// \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a
216 /// minimum size). An exact size is useful, for example, when encoding to a field element size.
217 void Encode(byte *output, size_t outputLen, Signedness sign=UNSIGNED) const;
218
219 /// \brief Encode in big-endian format
220 /// \param bt BufferedTransformation object
221 /// \param outputLen length of the encoding
222 /// \param sign enumeration indicating Signedness
223 /// \details Unsigned means encode absolute value, signed means encode two's complement if negative.
224 /// \details outputLen can be used to ensure an Integer is encoded to an exact size (rather than a
225 /// minimum size). An exact size is useful, for example, when encoding to a field element size.
226 void Encode(BufferedTransformation &bt, size_t outputLen, Signedness sign=UNSIGNED) const;
227
228 /// \brief Encode in DER format
229 /// \param bt BufferedTransformation object
230 /// \details Encodes the Integer using Distinguished Encoding Rules
231 /// The result is placed into a BufferedTransformation object
232 void DEREncode(BufferedTransformation &bt) const;
233
234 /// \brief Encode absolute value as big-endian octet string
235 /// \param bt BufferedTransformation object
236 /// \param length the number of mytes to decode
237 void DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const;
238
239 /// \brief Encode absolute value in OpenPGP format
240 /// \param output big-endian byte array
241 /// \param bufferSize length of the byte array
242 /// \returns length of the output
243 /// \details OpenPGPEncode places result into the buffer and returns the
244 /// number of bytes used for the encoding
245 size_t OpenPGPEncode(byte *output, size_t bufferSize) const;
246
247 /// \brief Encode absolute value in OpenPGP format
248 /// \param bt BufferedTransformation object
249 /// \returns length of the output
250 /// \details OpenPGPEncode places result into a BufferedTransformation object and returns the
251 /// number of bytes used for the encoding
252 size_t OpenPGPEncode(BufferedTransformation &bt) const;
253
254 /// \brief Decode from big-endian byte array
255 /// \param input big-endian byte array
256 /// \param inputLen length of the byte array
257 /// \param sign enumeration indicating Signedness
258 void Decode(const byte *input, size_t inputLen, Signedness sign=UNSIGNED);
259
260 /// \brief Decode nonnegative value from big-endian byte array
261 /// \param bt BufferedTransformation object
262 /// \param inputLen length of the byte array
263 /// \param sign enumeration indicating Signedness
264 /// \note <tt>bt.MaxRetrievable() >= inputLen</tt>.
265 void Decode(BufferedTransformation &bt, size_t inputLen, Signedness sign=UNSIGNED);
266
267 /// \brief Decode from BER format
268 /// \param input big-endian byte array
269 /// \param inputLen length of the byte array
270 void BERDecode(const byte *input, size_t inputLen);
271
272 /// \brief Decode from BER format
273 /// \param bt BufferedTransformation object
274 void BERDecode(BufferedTransformation &bt);
275
276 /// \brief Decode nonnegative value from big-endian octet string
277 /// \param bt BufferedTransformation object
278 /// \param length length of the byte array
279 void BERDecodeAsOctetString(BufferedTransformation &bt, size_t length);
280
281 /// \brief Exception thrown when an error is encountered decoding an OpenPGP integer
282 class OpenPGPDecodeErr : public Exception
283 {
284 public:
285 OpenPGPDecodeErr() : Exception(INVALID_DATA_FORMAT, "OpenPGP decode error") {}
286 };
287
288 /// \brief Decode from OpenPGP format
289 /// \param input big-endian byte array
290 /// \param inputLen length of the byte array
291 void OpenPGPDecode(const byte *input, size_t inputLen);
292 /// \brief Decode from OpenPGP format
293 /// \param bt BufferedTransformation object
294 void OpenPGPDecode(BufferedTransformation &bt);
295 //@}
296
297 /// \name ACCESSORS
298 //@{
299 /// \brief Determines if the Integer is convertable to Long
300 /// \returns true if *this can be represented as a signed long
301 /// \sa ConvertToLong()
302 bool IsConvertableToLong() const;
303 /// \brief Convert the Integer to Long
304 /// \return equivalent signed long if possible, otherwise undefined
305 /// \sa IsConvertableToLong()
306 signed long ConvertToLong() const;
307
308 /// \brief Determines the number of bits required to represent the Integer
