Is there a Mathematician Cryptographr in the House.
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From: adacrypt on 18 Jul 2010 05:41 Both Key and Plaintext belong in the ASCII printable subset (elements 32 to 126 incl 95 elements) Treat these names Key and Plaintext as variable names in this model. X is a positive integer. Consider now, [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) Call, [(X +Key) + (X +Plaintext)], Sum. N must divide Sum just once (and once only) and leave the residue (Mod N) >= 0 Every possible combination of key and Plaintext is to be considered as usable for both key and plaintext at any instant. Then, question 1) What is the minimum starting value for X that enables any N to be deduced i.e. what is the value of this first N that satisfies the equation, [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >= 0 What is the value of X that will give me a discreet number of Ns say 14000. Theory. This is the algorithm that produces two sets of random keys in the following cipher in modular arithmetic. Encryption. [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >=0 Cipher text = residue N Decryption. Decryption Key = residue + N Plaintext (as messagetext) = Ciphertext + 2N Key Comment. This cipher comes from the same stable as your RSA cipher except that this cipher is totally, utterly and irrefutably unbreakable by any means. It is secured by two sets of random keys i.e. the set of eponymous keys (Key) and the set of Ns. Each of these two sets of random keys is made equal in length to the message length during encryption. Each of these two sets of random keys is used only once in any message. The cipher uses the concept of mutual database technology, i.e. the keys are read in sequential order from the synchronised arrays in the entities databases. The plaintext is either read in from external batch files (produced by non-specialist operators) or is keyed interactively at the computer keyboard (by non-specialist operators). The arrays are periodically scrambled and sliced in a controlled way by the entities. If there are readers who are academics and would like to justify this brainwave into formal presentation then I would welcome your interest and contribution. As I see it. Residue, Ciphertext and Decryption key are congruent modulo N. (editing restriction forces me to print it this way) There are N elements in each residue class, there N classes of residue. It would be nice to formalise this using proper mathematical notation but again the restrictions of this editor wont go that far. How would you do it just for comparison. Comment. This not a boring one-time pad cipher. This is a cipher for mathematicians. It is an adaptation of the Vigenere cipher that undocks the eponymous square from its static position at (0,0) and moves it along the line Y = - (X+x). The OTP is also another adaptation of the Vigenere cipher although sadly, no one seems to realise this. Major Joseph Mauborgne who was Head of the US Army Cryptological Research in 1920 did however and designed the OTP in conjunction with his contemporary Gilbert Vernam. In my opinion, one of the first things that should have been done with the inception of computer-driven cryptography is to have had another look at the OTP that had become a popular joke paradox in the previous half century. That is being done now albeit more a renaissance of the Vigenere cipher than the OTP. May I repeat, this is not a One-Time Pad cipher despite the resemblance in the caveats of the operation. Please dont make any comparison-based arguments. Please give this modular arithmetic your best shot, it is a cipher for the future. The theory is fully expounded on my website http://www.scalarcryptography.co.uk - adacrypt
From: Joseph Ashwood on 18 Jul 2010 08:32 "adacrypt" <austin.obyrne(a)hotmail.com> wrote in message news:4c20c901-d3c4-4e40-9112-0957a5f305a3(a)r27g2000yqb.googlegroups.com... > What is the minimum starting value for X that enables any N to be > deduced � i.e. what is the value of this first N that satisfies the > equation, The minimum value for X that allows that is 1, it would be lower but earlier there was a restriction that X is a positive integer. > What is the value of X that will give me a discreet number of N�s say > 14000. The minimum value of X that allows that is 1, it would be lower but there is still that X is a positive integer problem. > Theory. It is nothing of the sort. > This cipher comes from the same stable as your RSA cipher except that > this cipher is totally, utterly and irrefutably unbreakable by any > means. Actually it does not have any relation to RSA. The prime driver for using RSA and other assymetric algorithms is the assymetry. > The cipher uses the concept of mutual database technology, And so you have absolutely proven in less than 10 words two things: 1) You have no idea what asymmetric cryptography is. 2) That you have no idea about even the most basic concepts in cryptography. > If there are readers who are academics and would like to justify this > brainwave into formal presentation then I would welcome your interest > and contribution. It is doubtful anyone will waste any significant time on your ramblings, I'm only replying because I'm bored. It has no value in the real world. Your statements are outright lies. If you are in any formalized presentation it is likely to be in a "dumbest ever" concept. > This is a cipher for mathematicians. What you have presented is marginal at best. Even your attempts at explaining it have succeeded in proving absolutely that it meets none of your primary claims. > May I repeat, this is not a One-Time Pad cipher You're right, it isn't. You have a database keyed stream cipher with a complex combinor. A quick look at the Unicity Distance will tell you everything you need to know about the perfect secrect claim. > Please don�t make any > comparison-based arguments. Afraid of reality creeping in on your delusions? > Please give this modular arithmetic your best shot, it is a cipher for > the future. It still suffers from the worst of your problems. It was you who brought up if we were talking about operas, unlike you I realize that there have been operas written in Chinese as well. > The theory is fully refuted with high school mathematics. Joe
