A second part of the last note has to be written. Not only because finally I didn't write about the decelerator, also because there are more things to take into account about the antimatter: the annihilation.
The matter and the antimatter can not live together. Our universe is composed by matter, but an antimatter universe can exist. It is not possible to distinguish if your existence is in a matter world or in an antimatter one. The antimatter particles has the same stability than matter, but in their universe. The antimatter in a matter world is easily annihilated when it meet its respective matter particle.
This annihilation has some properties because the universe has some rules. There are things that it needs to conserve, like the energy or the momentum. A pair of matter-antimatter, when they annihilate it selves, has to conserve. Then some other types of particles has to be created (mass less like photons, or other exotic particles.
2007/11/23
2007/11/22
Decelerator
Do you think I am working on a freak machine? This one is not much freak that a decelerator... Today, comming back home in the train I was talking with a friend (and also a work collegue) about one his lasts jobs, the cern antimatter factory. Less that a year working on a synchrotron and there is no one day that I didn't learn new and new things...
What an antiparticle is? Every particle that compound our matter have it 'specular' particle with the same characteristics but with an opposite charge. Electrons has its antimatter particle with the positron. This two particles have the same mass: 0.510 MeV/c^2, the same spin, the same electric charge: {+,–}1.602176487*10^-19 C, but with an opposite sign. That is, the behaviour of a positron is the same than the electron, but positive. The proton have a mass of 938.272 MeV/c^2, and a charge of 1.60217653*10^-19 C (note that it differs to the electron in -4.3*10^-27, small but not the same); an its antiparticle is the antiproton with the exactly the same values but with negative charge.
But an exception could be to this definition. What about the neutron? This matter particle have no charge, but it doesn't means that it haven't antiparticle (or it is by itself). The neutron have its antineutron, that complain with the characteristic of an antiparticle.
Protons and neutrons are not fundamental particles, this particles are composed by quarks. This basic constituents of the matter, yes, have charge, and the neutrons are composed by two quarks down and one quark up. The down quark have a charge of -1/3 of the electron charge; and the up quark have +2/3 of the electron charge. Two down have (-1/3)+(-1/3)=-2/3, an oposite charge that the up quark that rest in the components of the neutron.
A really good explanation for non physicians can b found in the Tamiz.
The antineutron has to be composed by antiquarks. Then it consist of two anti-down quarks and one anti-up quark. The same but with opposite charges, adds also 0. In the wikipedia's antineutrons article is explained that the opposition that the antineutron has against the neutron is the magnetic moment.
After too much words I didn't say anything about the decelerator, but this is because I need to learn many things to not say something wrong... Next time.
What an antiparticle is? Every particle that compound our matter have it 'specular' particle with the same characteristics but with an opposite charge. Electrons has its antimatter particle with the positron. This two particles have the same mass: 0.510 MeV/c^2, the same spin, the same electric charge: {+,–}1.602176487*10^-19 C, but with an opposite sign. That is, the behaviour of a positron is the same than the electron, but positive. The proton have a mass of 938.272 MeV/c^2, and a charge of 1.60217653*10^-19 C (note that it differs to the electron in -4.3*10^-27, small but not the same); an its antiparticle is the antiproton with the exactly the same values but with negative charge.
But an exception could be to this definition. What about the neutron? This matter particle have no charge, but it doesn't means that it haven't antiparticle (or it is by itself). The neutron have its antineutron, that complain with the characteristic of an antiparticle.
Protons and neutrons are not fundamental particles, this particles are composed by quarks. This basic constituents of the matter, yes, have charge, and the neutrons are composed by two quarks down and one quark up. The down quark have a charge of -1/3 of the electron charge; and the up quark have +2/3 of the electron charge. Two down have (-1/3)+(-1/3)=-2/3, an oposite charge that the up quark that rest in the components of the neutron.
A really good explanation for non physicians can b found in the Tamiz.
The antineutron has to be composed by antiquarks. Then it consist of two anti-down quarks and one anti-up quark. The same but with opposite charges, adds also 0. In the wikipedia's antineutrons article is explained that the opposition that the antineutron has against the neutron is the magnetic moment.
After too much words I didn't say anything about the decelerator, but this is because I need to learn many things to not say something wrong... Next time.
