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additional Domains for ECC

(up to 1033 bit length)

The elliptic curve domains presented here were created by me(Michael Anders).

You are welcome to use them(at no cost) for noncommercial purpose.

They have a

Actually a 256 bit domain size is considered perfectly safe for decades. I created the domains to give my crypto software "Academic Signature" somewhat of a challenge regarding execution speed.

A side purpose is to satisfy the overkill safety needs of full blown hyper-paranoiacs and -admittedly- to show off a little bit .... ;-)

I felt free to incorporate some hex-wordart.

I incorporated the sha256-hash of a copyright note.

They were created on my normal office desktop pc with some substantial help by software written by Mike (in these times I better not mention his full name - he knows its him).

They were not fine tuned to contain any weakness - heaven how could I by just using a normal office pc!

They are stored in human readable form(hibyte left) that is also importable into the ECC-program "Academic Signature".

You can easily inspect them and find that all degrees of freedom have been used to introduce either hex-wordart or else to engrave the copyright hash. Other than that, they only contain strings of zeroes or ffff's to fill them up to the required bitlength. The small numbers at the end of modulus and parameter "B" result from counting up the modulus trial-value until a prime is hit and counting up the value of the parameter B until a prime Galois group order is encountered, respectively. Coefficient A is either used for hex-art or kept close to the modulus for a speedier computation.

The lower half of the galois group order ("q-Modul") and the y-coordinate of the used primitive point("Y0) are beyond my disposition and thus look random.

X0 can be almost freely selected and may again be subject to hex-art.

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Domain name: anders_1032_1

Filename

and Link: anders_1032_1.els my aca_sig ecdsa-signature

Prime size: 1033 bit

Content:

MODUL: fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc73

coeff_A: fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc70

coeff_B: d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d0015b3

q_MODUL: 0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000184ce99c462d57387687f83e43f191166f0a07b527136b230558cabe982fc856bf6239a1c95e44421a71c553d223e1e8b6941687648973a94d4027ca61abe02331

X0: 0d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d001500acc1de24000000d02a1d001500bad000000d02a1d001500f0e000000d02a1d0015d

Y0: 57029d58aeccbf320f5c337d84b7b30d8a412149ed8c526a4d9c0faa829f4ebfbb966bd235bf7dbcb21679b463ecdf73eb80031fb1855e96d37b67731863374e4295dcf904eac0f4cf22604bbfb66c6e4b1e72de7ad6a7289b6c921f8bebf2fcef346ba5f9ce1d6ce660510e345118d42168edb704be01b3ac41f7e485cfdd3df9

END

Comment:

The basic prime modulus contains many "ff"-bytes to facilitate modulo-reductions.

coeff_B does not contain a copyright note.

It just happened to look like a human readable political rant incited by current utterings of a powerful man and is terminated by the counter value when a prime group order was encountered for the first time. Just like anyone else, for this domain the commercial sector is explicitly welcome to use this domain without cost, if they got the guts to do that.

The prime motivation for creating this 1033-bit domain was the desire to clarify that activists in our western democracies reject to accept limits to the cryptographic strength of freely available crypto tools imposed by our self-appointed godfathers of mass surveillance and eavesdropping.

As I understand, "exporting" info about crypto surpassing the 512-bit security level can get you into jail e.g. if you are an australian citizen. Since half the bitlength is considered to be the security level for ECC, I needed more than 1024 bit to clearly trespass this "red line" of the "nobus"-agencies of the "five eyes" countries. As I am german, publishing this domain should be safe for me. Australians in such legal trouble could point to this page and claim that freely available post 512-bit security is already out there. Let's see when the impressive, professionally managed project bouncy castle will offer past 1024 bit ECC.....

Domain name: DT_1033

Filename

and Link: DT_1033.els my aca_sig ecdsa-signature

Prime size: 1033 bit

Content:

MODUL: fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc73

coeff_A: fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc70

coeff_B: d02a1d001500a00bad0011a20000d02a1d001500a00bad00fa5c1540000d02a1d001500a2001d10400000000d02a1d001500a00bad0011a20000d02a1d001500a00bad00fa5c1540000d02a1d001500a2001d104000000000000d02a1d001500a00fa5c154001500a00fa5c154001500a00fa5c154001500a00fa5c15400000018

q_MODUL: 0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000077642f0c9ae72397d016f3deb9df558290e220f6ab7e15cefdc1f624ed659d99253aea217d79df374951b7f1b47f5d0944a9a4602723e8035bb8a13b381f216cd