309 /// \returns number of significant bits = floor(log2(abs(*this))) + 1
310 unsigned int BitCount() const;
311 /// \brief Determines the number of bytes required to represent the Integer
312 /// \returns number of significant bytes = ceiling(BitCount()/8)
313 unsigned int ByteCount() const;
314 /// \brief Determines the number of words required to represent the Integer
315 /// \returns number of significant words = ceiling(ByteCount()/sizeof(word))
316 unsigned int WordCount() const;
317
318 /// \brief Provides the i-th bit of the Integer
319 /// \returns the i-th bit, i=0 being the least significant bit
320 bool GetBit(size_t i) const;
321 /// \brief Provides the i-th byte of the Integer
322 /// \returns the i-th byte
323 byte GetByte(size_t i) const;
324 /// \brief Provides the low order bits of the Integer
325 /// \returns n lowest bits of *this >> i
326 lword GetBits(size_t i, size_t n) const;
327
328 /// \brief Determines if the Integer is 0
329 /// \returns true if the Integer is 0, false otherwise
330 bool IsZero() const {return !*this;}
331 /// \brief Determines if the Integer is non-0
332 /// \returns true if the Integer is non-0, false otherwise
333 bool NotZero() const {return !IsZero();}
334 /// \brief Determines if the Integer is negative
335 /// \returns true if the Integer is negative, false otherwise
336 bool IsNegative() const {return sign == NEGATIVE;}
337 /// \brief Determines if the Integer is non-negative
338 /// \returns true if the Integer is non-negative, false otherwise
339 bool NotNegative() const {return !IsNegative();}
340 /// \brief Determines if the Integer is positive
341 /// \returns true if the Integer is positive, false otherwise
342 bool IsPositive() const {return NotNegative() && NotZero();}
343 /// \brief Determines if the Integer is non-positive
344 /// \returns true if the Integer is non-positive, false otherwise
345 bool NotPositive() const {return !IsPositive();}
346 /// \brief Determines if the Integer is even parity
347 /// \returns true if the Integer is even, false otherwise
348 bool IsEven() const {return GetBit(0) == 0;}
349 /// \brief Determines if the Integer is odd parity
350 /// \returns true if the Integer is odd, false otherwise
351 bool IsOdd() const {return GetBit(0) == 1;}
352 //@}
353
354 /// \name MANIPULATORS
355 //@{
356 /// \brief Assignment
357 Integer& operator=(const Integer& t);
358
359 /// \brief Addition Assignment
360 Integer& operator+=(const Integer& t);
361 /// \brief Subtraction Assignment
362 Integer& operator-=(const Integer& t);
363 /// \brief Multiplication Assignment
364 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
365 Integer& operator*=(const Integer& t) {return *this = Times(t);}
366 /// \brief Division Assignment
367 Integer& operator/=(const Integer& t) {return *this = DividedBy(t);}
368 /// \brief Remainder Assignment
369 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
370 Integer& operator%=(const Integer& t) {return *this = Modulo(t);}
371 /// \brief Division Assignment
372 Integer& operator/=(word t) {return *this = DividedBy(t);}
373 /// \brief Remainder Assignment
374 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
375 Integer& operator%=(word t) {return *this = Integer(POSITIVE, 0, Modulo(t));}
376
377 /// \brief Left-shift Assignment
378 Integer& operator<<=(size_t n);
379 /// \brief Right-shift Assignment
380 Integer& operator>>=(size_t n);
381
382 /// \brief Bitwise AND Assignment
383 /// \param t the other Integer
384 /// \returns the result of *this & t
385 /// \details operator&=() performs a bitwise AND on *this. Missing bits are truncated
386 /// at the most significant bit positions, so the result is as small as the
387 /// smaller of the operands.
388 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
389 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
390 /// the integer should be converted to a 2's compliment representation before performing
391 /// the operation.
392 /// \since Crypto++ 6.0
393 Integer& operator&=(const Integer& t);
394 /// \brief Bitwise OR Assignment
395 /// \param t the second Integer
396 /// \returns the result of *this | t
397 /// \details operator|=() performs a bitwise OR on *this. Missing bits are shifted in
398 /// at the most significant bit positions, so the result is as large as the
399 /// larger of the operands.