2007/11/17
Secret sharing
Before to write about the possible implementation of elliptic curves over fields of characteristic 2, I want to propose another option: do some implementation over multi-public-key cryptography. This is if you have a secret that can not be trusted in only one person you can divide your secret in parts and give only one to one person. But under one reconstruction of this secret, you need all the people present.
If the secret that I said before is divided using a (n, t)-threshold scheme then your secret is shared between n players, but it can be reconstructed with t survivants from an attacker conspirator (this becomes from the thriller films).
You can create schemas with all the combination that you imagination gives. If you have a group of 10 people with a two heads, and two subgroups of four; and what you want if to have present two people of each subgroups and one of the heads (at least) you should have an schema (3-3)-threshold for the main secret and this keys to the shared secret will be re-shared as a (2-1)-threshold for the heads, and 2 (4-2)-threshold for each subgroup.
In Barcelona there are people working in this things. I meet some of them in some congresses and they are really nice people. For a long time, the secret sharing schemas have had charm for me. Could be interesting to implement this over embedded systems...
If the secret that I said before is divided using a (n, t)-threshold scheme then your secret is shared between n players, but it can be reconstructed with t survivants from an attacker conspirator (this becomes from the thriller films).
You can create schemas with all the combination that you imagination gives. If you have a group of 10 people with a two heads, and two subgroups of four; and what you want if to have present two people of each subgroups and one of the heads (at least) you should have an schema (3-3)-threshold for the main secret and this keys to the shared secret will be re-shared as a (2-1)-threshold for the heads, and 2 (4-2)-threshold for each subgroup.
In Barcelona there are people working in this things. I meet some of them in some congresses and they are really nice people. For a long time, the secret sharing schemas have had charm for me. Could be interesting to implement this over embedded systems...
Libgcrypt
As a continuation of the yesterday brainstorming, I want to write something more about the research project. Today I will think about what can make to contribute in the libgcrypt. In this library, the ECDSA that I did in my last research project, was rewritten. This was the objective of the project, to contribute in the free software.
It is necessary to do somethings in this library. The file 'cipher/ecc.c' contains a TODO list with the necessary improvements that this library needs:
How the project was adapted to the libgcrypt? The patch from it comes was written in a monolithic file in the way to do as less modifications as possible in the gnupg (in the 1.4 branch).
Then Werner made a good work moving the particular elliptic data structures to 'src/mpi.h' maintaining in the cryptofile 'cipher/ecc.c' the ones that have a direct relation with the pub and the private keys. Then, there are another file 'mpi/ec.c' that have everything about the mathematics background. But, in my opinion, this have one problem: the elliptic curve discrete logarithm problem (ecdlp) can be brought over primary fields (F_p) and also over fields of characteristic 2 (F_{2^m}), and this file should be split in this two mathematics bases.
This last paragraph propose another possible research project, that is implement what we had over primary fields but over characteristic 2 fields...
It is necessary to do somethings in this library. The file 'cipher/ecc.c' contains a TODO list with the necessary improvements that this library needs:
- If we support point compression we need to decide how to compute the keygrip - it should not change due to compression.
- In mpi/ec.c we use mpi_powm for x^2 mod p: Either implement a special case in mpi_powm or check whether mpi_mulm is faster.
- Decide whether we should hide the mpi_point_t definition.
- Support more than just ECDSA.
How the project was adapted to the libgcrypt? The patch from it comes was written in a monolithic file in the way to do as less modifications as possible in the gnupg (in the 1.4 branch).
Then Werner made a good work moving the particular elliptic data structures to 'src/mpi.h' maintaining in the cryptofile 'cipher/ecc.c' the ones that have a direct relation with the pub and the private keys. Then, there are another file 'mpi/ec.c' that have everything about the mathematics background. But, in my opinion, this have one problem: the elliptic curve discrete logarithm problem (ecdlp) can be brought over primary fields (F_p) and also over fields of characteristic 2 (F_{2^m}), and this file should be split in this two mathematics bases.
This last paragraph propose another possible research project, that is implement what we had over primary fields but over characteristic 2 fields...
2007/11/16
Elliptic curve isogeny
A few days a go (the 9th of November) a new patch about elliptic curves on GnuPG had been published. With two month delay since Mikael sent the code to me... As I read in the esr's book this is long longer time than acceptable.I'm sorry.
