Kinda' Big Primes

These are some Sophie Germain prime numbers that I've generated. I hereby release these numbers into the public domain - whatever that means.

These primes are well suited for use in Diffie-Hellman key exchange. i.e. not only are they prime, but the number (p - 1) / 2 is also prime. The numbers are encoded in hexadecimal (base 16). These take a little while to discover. Finding secure generators for these numbers is easy, as the prime factorization of (p - 1) is known. Some people involved in the standardization process of IPSec indicate that to ephemerally generate a 128-bit session key, a modulus of 2550 bits is of the appropriate minimum strength. This is when time is the constraint on a brute-force search. See the collected notes below for further details.

2048-bit secure Diffie-Hellman modulus #1
This is too small to protect a 128-bit generation at full strength.
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2048-bit secure Diffie-Hellman modulus #2
This is too small to protect a 128-bit generation at full strength.
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2048-bit secure Diffie-Hellman modulus #3
This is too small to protect a 128-bit generation at full strength.
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2560-bit secure Diffie-Hellman modulus #1
This is adequately-sized to support 128-bit generations at full strength.
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3072-bit secure Diffie-Hellman modulus #1
Unknown strength greater than 128-bit, less than 192-bit.
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3584-bit secure Diffie-Hellman modulus #1
Unknown strength greater than 128-bit, less than 192-bit.
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4096-bit secure Diffie-Hellman modulus #1
Whoah, Nellie!!! I consider myself lucky to have generated this one.
It only took a short time compared to 3072 #1.
ASCII-hexadecimal representations of this modulus and the session keys generated with it are 1024 bytes long.
That may be handy for you.
Unknown strength greater than 128-bit, less than 192-bit.
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8192-bit secure Diffie-Hellman modulus #1
Ew Dawggie!!!
This one took over 2 months of compute time on my 1.7 GHz P4.
Clearly I don't use an operating system from Washington, USA for this work.
Binary representations of this modulus and the session keys generated with it are 1024 bytes long.
That may be handy for you.
Unknown strength greater than 192-bit, less than 256-bit.
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16384-bit secure Diffie-Hellman modulus #1
July 2013: Well, compute horsepower has caught up with this hobby.
This one only took a weekend on one core of an i7
Should be adequate for 256-bit session key generation at full strength.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16384-bit secure Diffie-Hellman modulus #2
This one was generated in parallel with 16384 #1 over the same weekend
Should be adequate for 256-bit session key generation at full strength.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3f4f48e79e32f65b7523f967be1bb098b2d03dbbefbb7225c781c394feb3b2f0
17ac6fc83c36178d8987c52e8dc7882e5bf2fef1b197fec43e3755aeff9ac790
745bbf27ede558a2c92332a7bd2f61f721500dab94384f2ab624c8a9c92dbe22
f35e7407c7d11901d140209541fc7fa9be755299b4d41e31929c80c8e58eb7d8
343e5fb10751d56ba1bbc93529db87f27eb498197a9935e5431e150e9fc0c382
0589ad5d65ac954412a60abf93f7f0963da597e1d6a463a2de9e110e6dc6a488
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328c0c59aa98b6a4a2a2130c1bcbc50e516e283435bd74ea924db3f12cafb34d
24c1c30aa7f5c12e97d31c2b34a737aef985d0cd5c97cc43f220f44b9f492ff2
971acbf0ce2acd4da3d5c671544e50b6927b8f77e82741e47754ab55c716a8cd
2ee290a376b022cc753912da3e8ae43dce4980bfb97f408e0ad724af65e5b5ea
9cb45c799e5f30306ca1b25085ff5e7da53db4b068021c6be11ccfc17d60c4f8
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07107ee66d4de3ec0e463467bac0a595241d1f57fd5e457f234ddd4ab1e0ef0b
91867dfd5b6129dd3d763d82fdec8e839e78e777b74d8b38a32e26e4d441c335
4814970ced5d55b725b7ebfbb22e5b9001cf60ce1f270d34c076b72fde1896ed
1d1565f277b725b40db4b9e1ede1b0e277f63ac7dc239a967d93915a84bbfbc0
a515e204f582d22f6c8463996fb00791e8d1197d4f21a131efa542ec532f3a4c
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5ac8f269a4a209b211ebf06e4b6524be577a10f69040ec4dc61d06514d6d0682
9111b9a01f2f487276812ab0d4080cf39247ea32ab9acbcf9e13de0233d25c6d
76d068d9f6f1d7bc8dc1fdf00d3438888ef3c72573fc7a1539fd24022d096b98
3c7ccc5e4178ba773aa1a0f62b53dc4c6f2430d1b74d2ef9b321acf4723499a1
2322bb413cacc4e63ecd11d3f5aa3be474a2fee019591133ec62f461eef871ab
ca586c99c31c1db9fc8f289eb1ec0ca46578781db5fed330f5e8ba43b19e7976
