A Python wrapper over GMP-ECM
ecmx is a simple, easily deployed wrapper over GMP-ECM which consists of a single Python file.
You will need Python (anything >= 3.3 should be OK), and of course GMP-ECM. Once you have a Python environment and GMP-ECM in your PATH, create a text file containing the number you want to factor e.g.
> echo "(10^353-1)/(9*1781225293*1044667255801249)" > 10m353.n
Now, to run 128 curves at B1=26e7 using 16 threads with progress output every two hours, you would enter
> ecmx.py -t 16 -d 7200 -i 10m353.n -o 10m353_26e7.out -cs 128 26e7
After completion of the curves, the output file 10m353_26e7.out will contain the output produced by the 16 instances of GMP-ECM and if a factor is found it is reported to the console. Option -d is the number of seconds you want between progress output.
Here is an example with a smaller number chosen to show the ouptut we get when a factor is found and the cofactor is a probable prime which ends the factorization:
> echo "(10^20+39)*(10^31+33)" > test.n
> ecmx.py -t 2 -d 10 -i test.n -o test.out -cs 50 11e3
ecmx version 0.4.1
Copyright Youcef Lemsafer (May 2014 - Jan 2016).
| 2016-01-17 18:04:05,786 |
| 2016-01-17 18:04:05,787 | ecmx version 0.4.1
| 2016-01-17 18:04:05,787 |
| 2016-01-17 18:04:06,789 | Running 25 curves at 11e3 (thread 1)...
| 2016-01-17 18:04:06,789 | Running 25 curves at 11e3 (thread 2)...
| 2016-01-17 18:04:08,793 | A factor has been found (thread 1), the cofactor is PRP!
| 2016-01-17 18:04:08,797 | GMP-ECM output (thread 1):
GMP-ECM 6.4.4 [configured with GMP 6.1.0, --enable-asm-redc] [ECM]
Running on <hostname>
Input number is (10^20+39)*(10^31+33) (52 digits)
[Sun Jan 17 18:04:07 2016]
Using MODMULN [mulredc:0, sqrredc:0]
Using B1=11000, B2=11000-1873422, polynomial x^1, sigma=3881101407
dF=256, k=3, d=2310, d2=13, i0=-8
Expected number of curves to find a factor of n digits:
35 40 45 50 55 60 65 70 75 80
2924742 1.8e+08 1.5e+10 Inf Inf Inf Inf Inf Inf Inf
Step 1 took 8ms
Using 8 small primes for NTT
Estimated memory usage: 586K
Initializing tables of differences for F took 0ms
Computing roots of F took 0ms
Building F from its roots took 0ms
Computing 1/F took 0ms
Initializing table of differences for G took 4ms
Computing roots of G took 0ms
Building G from its roots took 0ms
Computing roots of G took 0ms
Building G from its roots took 0ms
Computing G * H took 4ms
Reducing G * H mod F took 0ms
Computing roots of G took 0ms
Building G from its roots took 0ms
Computing G * H took 4ms
Reducing G * H mod F took 0ms
Computing polyeval(F,G) took 4ms
Computing product of all F(g_i) took 0ms
Step 2 took 16ms
********** Factor found in step 2: 100000000000000000039
Found probable prime factor of 21 digits: 100000000000000000039
Probable prime cofactor ((10^20+39)*(10^31+33))/100000000000000000039 has 32 digits
| 2016-01-17 18:04:08,797 | Number is fully factored!!
| 2016-01-17 18:04:08,798 | Ran 33 curves @ B1=11e3
Another example, to show how you can reduce the output of GMP-ECM, the following example will also exhibit progress output and that ecmx keeps running curves when a factor is found and the cofactor is composite.
