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# Module number

Functions

 size(N) size(N:long) : int Returns the size of the number N in bits.

 getRandomNumber(N, randfunc=None) Deprecated. Use getRandomInteger or getRandomNBitInteger instead.

 getRandomInteger(N, randfunc=None) getRandomInteger(N:int, randfunc:callable):long Return a random number with at most N bits.

 getRandomRange(a, b, randfunc=None) getRandomRange(a:int, b:int, randfunc:callable):long Return a random number n so that a <= n < b.

 getRandomNBitInteger(N, randfunc=None) getRandomInteger(N:int, randfunc:callable):long Return a random number with exactly N-bits, i.e. a random number between 2**(N-1) and (2**N)-1.

 GCD(x, y) GCD(x:long, y:long): long Return the GCD of x and y.

 inverse(u, v) inverse(u:long, v:long):long Return the inverse of u mod v.

 getPrime(N, randfunc=None) getPrime(N:int, randfunc:callable):long Return a random N-bit prime number.

 getStrongPrime(N, e=0, false_positive_prob=1e-06, randfunc=None) getStrongPrime(N:int, e:int, false_positive_prob:float, randfunc:callable):long Return a random strong N-bit prime number. In this context p is a strong prime if p-1 and p+1 have at least one large prime factor. N should be a multiple of 128 and > 512.

 isPrime(N, false_positive_prob=1e-06, randfunc=None) isPrime(N:long, false_positive_prob:float, randfunc:callable):bool Return true if N is prime.

 long_to_bytes(n, blocksize=0) long_to_bytes(n:long, blocksize:int) : string Convert a long integer to a byte string.

 bytes_to_long(string) : long Convert a byte string to a long integer.

 long2str(n, blocksize=0)

 str2long(s)
 Variables __revision__ = `'\$Id\$'` sieve_base = `(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, ...` __package__ = `'Crypto.Util'`
 Function Details

### getRandomInteger(N, randfunc=None)

getRandomInteger(N:int, randfunc:callable):long Return a random number with at most N bits.

If randfunc is omitted, then Random.new().read is used.

This function is for internal use only and may be renamed or removed in the future.

### getRandomRange(a, b, randfunc=None)

getRandomRange(a:int, b:int, randfunc:callable):long Return a random number n so that a <= n < b.

If randfunc is omitted, then Random.new().read is used.

This function is for internal use only and may be renamed or removed in the future.

### getRandomNBitInteger(N, randfunc=None)

getRandomInteger(N:int, randfunc:callable):long Return a random number with exactly N-bits, i.e. a random number between 2**(N-1) and (2**N)-1.

If randfunc is omitted, then Random.new().read is used.

This function is for internal use only and may be renamed or removed in the future.

### getPrime(N, randfunc=None)

getPrime(N:int, randfunc:callable):long Return a random N-bit prime number.

If randfunc is omitted, then Random.new().read is used.

### getStrongPrime(N, e=0, false_positive_prob=1e-06, randfunc=None)

getStrongPrime(N:int, e:int, false_positive_prob:float, randfunc:callable):long Return a random strong N-bit prime number. In this context p is a strong prime if p-1 and p+1 have at least one large prime factor. N should be a multiple of 128 and > 512.

If e is provided the returned prime p-1 will be coprime to e and thus suitable for RSA where e is the public exponent.

The optional false_positive_prob is the statistical probability that true is returned even though it is not (pseudo-prime). It defaults to 1e-6 (less than 1:1000000). Note that the real probability of a false-positive is far less. This is just the mathematically provable limit.

randfunc should take a single int parameter and return that many random bytes as a string. If randfunc is omitted, then Random.new().read is used.

### isPrime(N, false_positive_prob=1e-06, randfunc=None)

isPrime(N:long, false_positive_prob:float, randfunc:callable):bool Return true if N is prime.

The optional false_positive_prob is the statistical probability that true is returned even though it is not (pseudo-prime). It defaults to 1e-6 (less than 1:1000000). Note that the real probability of a false-positive is far less. This is just the mathematically provable limit.

If randfunc is omitted, then Random.new().read is used.

### long_to_bytes(n, blocksize=0)

long_to_bytes(n:long, blocksize:int) : string Convert a long integer to a byte string.

If optional blocksize is given and greater than zero, pad the front of the byte string with binary zeros so that the length is a multiple of blocksize.

### bytes_to_long(s)

bytes_to_long(string) : long Convert a byte string to a long integer.

This is (essentially) the inverse of long_to_bytes().

 Variables Details

### sieve_base

Value:
 ````(`2`,` 3`,` 5`,` 7`,` 11`,` 13`,` 17`,` 19`,` `...` ```

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