bf205445bee5b8274b3ac50b99fd5dd4f71e00290fd6402846d5d3d184e72da8
16c1b0f43bcf0a05715e5e6b0043babeadc590a2aa3791c10a47e70c047ecc0d
7c5e06333ce203f7a0ac01499df98e77df674d2df392971f9bd39a2e8026a93e
8edd46d6e72fb00d6455e90bee5b40486abefc51bebddfd2bbd100cc29a39159
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f3dc46717d71dbbb2c9ff42d19120c8c726325cde3d0ff19c1b213d7f969ff6e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24576-bit secure Diffie-Hellman modulus #1
November 2013: Go big or go home!
This one took about two months on four cores of an i7 to generate.
Should be adequate for >256-bit session key generation at full strength.
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a88fe28cbb72fccde1bed9058156c45e29aba3c760343442a20ef261d34592a8
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2d37e8fc4acccad21c77e90e8405eb8356fbce393281499eb83a59c63fb4590a
3698ec7a9666b6b2f743ad31ec47069da25f10f82bba3c256c510889dcb35b3c
20b3b67367a5d0fd50000fa866265768063ba2075b1fb47f3a68d2a63e9417ee
ff714e597139bd124b105c3b75c37dad153eb869bdd36f5783c72013fef6b586
d32028b59e1ff9d7b9307f0aa7f4ef371821a04fc9b140bc067a74f4aef99156
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2bdc3ebc844f3a4b7a3b1cee1f9018530d474749ba2890d840fba2babe804a6e
32d31ad04eabdf8781ba9fad2ab276cc0354da4efe775c322d3ac2f2e0201b06
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0ab9e2f6c8536ed306d0eeb040de3502be52af26bd6b858fc3728a161243aa30
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7e7559e1b0f2fbe42b96af8cc54d89caca4aa87b8de11614ac146de1cac404d7
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d8cd4d6d38d87b35d2451cd54d754eae8921be0c32626a111aec6242cd288c80
86e94f692bfb3107ae12fbb15187d53ae611173434dc69dd455abd636a002c3b
c170c5356d1b5f5620530515b74ed214de82fd6786778d0fe2c4368b0418be48
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95e2b2ab7b86985e7a67f7aa6014e35872921736b5af66f6251fae90cad06876
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95952fbcb41decd871d440f5cb2812e4d8e1ade2bda89c2394e42671c6d1e36f
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882f64f187fd2a294a23f5e31825fbba993ce9bdb19b82c8aa03eea5c247c662
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07d9b04fdc6ef8fec1290579036860eb63b437f2f953c5090b65a96ab700ea2c
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0682ba0c6428e39427b55b9f27736e88259cb710dc1656325a1ce30c703f9f43
460cc816499b166645d3625fb9f626fe111de30aa8a59615545f776de47aaf4c
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7c1f24259e19fd6f9164d11bd9f7b242461745ac868ce97015bb29460949a7eb
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0e11a0ed88215cd5510b7932c800f5ff2923ef3b92452e2e22f600a975609eed
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a4c0cdab82795a9c85b26e4993a0c34814de084b374d3376b421adf47a8eca73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32768-bit secure Diffie-Hellman modulus #1
March 2014: oh, yeah!
This one took about five months on four cores of an i7 to generate.
Should be adequate for >256-bit session key generation at full strength.
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4c9b71a81d06b0251aba2a39a3c689faecc4d579e9263ceccbaf29f7dc18f6b8
b2a4305bcb52464e5efdce4d3ed13b5fb8196c77284a86f55f0f7dea3ef32424
8b35b213a84fff1cfa187b7af271ae3ed2966c79f4459fc68be8225b2013b6a2
1f9ea01277507896d884175d1eae827a1ec25e1c42a74ef0194f26960c6cfa83
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a20e23f6cd821bb9c5d44372544c7cb2fc6c9bc3512a36d6818ab211019d5864
bd5e08d4cfb97d4ad3280fc66455cb42e0fc19df5423cf92ba06758be89f3653
bfa8fa98261644bee42d7d1badcedcd99b5cd87fd5ad8eedcc164a48b64b0458
78ea8c6ad5f3b90e43cbedc9b690037afd15675132abb4e30db63c74db3b13cd
b2ace3f31e80db7384b6f06394a4c430e2b4be250705868787abc777ccc615d8
126cf217d09444e20f7be9f9f865be82d814eacffc0fcbebb204dafbdfb5fb79
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6417af8fcb14017cbce38cff4d192773ebff6c7461bc3cbe9593e87845b90651
5812efd1b0d77f9d855b4b6d56b737e6bcf9e5dbc85725ea4fc1ce936d0524dc
cc91ec91f7a39d9e86f6ed790e1d1ac2c288ccbd54342d728174b56fa046bec3
3f952b276652b9b5609786c3ee1b319c3c70ee55582c8c219b26532c9e3a8087
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4fe7ac9252696a98b1dc3d091ea95d21972a73c171ae7080ab917a26455da5c1
8894a3f223271f94f1bbd93398e473f35b2d9832db39525adf59acd389a9a6bb
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a085d7bdb98dc6ee0b1a4f6f17b6b7be14c4ee7cb890ca76e53a8974fa911daf
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NOTES:
LOCATION: Neohapsis / Archives / Crypto / Message Index / Fwd: New Time and Space Based Key Size Equivalents for RSA and Diffie-Hellman