400 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
401 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
402 /// the integer should be converted to a 2's compliment representation before performing
403 /// the operation.
404 /// \since Crypto++ 6.0
405 Integer& operator|=(const Integer& t);
406 /// \brief Bitwise XOR Assignment
407 /// \param t the other Integer
408 /// \returns the result of *this ^ t
409 /// \details operator^=() performs a bitwise XOR on *this. Missing bits are shifted
410 /// in at the most significant bit positions, so the result is as large as the
411 /// larger of the operands.
412 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
413 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
414 /// the integer should be converted to a 2's compliment representation before performing
415 /// the operation.
416 /// \since Crypto++ 6.0
417 Integer& operator^=(const Integer& t);
418
419 /// \brief Set this Integer to random integer
420 /// \param rng RandomNumberGenerator used to generate material
421 /// \param bitCount the number of bits in the resulting integer
422 /// \details The random integer created is uniformly distributed over <tt>[0, 2<sup>bitCount</sup>]</tt>.
423 void Randomize(RandomNumberGenerator &rng, size_t bitCount);
424
425 /// \brief Set this Integer to random integer
426 /// \param rng RandomNumberGenerator used to generate material
427 /// \param min the minimum value
428 /// \param max the maximum value
429 /// \details The random integer created is uniformly distributed over <tt>[min, max]</tt>.
430 void Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max);
431
432 /// \brief Set this Integer to random integer of special form
433 /// \param rng RandomNumberGenerator used to generate material
434 /// \param min the minimum value
435 /// \param max the maximum value
436 /// \param rnType RandomNumberType to specify the type
437 /// \param equiv the equivalence class based on the parameter \p mod
438 /// \param mod the modulus used to reduce the equivalence class
439 /// \throw RandomNumberNotFound if the set is empty.
440 /// \details Ideally, the random integer created should be uniformly distributed
441 /// over <tt>{x | min <= x <= max</tt> and \p x is of rnType and <tt>x \% mod == equiv}</tt>.
442 /// However the actual distribution may not be uniform because sequential
443 /// search is used to find an appropriate number from a random starting
444 /// point.
445 /// \details May return (with very small probability) a pseudoprime when a prime
446 /// is requested and <tt>max > lastSmallPrime*lastSmallPrime</tt>. \p lastSmallPrime
447 /// is declared in nbtheory.h.
448 bool Randomize(RandomNumberGenerator &rng, const Integer &min, const Integer &max, RandomNumberType rnType, const Integer &equiv=Zero(), const Integer &mod=One());
449
450 /// \brief Generate a random number
451 /// \param rng RandomNumberGenerator used to generate material
452 /// \param params additional parameters that cannot be passed directly to the function
453 /// \returns true if a random number was generated, false otherwise
454 /// \details GenerateRandomNoThrow attempts to generate a random number according to the
455 /// parameters specified in params. The function does not throw RandomNumberNotFound.
456 /// \details The example below generates a prime number using NameValuePairs that Integer
457 /// class recognizes. The names are not provided in argnames.h.
458 /// <pre>
459 /// AutoSeededRandomPool prng;
460 /// AlgorithmParameters params = MakeParameters("BitLength", 2048)
461 /// ("RandomNumberType", Integer::PRIME);
462 /// Integer x;
463 /// if (x.GenerateRandomNoThrow(prng, params) == false)
464 /// throw std::runtime_error("Failed to generate prime number");
465 /// </pre>
466 bool GenerateRandomNoThrow(RandomNumberGenerator &rng, const NameValuePairs &params = g_nullNameValuePairs);
467
468 /// \brief Generate a random number
469 /// \param rng RandomNumberGenerator used to generate material
470 /// \param params additional parameters that cannot be passed directly to the function
471 /// \throw RandomNumberNotFound if a random number is not found
472 /// \details GenerateRandom attempts to generate a random number according to the
473 /// parameters specified in params.
474 /// \details The example below generates a prime number using NameValuePairs that Integer
475 /// class recognizes. The names are not provided in argnames.h.