X0: d02a1d001500a00bad0011a20000d02a1d001500a00bad00fa5c1540000d02a1d001500a2001d10400000000d02a1d001500a00bad0011a20000d02a1d001500a00bad00fa5c1540000d02a1d001500a2001d104000000000000d02a1d001500a00fa5c154001500a00fa5c154001500a00fa5c154001500a00fa5c15400000001

Y0: 4aa949ac925d3b2b859d17a8e012bd073d4d4c79f35725e3504317b48be11c18a58d3e0d3f077b0774a7b2d9f8f9d586564f640b6c8694b48625196b39778eb860579fa53e568f1da7263e229d16f1bc31417990a4b9192c3d3696e68bd977e1f5aac333a378b68175da55f99d80b6c0fb2fe02cffb64c11c69d578d6cc4abe438

END

Comment:

This is a sister domain of anders_1032_1. As you can see this domain shares the basic prime module with the sister domain. (This does not pose any cryptographic problem.)

Of course it has a different group order.

As you can see from the meager counter value of " ....000018" at the tail of search parameter B, I hit a prime almost immediately. The search finished quickly. Fortuna apparently liked reading B.....

Domain name: anders_1024_1

Filename

and Link: anders_1024_1.els my aca_sig ecdsa-signature

Prime size: 1024 bit

Content:

MODUL: fa00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007

coeff_A: fa00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004

coeff_B: de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000000000b0b0000000000000d672c90d27a8070266ee8fc8e4b016d9ec4f0edbef9abd2dfd1e8c429db5e2c400000000000000000000000000a11ce000000000000000000000000000000000000000005

q_MODUL: fa000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c6962c2d0c03cabd2665e5763d5c7fb9fc8e9f7438d5ebc58b50780fb9de0df58a6e3bb579921d612530f353e569e1d3527589b979ea4bfa07ac5caaa97f2707

X0: 0de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000deadbeef15badf00d00400a11ce00a2d00b0b000000000000000000000000

Y0: 19f0536939e17b5ebe9bd4e4d3c06b0ad43acae9724a73b2410b17975bbc35d62a5ff6a86931d82f92fb6c84c60e05a18a569d2a437df946f454bc74f3c2894d0e59fc8864ba37fb90273c6a833352ef614075fff1622e4df17ad7f900c2a9ad3aa2f52c12c3112a82a87c584d5be050a49a17bc618b85edee26a78b4bb53650

END

Comment:

The modulus contains many zero bytes to facilitate modulo-reductions.

coeff_B contains the hex-art statement:

"DES is dead AES is good FLEAS is best FLEAS is cool FLEAS is ... ...." (please excuse my hubris) followed by zeroes, followed by the sha256 of my copyright note followed by zeroes, followed by a small obeisance to a crypto celebrity, followed by the counter value when a prime group order was encountered for the first time.

As you can see from the meager counter value I got very lucky with the group order and hit a prime at attempt #5, when about 1000 attempts are to be expected statistically.

Domain name: anders_1024_2

Filename

and Link: anders_1024_2.els my aca_sig ecdsa-signature

Prime size: 1024 bit

Content:

MODUL: deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00000553

coeff_A: b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce00b0b00ad02e500a11ce000000000000000000

coeff_B: de5001500dead0000ae5001500900d0000f1ea5001500be540000f1ea5001500c0010000f1ea5ff15ff25a5afe00000000000000000000000000000006c06c057a813fe4fc86eea79422c2f42581b924c73626b35043223f6c24edb1b00000000000000000000000000000000000000000000000000000000000000000000163

q_MODUL: deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00deadbeef001500bad00f00d00dea795ed3665842e7c5bbe6164c8694f28bfecbbdccaf14eb1d029be82868f7167ee3d3492126a4eee72ff26a1a9461187a59b40cc8bcfbe87af0405c66f562d68d

X0: 0de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000deadbeef15badf00d00400a11ce00a2d00b0b000000000000000000000001

Y0: 26f3cec2a668d0d3262431b83d8324cb8314c306a7e619c40cd25964492c5dbcf2a179da1d75c1758a158939c351c4cfcab769575fc6c4c31e9505ce161d800c7b49255813c3190a5595b5f6a7514a60f8efc8b9eef49c4cb1c536cbba81e3bf81816790d45b71b14c886c00915e2c9180a6a249eec84097c3cd8f85eb0d05fd

END

Comment:

The modulus has no special form and does not allow for using any special shortcuts to speed up calculations. Thus calculations take about threefold time compared to anders_1024_1 and signature verification thus takes about 1 second on my office desktop pc. The modulus has my favourite "deadbeef is bad food"- form.

coeff_A contains the hex-art statement:

--find out for yourself, this is a very affectionate statement ;-) .... followed by some zeroes

coeff_B contains the hex-art statement:

"DES is dead AES is good FLEAS is best FLEAS is cool FLEAS is ... ...." (again, please excuse my hubris) followed by zeroes, followed by the sha256 of another copyright note followed by zeroes, followed by the counter value when a prime group order was encountered for the first time.