Subject: Fwd: New Time and Space Based Key Size Equivalents for RSA and Diffie-Hellman
From: Alex Alten (Alten@home.com)
Date: Thu Dec 14 2000 - 23:26:53 CST

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I thought this might be of interest to the coderpunks community, it arrived
on several other security lists. The only thing that puzzles me is that
I would have thought a time-only RSA key could have been shorter than a
corresponding time-and-space RSA key (assuming that the time to crack is
equivalent to a key's strength).

- Alex

-----Original Message-----
From: FRousseau@chrysalis-its.com [mailto:FRousseau@chrysalis-its.com]
Sent: Wednesday, December 13, 2000 9:37 PM
To: IETF Transport Layer Security WG
Cc: ietf-pkix@imc.org
Subject: [ietf-tls] New Time and Space Based Key Size Equivalents for RSA
and Diffie- Hellman

I am sorry for the multiple postings, but I thought this particular
subject, although probably quite controversial, might be of interest to the
many peoples following these mailing lists, especially because of the
upcoming adoption of the AES algorithm by many IETF protocols.

As symmetric keys grow, they can be attacked by more processors without a
change in processor technology since the memory requirements for breaking
symmetric keys remain trivial. However, for the Number Field Sieve (NFS)
algorithm, which is currently the most efficient method to break RSA keys,
this is not true. Based on this premise, the "time and space" based RSA
key size equivalents previously published in the RSA Labs Bulletin #13 of
April 2000 by Robert Silverman (http://www.rsalabs.com/bulletins/) have
recently been extended to cover all the AES symmetric key sizes in the
latest draft of ANSI X9.44, which will eventually become the ANSI standard
for RSA key transport:

Time and Space
Symmetric Equivalent
Key Size RSA Key Size
(in bits) (in bits)

64 450
128 1620
192 2500
256 4200

These "time and space" based key sizes equivalents assume that both time
and memory are binding constraints in order to break RSA keys. This same
draft also indicates that beyond RSA key sizes of 768 bits one can no
longer effectively utilize 32-bit processors with the NFS algorithm because
the required memory exceeds what can be addressed in 32 bits; one is forced
to use 64-bit machines. Beyond RSA key sizes of about 2500 bits, the
memory requirements for the NFS algorithm exceed what can be addressed even
on 64 bit machines.

For your information, here are also the estimated "time" only based RSA key
size equivalents for solving the NFS problem from the same ANSI draft:

Time Only
Symmetric Equivalent
Key Size RSA Key Size
(in bits) (in bits)

64 512
128 2550
192 6700
256 13500

Note that either of these sets of RSA key size equivalents could be used
with Diffie-Hellman for solving the value of "p" since the NFS algorithm is
also the most efficient method to break Diffie-Hellman algorithm today.
Note also that these time only equivalents numbers are slightly smaller
than those from ANSI X9.42 for Diffie-Hellman (i.e. 2550 vs 3072 for 128
bits, 6700 vs 7680 for 192 bits and 13500 vs 15360 for 256 bits) and the
numbers in Hilarie Orman's Internet Draft (i.e.
draft-orman-public-key-lengths-01.txt).

Shouldn't IETF standards mention these new "time and space" based key size
equivalents in addition to existing "time" only based key size equivalents,
and possibly even suggest that "time and space" based key size equivalents
be used for RSA and Diffie-Hellman? Why mandate larger equivalent key
sizes when smaller equivalent key sizes can probably suffice?

Food for thought!

Cheers,

Francois
___________________________________
Francois Rousseau
Director of Standards and Conformance
Chrysalis-ITS
1688 Woodward Drive
Ottawa, Ontario, CANADA, K2C 3R7
frousseau@chrysalis-its.com Tel. (613) 723-5076 ext. 419
http://www.chrysalis-its.com Fax. (613) 723-5078

--
Alex Alten
Alten@Home.Com

--------------------------------------------------------------------

From: draft-ietf-ipsec-ciph-aes-cbc-01.html
+===========+=================+================+===============+
| Key Size | Exponent Size | Modulus Size | Group Type |
+===========+=================+================+===============+
| 128 | 256 | 3240 | MODP |
+-----------+-----------------+----------------+---------------+
| 128 | 248 | 248 | EC2N |
+-----------+-----------------+----------------+---------------+
| 192 | 384 | 7945 | MODP |
+-----------+-----------------+----------------+---------------+
| 192 | 376 | 376 | EC2N |
+-----------+-----------------+----------------+---------------+
| 256 | 512 | 15430 | MODP |
+-----------+-----------------+----------------+---------------+
| 256 | 504 | 504 | EC2N |
+-----------+-----------------+----------------+---------------+