476 /// <pre>
477 /// AutoSeededRandomPool prng;
478 /// AlgorithmParameters params = MakeParameters("BitLength", 2048)
479 /// ("RandomNumberType", Integer::PRIME);
480 /// Integer x;
481 /// try { x.GenerateRandom(prng, params); }
482 /// catch (RandomNumberNotFound&) { x = -1; }
483 /// </pre>
484 void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params = g_nullNameValuePairs)
485 {
486 if (!GenerateRandomNoThrow(rng, params))
487 throw RandomNumberNotFound();
488 }
489
490 /// \brief Set the n-th bit to value
491 /// \details 0-based numbering.
492 void SetBit(size_t n, bool value=1);
493
494 /// \brief Set the n-th byte to value
495 /// \details 0-based numbering.
496 void SetByte(size_t n, byte value);
497
498 /// \brief Reverse the Sign of the Integer
499 void Negate();
500
501 /// \brief Sets the Integer to positive
502 void SetPositive() {sign = POSITIVE;}
503
504 /// \brief Sets the Integer to negative
505 void SetNegative() {if (!!(*this)) sign = NEGATIVE;}
506
507 /// \brief Swaps this Integer with another Integer
508 void swap(Integer &a);
509 //@}
510
511 /// \name UNARY OPERATORS
512 //@{
513 /// \brief Negation
514 bool operator!() const;
515 /// \brief Addition
516 Integer operator+() const {return *this;}
517 /// \brief Subtraction
518 Integer operator-() const;
519 /// \brief Pre-increment
520 Integer& operator++();
521 /// \brief Pre-decrement
522 Integer& operator--();
523 /// \brief Post-increment
524 Integer operator++(int) {Integer temp = *this; ++*this; return temp;}
525 /// \brief Post-decrement
526 Integer operator--(int) {Integer temp = *this; --*this; return temp;}
527 //@}
528
529 /// \name BINARY OPERATORS
530 //@{
531 /// \brief Perform signed comparison
532 /// \param a the Integer to comapre
533 /// \retval -1 if <tt>*this < a</tt>
534 /// \retval 0 if <tt>*this = a</tt>
535 /// \retval 1 if <tt>*this > a</tt>
536 int Compare(const Integer& a) const;
537
538 /// \brief Addition
539 Integer Plus(const Integer &b) const;
540 /// \brief Subtraction
541 Integer Minus(const Integer &b) const;
542 /// \brief Multiplication
543 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
544 Integer Times(const Integer &b) const;
545 /// \brief Division
546 Integer DividedBy(const Integer &b) const;
547 /// \brief Remainder
548 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
549 Integer Modulo(const Integer &b) const;
550 /// \brief Division
551 Integer DividedBy(word b) const;
552 /// \brief Remainder
553 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
554 word Modulo(word b) const;
555
556 /// \brief Bitwise AND
557 /// \param t the other Integer
558 /// \returns the result of <tt>*this & t</tt>
559 /// \details And() performs a bitwise AND on the operands. Missing bits are truncated
560 /// at the most significant bit positions, so the result is as small as the
561 /// smaller of the operands.
562 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
563 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
564 /// the integer should be converted to a 2's compliment representation before performing
565 /// the operation.
566 /// \since Crypto++ 6.0
567 Integer And(const Integer& t) const;
568
569 /// \brief Bitwise OR
570 /// \param t the other Integer
571 /// \returns the result of <tt>*this | t</tt>
572 /// \details Or() performs a bitwise OR on the operands. Missing bits are shifted in
573 /// at the most significant bit positions, so the result is as large as the
574 /// larger of the operands.
575 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
576 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
577 /// the integer should be converted to a 2's compliment representation before performing
578 /// the operation.
579 /// \since Crypto++ 6.0
580 Integer Or(const Integer& t) const;
581
582 /// \brief Bitwise XOR
583 /// \param t the other Integer
584 /// \returns the result of <tt>*this ^ t</tt>
585 /// \details Xor() performs a bitwise XOR on the operands. Missing bits are shifted in
586 /// at the most significant bit positions, so the result is as large as the
587 /// larger of the operands.
588 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
589 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
590 /// the integer should be converted to a 2's compliment representation before performing
591 /// the operation.