Now it's time to retrieve the projects. It is necessary to recuperate the gumstix development and also this year I will do my master degree research project. Against about elliptic curves. But what I said is really generic. I have some ideas, that I wanna write in this blog to be used as a brain storming to specify what is able to do and discard something else. Today is the turn elliptic curve isogeny.
Without speak on mathematics, and as far as I know, if you have a cryptoanalyst against finite fields and your paranoia says you that your privacy could be compromised, the only option that you have is increase your keylength... Use a bigger RSA or ElGamal key. Over elliptic curves you have one option before this: you can change the elliptic curve (and propose the elliptic discrete logarithm problem over a complete new one field). Nothing that the cryptoanalist computes for the old field can be used here.
But the cost to generate a new curve every key generation is hard. There are too much proprties and characteristics to test and be sure that this curve have good cryptographyc properties. One way to generate a new curve with a guarantee that it has cryptographyc characteristics is to perform some isogeny transformations to one curve that you know that it has this properties.
There exist algorithms to obtain a graph where the nodes represents elliptic curves and the edges represents an isogeny transformation. I don't need to go so far to know about isogenies, in the same university research group with I am studying they are specialists on this. For a long time a go I am listening conversations talking about this transformations an its advantages. The data structures that this isogeny transformation creates receive the name volcanus, and a join of volcanus receive the name of cordillera.
But! If the attacker knows the steps that you did in the volcanus to obtain your new isogeny curve, and it has good knowledge on isogenies transformation, it is possible to 'migrate' all the computation work that before I said that should be not useful, to the new field and continue the attack. This means that the isogeny could only generates more work to the attacker but it maybe doesn't improve the security.
An option, is to perform the transformation in secret. Generate a way in the volcanus during the key generation, from then you use the new elliptic curve and forget the relation with the one from it came... If the attacker is not able to stablish the path from one to the other, the system is secure.
Long time a go I was talking about this with Mikael, and he shows me that there are many people in the world that propose to use a public key isogeny cryptosystem, where the secret key is precisely this path in the volcanus.
Then the question is: Are we complicating so much the problem? In the low level we need to be careful with the AES symmetric cryptoanalysis. In the centre we have to beware if some algorithm better that pollard's-rho has been discovered. An then a third front we will have this transformation that could be grateful to reset a hole smartcard cryptosystem.
Yes, it is a grate thing to have the possibility to reset a institution smart card system without increase the keylength but with a restablishment of the security against an attacker.
Now it's time to retrieve the projects. It is necessary to recuperate the gumstix development and also this year I will do my master degree research project. Against about elliptic curves. But what I said is really generic. I have some ideas, that I wanna write in this blog to be used as a brain storming to specify what is able to do and discard something else. Today is the turn elliptic curve isogeny.
Without speak on mathematics, and as far as I know, if you have a cryptoanalyst against finite fields and your paranoia says you that your privacy could be compromised, the only option that you have is increase your keylength... Use a bigger RSA or ElGamal key. Over elliptic curves you have one option before this: you can change the elliptic curve (and propose the elliptic discrete logarithm problem over a complete new one field). Nothing that the cryptoanalist computes for the old field can be used here.
But the cost to generate a new curve every key generation is hard. There are too much proprties and characteristics to test and be sure that this curve have good cryptographyc properties. One way to generate a new curve with a guarantee that it has cryptographyc characteristics is to perform some isogeny transformations to one curve that you know that it has this properties.
There exist algorithms to obtain a graph where the nodes represents elliptic curves and the edges represents an isogeny transformation. I don't need to go so far to know about isogenies, in the same university research group with I am studying they are specialists on this. For a long time a go I am listening conversations talking about this transformations an its advantages. The data structures that this isogeny transformation creates receive the name volcanus, and a join of volcanus receive the name of cordillera.
But! If the attacker knows the steps that you did in the volcanus to obtain your new isogeny curve, and it has good knowledge on isogenies transformation, it is possible to 'migrate' all the computation work that before I said that should be not useful, to the new field and continue the attack. This means that the isogeny could only generates more work to the attacker but it maybe doesn't improve the security.