> echo "(10^22+9)*(10^35+69)*(10^36+67)" > test.n
> ecmx.py -q -t 2 -d 30 -i test.n -o test.out -cs 50 5e4
ecmx version 0.4.1
Copyright Youcef Lemsafer (May 2014 - Jan 2016).
| 2016-01-17 18:18:58,852 |
| 2016-01-17 18:18:58,852 | ecmx version 0.4.1
| 2016-01-17 18:18:58,852 |
| 2016-01-17 18:18:59,854 | Running 100 curves at 5e4 (thread 1)...
| 2016-01-17 18:18:59,854 | Running 100 curves at 5e4 (thread 2)...
| 2016-01-17 18:19:03,860 | GMP-ECM output (thread 2):
GMP-ECM 6.4.4 [configured with GMP 6.1.0, --enable-asm-redc] [ECM]
Input number is (10^22+9)*(10^35+69)*(10^36+67) (94 digits)
Using B1=50000, B2=50000-12746592, polynomial x^2, sigma=2790862391
Step 1 took 76ms
Step 2 took 68ms
********** Factor found in step 2: 10000000000000000000009
Found probable prime factor of 23 digits: 10000000000000000000009
Composite cofactor ((10^22+9)*(10^35+69)*(10^36+67))/10000000000000000000009 has 72 digits
| 2016-01-17 18:19:04,857 | 55 curves completed @ B1=5e4 out of 200 (Elapsed time: 0:00:05.001352, avg curve duration: 0:00:00.090934s, ETA: 0:00:13.185383s).
| 2016-01-17 18:19:05,861 | GMP-ECM output (thread 1):
GMP-ECM 6.4.4 [configured with GMP 6.1.0, --enable-asm-redc] [ECM]
Input number is (10^22+9)*(10^35+69)*(10^36+67) (94 digits)
Using B1=50000, B2=50000-12746592, polynomial x^2, sigma=1877786664
Step 1 took 56ms
Step 2 took 48ms
********** Factor found in step 2: 10000000000000000000009
Found probable prime factor of 23 digits: 10000000000000000000009
Composite cofactor ((10^22+9)*(10^35+69)*(10^36+67))/10000000000000000000009 has 72 digits
| 2016-01-17 18:19:10,863 | 160 curves completed @ B1=5e4 out of 200 (Elapsed time: 0:00:11.007507, avg curve duration: 0:00:00.068797s, ETA: 0:00:02.751877s).
| 2016-01-17 18:19:11,868 | A factor has been found (thread 2)!
| 2016-01-17 18:19:13,870 | A factor has been found (thread 1)!
| 2016-01-17 18:19:13,870 | Ran 200 curves @ B1=5e4
That's it, happy factoring!
To get some help, invoke ecmx with option -h (--help):
> ecmx.py --help
ecmx version 0.4.1
Copyright Youcef Lemsafer (May 2014 - Jan 2016).
usage: ecmx.py [-h] [-v] -t THREADS [-d DELTA_PROGRESS] [-q]
[-maxmem MAX_MEMORY] [-k STAGE2_STEPS] [-n] [-nn] -i INPUT_FILE
-o OUTPUT_PATH [-e ECM_PATH] -cs NUMBER_OF_CURVES B1
optional arguments:
-h, --help show this help message and exit
-v, --verbosity Increase verbosity level.
-t THREADS, --threads THREADS
Number of threads.
-d DELTA_PROGRESS, --delta_progress DELTA_PROGRESS
The number of seconds between progress outputs.
-q, --quiet Make GMP-ECM less verbose.
-maxmem MAX_MEMORY, --max_memory MAX_MEMORY
Maximum memory usage per thread.
-k STAGE2_STEPS, --stage2_steps STAGE2_STEPS
Number of steps to perform in stage 2.
-n, --nice Run ecm in "nice" mode (below normal priority).
-nn, --very_nice Run ecm in "very nice" mode (idle priority).
-i INPUT_FILE, --input_file INPUT_FILE
Input file.
-o OUTPUT_PATH, --output_path OUTPUT_PATH
Output file path.
-e ECM_PATH, --ecm_path ECM_PATH
Path of ecm executable.
-cs NUMBER_OF_CURVES B1, --curves_spec NUMBER_OF_CURVES B1
Curves specification as <number of curves> <B1> (the
option can be specified multiple times e.g. -cs 960
1e6 -cs 2400 3e6).
The following options are passed as is to GMP-ECM: -maxmem MAX_MEMORY, -k STAGE2_STEPS, -n (--nice), -nn (--very_nice), refer GMP-ECM documentation for more details about them.
Note that in case ecm is not in PATH or you want to use another executable than the one in path option -e (--ecm_path) can be used to specify the path of the GMP-ECM executable.
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