592 /// \since Crypto++ 6.0
593 Integer Xor(const Integer& t) const;
594
595 /// \brief Right-shift
596 Integer operator>>(size_t n) const {return Integer(*this)>>=n;}
597 /// \brief Left-shift
598 Integer operator<<(size_t n) const {return Integer(*this)<<=n;}
599 //@}
600
601 /// \name OTHER ARITHMETIC FUNCTIONS
602 //@{
603 /// \brief Retrieve the absolute value of this integer
604 Integer AbsoluteValue() const;
605 /// \brief Add this integer to itself
606 Integer Doubled() const {return Plus(*this);}
607 /// \brief Multiply this integer by itself
608 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
609 Integer Squared() const {return Times(*this);}
610 /// \brief Extract square root
611 /// \details if negative return 0, else return floor of square root
612 Integer SquareRoot() const;
613 /// \brief Determine whether this integer is a perfect square
614 bool IsSquare() const;
615
616 /// \brief Determine if 1 or -1
617 /// \returns true if this integer is 1 or -1, false otherwise
618 bool IsUnit() const;
619 /// \brief Calculate multiplicative inverse
620 /// \returns MultiplicativeInverse inverse if 1 or -1, otherwise return 0.
621 Integer MultiplicativeInverse() const;
622
623 /// \brief Extended Division
624 /// \param r a reference for the remainder
625 /// \param q a reference for the quotient
626 /// \param a a reference to the dividend
627 /// \param d a reference to the divisor
628 /// \details Divide calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)).
629 static void CRYPTOPP_API Divide(Integer &r, Integer &q, const Integer &a, const Integer &d);
630
631 /// \brief Extended Division
632 /// \param r a reference for the remainder
633 /// \param q a reference for the quotient
634 /// \param a a reference to the dividend
635 /// \param d a reference to the divisor
636 /// \details Divide calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)).
637 /// This overload uses a faster division algorithm because the divisor is short.
638 static void CRYPTOPP_API Divide(word &r, Integer &q, const Integer &a, word d);
639
640 /// \brief Extended Division
641 /// \param r a reference for the remainder
642 /// \param q a reference for the quotient
643 /// \param a a reference to the dividend
644 /// \param n a reference to the divisor
645 /// \details DivideByPowerOf2 calculates r and q such that (a == d*q + r) && (0 <= r < abs(d)).
646 /// It returns same result as Divide(r, q, a, Power2(n)), but faster.
647 /// This overload uses a faster division algorithm because the divisor is a power of 2.
648 static void CRYPTOPP_API DivideByPowerOf2(Integer &r, Integer &q, const Integer &a, unsigned int n);
649
650 /// \brief Calculate greatest common divisor
651 /// \param a a reference to the first number
652 /// \param n a reference to the secind number
653 /// \returns the greatest common divisor <tt>a</tt> and <tt>n</tt>.
654 static Integer CRYPTOPP_API Gcd(const Integer &a, const Integer &n);
655
656 /// \brief Calculate multiplicative inverse
657 /// \param n a reference to the modulus
658 /// \returns an Integer <tt>*this % n</tt>.
659 /// \details InverseMod returns the multiplicative inverse of the Integer <tt>*this</tt>
660 /// modulo the Integer <tt>n</tt>. If no Integer exists then Integer 0 is returned.
661 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
662 Integer InverseMod(const Integer &n) const;
663
664 /// \brief Calculate multiplicative inverse
665 /// \param n the modulus
666 /// \returns a word <tt>*this % n</tt>.
667 /// \details InverseMod returns the multiplicative inverse of the Integer <tt>*this</tt>
668 /// modulo the word <tt>n</tt>. If no Integer exists then word 0 is returned.
669 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
670 word InverseMod(word n) const;
671 //@}
672
673 /// \name INPUT/OUTPUT
674 //@{
675 /// \brief Extraction operator
676 /// \param in a reference to a std::istream
677 /// \param a a reference to an Integer
678 /// \returns a reference to a std::istream reference
679 friend CRYPTOPP_DLL std::istream& CRYPTOPP_API operator>>(std::istream& in, Integer &a);
680
681 /// \brief Insertion operator
682 /// \param out a reference to a std::ostream
683 /// \param a a constant reference to an Integer
684 /// \returns a reference to a std::ostream reference
685 /// \details The output integer responds to std::hex, std::oct, std::hex, std::upper and
686 /// std::lower. The output includes the suffix \a \b h (for hex), \a \b . (\a \b dot, for dec)
687 /// and \a \b o (for octal). There is currently no way to suppress the suffix.