As you can see from the counter value I got not so lucky with the group order this time and hit a prime at attempt #355, multiply this by 6 threads on my quadcore to get 2130 trials when about 1000 attempts were to be expected statistically -aaargh.

Domain name: anders_800_1

Filename

and Link: anders_800_1.els my aca_sig ecdsa-signature

Prime size: 800 bit

Content:

MODUL: ff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000047

coeff_A: ff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044

coeff_B: de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe00000000000000000000000000d672c90d27a8070266ee8fc8e4b016d9ec4f0edbef9abd2dfd1e8c429db5e2c4000000000000000003bf

q_MODUL: ff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000569d604b9866f4c07149d7adbc08639860bec66de3ac32bfffb4a8a301ef80ce26685b2fbca6c4d3f073566a7efadf547d05

X0: de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afede5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afeffffffffffffffff

Y0: 5ef7703d1143a5ccc4d9c0b5cf4074ec9376f6aefb6168e7797484e1759b4b45444708331e294ae6d974985b93b7695a0ec3a599f894d43c731f836de9bb9c6c7a2faee44aac9c0f0b0bf9f1e88f71f8db383aa4e35b9eff511f465a8c901f9f90248f8a

Comment:

As you can see from the counter value of parameter B, I was not too lucky with the 800-bit domain again and hit a prime group order well beyond the statistical expectation value(five threads ran in parallel, so I had to determine galois group order of an 800 bit elliptic curve several thousand times... I cursed more than once during two weeks of number crunching on my poor little office-PC.)

Domain name: anders_768_1

Filename

and Link: anders_768_1.els my aca_sig ecdsa-signature

Prime size: 768 bit

Content:

MODUL: fb00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e7

coeff_A: fb00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e4

coeff_B: de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afe0000000000f0000000d672c90d27a8070266ee8fc8e4b016d9ec4f0edbef9abd2dfd1e8c429db5e2c400000000000000000185

q_MODUL: faffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff823dec7f8ef180dc44c9e5cd2c1e351b51faf52779db9decc9a3e13d526b0eb2b1816ddd401d83de0dd0f3999de2fc4f

X0: de5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afede5ff15ffdeadffffae5ff15ff900dfffff1ea5ff15ffbe54fffff1ea5ff15ffc001fffff1ea5ff15ff25a5afeffffffffffff

Y0: 0559cdf3dc6b1e8e0364eb9bdac0b9b72e714c2a6e14a2cc9a188a4e6f67599b83886d1cdf4e1272f282c51b2bfee63f425f210a7f5b80de67d1d64a19bb8f4e1739d16acf3635efc7a8ff6840f93f0d4c6e6be5298275b2bad0b84aef2dec95

END

Domain name: anders_640_1

Filename

and Link: anders_640_1.els my aca_sig ecdsa-signature

Prime size: 640 bit

Content:

MODUL: b0b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000217

coeff_A: b0b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000214

coeff_B: a11ceffffb0bffffa2dffffecd5affffffffffffffffd672c90d27a8070266ee8fc8e4b016d9ec4f0edbef9abd2dfd1e8c429db5e2c4ffffffffffffffff00000000000000000000000000000000011d

q_MODUL: b0b0000000000000000000000000000000000000000000000000000000000000000000000000000040693ef5b986c36e8e4e3875d3ad5a90a01902f487c64bde90c26dc557013ab00756f5a9101b5c09

X0: a11ce00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000b0b

Y0: 3ceeebfa34aa8c9a9ed635296e74987e688cba0b772498be4660ac8977d4751b43b087d718d608396b7e82721dd423bc433f76cc76c18d3d3ac00c719f9f22662676189eebdfa4d7f347364daaf766e2

END

Just for your Infomation:

I append the largest openly available domain from other sources, NIST-521, in "els"-format below.

Depending on what country you reside in, you may be able to manually copy&paste it for import into "Academic Signature" without risking legal threats about alleged patent infringement(?). This domain can be used in the more advanced of commercial crypto-products.

Beware! the NSA may have backdoors in place. Use at own risk.

MODUL:

01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

coeff_A:

01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc

coeff_B:

51953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00

q_MODUL:

01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409

X0:

c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66

Y0:

011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650

END

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