bcpowmod(3) [php man page]
BCPOWMOD(3) 1 BCPOWMOD(3) bcpowmod - Raise an arbitrary precision number to another, reduced by a specified modulus SYNOPSIS
string bcpowmod (string $left_operand, string $right_operand, string $modulus, [int $scale = int]) DESCRIPTION
Use the fast-exponentiation method to raise $left_operand to the power $right_operand with respect to the modulus $modulus. PARAMETERS
o $left_operand - The left operand, as a string. o $right_operand - The right operand, as a string. o $modulus - The modulus, as a string. o $ scale -This optional parameter is used to set the number of digits after the decimal place in the result. You can also set the global default scale for all functions by using bcscale(3). RETURN VALUES
Returns the result as a string, or NULL if $modulus is 0. NOTES
Note Because this method uses the modulus operation, numbers which are not positive integers may give unexpected results. EXAMPLES
The following two statements are functionally identical. The bcpowmod(3) version however, executes in less time and can accept larger parameters. <?php $a = bcpowmod($x, $y, $mod); $b = bcmod(bcpow($x, $y), $mod); // $a and $b are equal to each other. ?> SEE ALSO
bcpow(3), bcmod(3). PHP Documentation Group BCPOWMOD(3)
Check Out this Related Man Page
MODULI(5) BSD File Formats Manual MODULI(5) NAME
moduli -- Diffie Hellman moduli DESCRIPTION
The /etc/ssh/moduli file contains prime numbers and generators for use by sshd(8) in the Diffie-Hellman Group Exchange key exchange method. New moduli may be generated with ssh-keygen(1) using a two-step process. An initial candidate generation pass, using ssh-keygen -G, calcu- lates numbers that are likely to be useful. A second primality testing pass, using ssh-keygen -T provides a high degree of assurance that the numbers are prime and are safe for use in Diffie Hellman operations by sshd(8). This moduli format is used as the output from each pass. The file consists of newline-separated records, one per modulus, containing seven space separated fields. These fields are as follows: timestamp The time that the modulus was last processed as YYYYMMDDHHMMSS. type Decimal number specifying the internal structure of the prime modulus. Supported types are: 0 Unknown, not tested 2 "Safe" prime; (p-1)/2 is also prime. 4 Sophie Germain; (p+1)*2 is also prime. Moduli candidates initially produced by ssh-keygen(1) are Sophie Germain primes (type 4). Futher primality testing with ssh-keygen(1) produces safe prime moduli (type 2) that are ready for use in sshd(8). Other types are not used by OpenSSH. tests Decimal number indicating the type of primality tests that the number has been subjected to represented as a bitmask of the following values: 0x00 Not tested 0x01 Composite number - not prime. 0x02 Sieve of Eratosthenes 0x04 Probabalistic Miller-Rabin primality tests. The ssh-keygen(1) moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02). Subsequent ssh-keygen(1) pri- mality tests are Miller-Rabin tests (flag 0x04). trials Decimal number indicating of primaility trials that have been performed on the modulus. size Decimal number indicating the size of the prime in bits. generator The recommended generator for use with this modulus (hexadecimal). modulus The modulus itself in hexadecimal. When performing Diffie Hellman Group Exchange, sshd(8) first estimates the size of the modulus required to produce enough Diffie Hellman out- put to sufficiently key the selected symmetric cipher. sshd(8) then randomly selects a modulus from /etc/ssh/moduli that best meets the size requirement. SEE ALSO
ssh-keygen(1), sshd(8), Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol, RFC 4419, 2006. BSD
June 26, 2008 BSD