688 /// \details If you want to print an Integer without the suffix or using an arbitrary base, then
689 /// use IntToString<Integer>().
690 /// \sa IntToString<Integer>
691 friend CRYPTOPP_DLL std::ostream& CRYPTOPP_API operator<<(std::ostream& out, const Integer &a);
692 //@}
693
694 /// \brief Modular multiplication
695 /// \param x a reference to the first term
696 /// \param y a reference to the second term
697 /// \param m a reference to the modulus
698 /// \returns an Integer <tt>(a * b) % m</tt>.
699 CRYPTOPP_DLL friend Integer CRYPTOPP_API a_times_b_mod_c(const Integer &x, const Integer& y, const Integer& m);
700 /// \brief Modular exponentiation
701 /// \param x a reference to the base
702 /// \param e a reference to the exponent
703 /// \param m a reference to the modulus
704 /// \returns an Integer <tt>(a ^ b) % m</tt>.
705 CRYPTOPP_DLL friend Integer CRYPTOPP_API a_exp_b_mod_c(const Integer &x, const Integer& e, const Integer& m);
706
707 protected:
708
709 // http://github.com/weidai11/cryptopp/issues/602
710 Integer InverseModNext(const Integer &n) const;
711
712 private:
713
714 Integer(word value, size_t length);
715 int PositiveCompare(const Integer &t) const;
716
717 IntegerSecBlock reg;
718 Sign sign;
719
720 #ifndef CRYPTOPP_DOXYGEN_PROCESSING
721 friend class ModularArithmetic;
722 friend class MontgomeryRepresentation;
723 friend class HalfMontgomeryRepresentation;
724
725 friend void PositiveAdd(Integer &sum, const Integer &a, const Integer &b);
726 friend void PositiveSubtract(Integer &diff, const Integer &a, const Integer &b);
727 friend void PositiveMultiply(Integer &product, const Integer &a, const Integer &b);
728 friend void PositiveDivide(Integer &remainder, Integer &quotient, const Integer &dividend, const Integer &divisor);
729 #endif
730 };
731
732 /// \brief Comparison
733 inline bool operator==(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)==0;}
734 /// \brief Comparison
735 inline bool operator!=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)!=0;}
736 /// \brief Comparison
737 inline bool operator> (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)> 0;}
738 /// \brief Comparison
739 inline bool operator>=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)>=0;}
740 /// \brief Comparison
741 inline bool operator< (const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)< 0;}
742 /// \brief Comparison
743 inline bool operator<=(const CryptoPP::Integer& a, const CryptoPP::Integer& b) {return a.Compare(b)<=0;}
744 /// \brief Addition
745 inline CryptoPP::Integer operator+(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Plus(b);}
746 /// \brief Subtraction
747 inline CryptoPP::Integer operator-(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Minus(b);}
748 /// \brief Multiplication
749 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
750 inline CryptoPP::Integer operator*(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Times(b);}
751 /// \brief Division
752 inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.DividedBy(b);}
753 /// \brief Remainder
754 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
755 inline CryptoPP::Integer operator%(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Modulo(b);}
756 /// \brief Division
757 inline CryptoPP::Integer operator/(const CryptoPP::Integer &a, CryptoPP::word b) {return a.DividedBy(b);}
758 /// \brief Remainder
759 /// \sa a_times_b_mod_c() and a_exp_b_mod_c()
760 inline CryptoPP::word operator%(const CryptoPP::Integer &a, CryptoPP::word b) {return a.Modulo(b);}
761
762 /// \brief Bitwise AND
763 /// \param a the first Integer
764 /// \param b the second Integer
765 /// \returns the result of a & b
766 /// \details operator&() performs a bitwise AND on the operands. Missing bits are truncated
767 /// at the most significant bit positions, so the result is as small as the
768 /// smaller of the operands.