An option, is to perform the transformation in secret. Generate a way in the volcanus during the key generation, from then you use the new elliptic curve and forget the relation with the one from it came... If the attacker is not able to stablish the path from one to the other, the system is secure.
Long time a go I was talking about this with Mikael, and he shows me that there are many people in the world that propose to use a public key isogeny cryptosystem, where the secret key is precisely this path in the volcanus.
Then the question is: Are we complicating so much the problem? In the low level we need to be careful with the AES symmetric cryptoanalysis. In the centre we have to beware if some algorithm better that pollard's-rho has been discovered. An then a third front we will have this transformation that could be grateful to reset a hole smartcard cryptosystem.
Yes, it is a grate thing to have the possibility to reset a institution smart card system without increase the keylength but with a restablishment of the security against an attacker.
2007/11/10
Planet atmosphere
During this time that I has learning for the theory fly exams I was think that I provide me too much thinks to write here. At the same time, the day only have 24 hours (strictly less than this, 23h 56min 4sec). But I have a huge list that I will write, from time to time.
Also last Thursday I fly. In combination with this, I will began with the idea to fly in Mars. How different are the parameters in this planet to take care in an hypothetical fly try?
First of all, the gravity. The main think that you need to fly is the lift force, to do a balanced fly the aircraft will create the same lift than weight but under an opposite direction. As Wikipedia says, the gravity in Mars is 3.69 m/s², that is to say 2.65 times less than in the Earth.
Back to the lift force. Witch other parameters have influence on it? Right now we know that with a half lift force than in the Earth you can fly in Mars, but it doesn't say that is easy to create lift to an object in Mars. The formula becames from the Bernoulli principle:
What is different in Mars? (C_L is the lift coefficient is experimentally calculated). The atmospheric density! In the Earth the density (rho) is 1.225 kg/m³, and Mars rho is 0.020 kg/m³, that is to say 61.25 times less than in the Earth. The Lift force is directly proportional to the air density. If this parameter of the formula is 60 times smaller, the other need to be increased in this order; the speed or the surface of the wing are the only options that you have.
You need a half lift force to fly in Mars, but in Mars is 60 times expensive to have lift force... Then I can deduce that is 30 times much more difficult to fly on mars...
In this las link about Mars in found too much information from this planet in comparison to the Earth values. There are curious values in the atmosphere composition. I study the Earth atmosphere composition for the fly exams, and the Mars one is really different.
The first curiosity is the most common gas: the carbon dioxide. This gas that in the Earth makes move too much ink, with the 0.038% proportion, and the responsible of the greenhouse effect, in Mars is the most common gas with the 95.32%. Far from the most common in the Earth that is the Nitrogen with the 78.084%.
Also last Thursday I fly. In combination with this, I will began with the idea to fly in Mars. How different are the parameters in this planet to take care in an hypothetical fly try?
First of all, the gravity. The main think that you need to fly is the lift force, to do a balanced fly the aircraft will create the same lift than weight but under an opposite direction. As Wikipedia says, the gravity in Mars is 3.69 m/s², that is to say 2.65 times less than in the Earth.
Back to the lift force. Witch other parameters have influence on it? Right now we know that with a half lift force than in the Earth you can fly in Mars, but it doesn't say that is easy to create lift to an object in Mars. The formula becames from the Bernoulli principle:
What is different in Mars? (C_L is the lift coefficient is experimentally calculated). The atmospheric density! In the Earth the density (rho) is 1.225 kg/m³, and Mars rho is 0.020 kg/m³, that is to say 61.25 times less than in the Earth. The Lift force is directly proportional to the air density. If this parameter of the formula is 60 times smaller, the other need to be increased in this order; the speed or the surface of the wing are the only options that you have.
You need a half lift force to fly in Mars, but in Mars is 60 times expensive to have lift force... Then I can deduce that is 30 times much more difficult to fly on mars...
In this las link about Mars in found too much information from this planet in comparison to the Earth values. There are curious values in the atmosphere composition. I study the Earth atmosphere composition for the fly exams, and the Mars one is really different.
The first curiosity is the most common gas: the carbon dioxide. This gas that in the Earth makes move too much ink, with the 0.038% proportion, and the responsible of the greenhouse effect, in Mars is the most common gas with the 95.32%. Far from the most common in the Earth that is the Nitrogen with the 78.084%.
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