From: adacrypt on 18 Jul 2010 10:19 On Jul 18, 10:41 am, adacrypt <austin.oby...(a)hotmail.com> wrote: > Both Key and Plaintext belong in the ASCII printable subset > (elements 32 to 126 incl 95 elements) > > Treat these names Key and Plaintext as variable names in this > model. > > X is a positive integer. > > Consider now, > > [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) > > Call, [(X +Key) + (X +Plaintext)], Sum. > > N must divide Sum just once (and once only) and leave the residue (Mod > N) >= 0 > > Every possible combination of key and Plaintext is to be considered as > usable for both key and plaintext at any instant. > > Then, question > > 1) > > What is the minimum starting value for X that enables any N to be > deduced i.e. what is the value of this first N that satisfies the > equation, > > [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >= 0 > > What is the value of X that will give me a discreet number of Ns say > 14000. > > Theory. > > This is the algorithm that produces two sets of random keys in the > following cipher in modular arithmetic. > > Encryption. > > [(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >=0 > > Cipher text = residue N > Decryption. > > Decryption Key = residue + N > > Plaintext (as messagetext) = Ciphertext + 2N Key > > Comment. > > This cipher comes from the same stable as your RSA cipher except that > this cipher is totally, utterly and irrefutably unbreakable by any > means. It is secured by two sets of random keys i.e. the set of > eponymous keys (Key) and the set of Ns. Each of these two sets of > random keys is made equal in length to the message length during > encryption. Each of these two sets of random keys is used only once > in any message. > > The cipher uses the concept of mutual database technology, i.e. the > keys are read in sequential order from the synchronised arrays in the > entities databases. The plaintext is either read in from external > batch files (produced by non-specialist operators) or is keyed > interactively at the computer keyboard (by non-specialist operators). > The arrays are periodically scrambled and sliced in a controlled > way by the entities. > > If there are readers who are academics and would like to justify this > brainwave into formal presentation then I would welcome your interest > and contribution. > > As I see it. > > Residue, Ciphertext and Decryption key are congruent modulo N. > (editing restriction forces me to print it this way) > > There are N elements in each residue class, there N classes of > residue. > > It would be nice to formalise this using proper mathematical notation > but again the restrictions of this editor wont go that far. How > would you do it just for comparison. > > Comment. > > This not a boring one-time pad cipher. > > This is a cipher for mathematicians. > > It is an adaptation of the Vigenere cipher that undocks the eponymous > square from its static position at (0,0) and moves it along the line Y > = - (X+x). > > The OTP is also another adaptation of the Vigenere cipher although > sadly, no one seems to realise this. Major Joseph Mauborgne who was > Head of the US Army Cryptological Research in 1920 did however and > designed the OTP in conjunction with his contemporary Gilbert Vernam. > > In my opinion, one of the first things that should have been done with > the inception of computer-driven cryptography is to have had another > look at the OTP that had become a popular joke paradox in the previous > half century. That is being done now albeit more a renaissance of the > Vigenere cipher than the OTP. > > May I repeat, this is not a One-Time Pad cipher despite the > resemblance in the caveats of the operation. Please dont make any > comparison-based arguments. > > Please give this modular arithmetic your best shot, it is a cipher for > the future. > > The theory is fully expounded on my websitehttp://www.scalarcryptography.co.uk > - adacrypt Hi, Consider now, >[(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >Call, [(X +Key) + (X +Plaintext)], Sum. >N must divide Sum just once (and once only) and leave the residue (Mod >N) >= 0 >Every possible combination of key and Plaintext is to be considered as >usable for both key and plaintext at any instant. Huge typo omission here, I should have stated that N is in the range (X +127) and 2(X+32). Then X works out to 63 (=> N =190) and the number of N's (as keys) works out to 14000 - 63. The strength of this cipher is then in the decryption equation being one equation in three unknowns - two of the unknowns are the random keys (Key and N) in the equation - being random makes them totally indeterminable to an adversary. My remark regarding this cipher coming from the same stable alludes to use of modular arithmetic - nothing else. No, I don't want to know whatever it is you ascribe to 'asymmetric' in a crypto sense - it is a redundant cosmetic property that is heading for the scrap heap anyway, never to be heard of again - I have no need for it whatever and nobody else will either in the long term future. Sorry about the error - adacrypt
From: Bruce Stephens on 18 Jul 2010 11:26 adacrypt <austin.obyrne(a)hotmail.com> writes: [...] > No, I don't want to know whatever it is you ascribe to 'asymmetric' in > a crypto sense - it is a redundant cosmetic property that is heading > for the scrap heap anyway, never to be heard of again - I have no need > for it whatever and nobody else will either in the long term future. By coincidence, <http://www.isc.org/press-release/isc-praises-momentous-step-forward-securing-domain-name-system> was released only a couple of days ago. Is that a waste of effort? If DNSSEC is too obscure, consider software updates: almost all are digitally signed nowadays. Or downloadable applications for mobile phones, almost all of which are digitally signed.
From: Mok-Kong Shen on 18 Jul 2010 13:19
adacrypt wrote: > Huge typo omission here, > > I should have stated that N is in the range (X +127) and 2(X+32). > > Then X works out to 63 (=> N =190) and the number of N's (as keys) > works out to 14000 - 63. > > The strength of this cipher is then in the decryption equation being > one equation in three unknowns - two of the unknowns are the random > keys (Key and N) in the equation - being random makes them totally > indeterminable to an adversary. Your formulation, also in the first post, is not clear for me. Anyway, if you want to exploit indeterminancy to enhance security, then simply xoring two pseudo-random strams R1 and R2 (assumed independent, both, say, of 32 bit units) will do the job: C = R1 ^ R2 ^ P where P and C are the plaintext and ciphertext units. This is of course equivalent to: R = R1 ^ R2 C = R ^ P So the xoring is properly to be considered to be internal to the single PRNG that generates R. One could however profitably do something more in the combination for achieving higer security, see my thread "A simple scheme of combining PRNGs" of 01.06.2010. M. K. Shen |