769 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
770 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
771 /// the integer should be converted to a 2's compliment representation before performing
772 /// the operation.
773 /// \since Crypto++ 6.0
774 inline CryptoPP::Integer operator&(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.And(b);}
775
776 /// \brief Bitwise OR
777 /// \param a the first Integer
778 /// \param b the second Integer
779 /// \returns the result of a | b
780 /// \details operator|() performs a bitwise OR on the operands. Missing bits are shifted in
781 /// at the most significant bit positions, so the result is as large as the
782 /// larger of the operands.
783 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
784 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
785 /// the integer should be converted to a 2's compliment representation before performing
786 /// the operation.
787 /// \since Crypto++ 6.0
788 inline CryptoPP::Integer operator|(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Or(b);}
789
790 /// \brief Bitwise XOR
791 /// \param a the first Integer
792 /// \param b the second Integer
793 /// \returns the result of a ^ b
794 /// \details operator^() performs a bitwise XOR on the operands. Missing bits are shifted
795 /// in at the most significant bit positions, so the result is as large as the
796 /// larger of the operands.
797 /// \details Internally, Crypto++ uses a sign-magnitude representation. The library
798 /// does not attempt to interpret bits, and the result is always POSITIVE. If needed,
799 /// the integer should be converted to a 2's compliment representation before performing
800 /// the operation.
801 /// \since Crypto++ 6.0
802 inline CryptoPP::Integer operator^(const CryptoPP::Integer &a, const CryptoPP::Integer &b) {return a.Xor(b);}
803
804 NAMESPACE_END
805
806 #ifndef __BORLANDC__
807 NAMESPACE_BEGIN(std)
808 inline void swap(CryptoPP::Integer &a, CryptoPP::Integer &b)
809 {
810 a.swap(b);
811 }
812 NAMESPACE_END
813 #endif
814
815 #endif
Exception
Base class for all exceptions thrown by the library.
Definition: cryptlib.h:158
ASN1Object::DEREncode
virtual void DEREncode(BufferedTransformation &bt) const =0
Encode this object into a BufferedTransformation.
Integer::SetNegative
void SetNegative()
Sets the Integer to negative.
Definition: integer.h:505
Integer::NotZero
bool NotZero() const
Determines if the Integer is non-0.
Definition: integer.h:333
operator*
inline ::Integer operator*(const ::Integer &a, const ::Integer &b)
Multiplication.
Definition: integer.h:750
Integer::operator/=
Integer & operator/=(word t)
Division Assignment.
Definition: integer.h:372
Integer::operator--
Integer operator--(int)
Post-decrement.
Definition: integer.h:526
ByteOrder
ByteOrder
Provides the byte ordering.
Definition: cryptlib.h:143
Integer::UNSIGNED
an unsigned value
Definition: integer.h:85
Integer::SetPositive
void SetPositive()
Sets the Integer to positive.
Definition: integer.h:502
operator%
inline ::Integer operator%(const ::Integer &a, const ::Integer &b)
Remainder.
Definition: integer.h:755
SecBlock
Secure memory block with allocator and cleanup.
Definition: secblock.h:688
cryptlib.h
Abstract base classes that provide a uniform interface to this library.
Integer::Signedness
Signedness
Used when importing and exporting integers.
Definition: integer.h:83
Integer::IsNegative
bool IsNegative() const
Determines if the Integer is negative.
Definition: integer.h:336
ModularArithmetic
Ring of congruence classes modulo n.
Definition: modarith.h:38
std
STL namespace.
RandomNumberGenerator
Interface for random number generators.
Definition: cryptlib.h:1383
stdcpp.h
Common C++ header files.
Integer::GenerateRandom
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params=g_nullNameValuePairs)
Generate a random number.
Definition: integer.h:484
BufferedTransformation
Interface for buffered transformations.
Definition: cryptlib.h:1598
Integer::IsPositive
bool IsPositive() const
Determines if the Integer is positive.
Definition: integer.h:342
Integer::NotNegative
bool NotNegative() const
Determines if the Integer is non-negative.
Definition: integer.h:339
operator==
bool operator==(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:733
operator+
inline ::Integer operator+(const ::Integer &a, const ::Integer &b)
Addition.
Definition: integer.h:745
Integer::Sign
Sign
Used internally to represent the integer.
Definition: integer.h:73
secblock.h
Classes and functions for secure memory allocations.
Integer::operator/=
Integer & operator/=(const Integer &t)
Division Assignment.
Definition: integer.h:367
operator-
inline ::Integer operator-(const ::Integer &a, const ::Integer &b)
Subtraction.
Definition: integer.h:747
Integer::ANY
a number with no special properties
Definition: integer.h:93
operator!=
bool operator!=(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:735
operator<=
bool operator<=(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:743
ASN1Object::BERDecode
virtual void BERDecode(BufferedTransformation &bt)=0
Decode this object from a BufferedTransformation.
Integer::IsZero
bool IsZero() const
Determines if the Integer is 0.
Definition: integer.h:330
Integer::OpenPGPDecodeErr
Exception thrown when an error is encountered decoding an OpenPGP integer.
Definition: integer.h:282
ASN1Object
Interface for encoding and decoding ASN1 objects.
Definition: cryptlib.h:3168
InitializeInteger
Performs static initialization of the Integer class.
Definition: integer.h:29
Integer
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
operator &
inline ::Integer operator &(const ::Integer &a, const ::Integer &b)
Bitwise AND.
Definition: integer.h:774
g_nullNameValuePairs
const NameValuePairs & g_nullNameValuePairs
An empty set of name-value pairs.
Definition: cryptlib.h:500
Integer::RandomNumberType
RandomNumberType
Properties of a random integer.
Definition: integer.h:91
Integer::IsEven
bool IsEven() const
Determines if the Integer is even parity.
Definition: integer.h:348
BIG_ENDIAN_ORDER
byte order is big-endian
Definition: cryptlib.h:147
Integer::operator*=
Integer & operator*=(const Integer &t)
Multiplication Assignment.
Definition: integer.h:365
operator>
bool operator>(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:737
operator^
inline ::Integer operator^(const ::Integer &a, const ::Integer &b)
Bitwise XOR.
Definition: integer.h:802
Integer::operator++
Integer operator++(int)
Post-increment.
Definition: integer.h:524
Integer::DivideByZero
Exception thrown when division by 0 is encountered.
Definition: integer.h:55
Integer::Squared
Integer Squared() const
Multiply this integer by itself.
Definition: integer.h:609
Integer::RandomNumberNotFound
Exception thrown when a random number cannot be found that satisfies the condition.
Definition: integer.h:63
MontgomeryRepresentation
Performs modular arithmetic in Montgomery representation for increased speed.
Definition: modarith.h:274
Integer::operator<<
Integer operator<<(size_t n) const
Left-shift.
Definition: integer.h:598
Integer::Doubled
Integer Doubled() const
Add this integer to itself.
Definition: integer.h:606
Integer::operator>>
Integer operator>>(size_t n) const
Right-shift.
Definition: integer.h:596
Integer::NotPositive
bool NotPositive() const
Determines if the Integer is non-positive.
Definition: integer.h:345
Integer::operator+
Integer operator+() const
Addition.
Definition: integer.h:516
CryptoPP
Crypto++ library namespace.
Integer::operator%=
Integer & operator%=(word t)
Remainder Assignment.
Definition: integer.h:375
GetByte
unsigned int GetByte(ByteOrder order, T value, unsigned int index)
Gets a byte from a value.
Definition: misc.h:1929
operator<
bool operator<(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:741
Integer::operator%=
Integer & operator%=(const Integer &t)
Remainder Assignment.
Definition: integer.h:370
operator|
inline ::Integer operator|(const ::Integer &a, const ::Integer &b)
Bitwise OR.
Definition: integer.h:788
Integer::IsOdd
bool IsOdd() const
Determines if the Integer is odd parity.
Definition: integer.h:351
operator>=
bool operator>=(const ::Integer &a, const ::Integer &b)
Comparison.
Definition: integer.h:739
operator/
inline ::Integer operator/(const ::Integer &a, const ::Integer &b)
Division.
Definition: integer.h:752
NameValuePairs
Interface for retrieving values given their names.
Definition: cryptlib.h:293