Patent Application: US-31840702-A

Abstract:
a system and method for an unconditionally secure protocol to create identical pads or keys between two parties communicating over any network is provided . the protocol is composed of three parts , as follows . firstly , the two parties generate an initial correlated string ka , kb by simultaneously observing common physical phenomena such as a satellite signal or recording round trip timing of messages being rallied back and forth , etc . secondly , the two parties engage in information consolidation and reconciliation in order to reconcile differences . finally , privacy amplification is used to cancel any information that an eavesdropper may have acquired and to produce the key or pad . this key agreement protocol creates unconditionally secure cryptography with a symmetric key cryptosystem . alternatively , the symmetric keys can be used as a one - time pad with unconditional security .

Description:
in a preferred embodiment , the key agreement scheme of the present invention comprises three phases . the first phase is construction of a permuted remnant bit string . two methods are presented . the first method is based on physical characteristics of the network , wherein , for example and not limitation , the two communicating parties , alice and bob , rally packets back and forth recording round - trip times . the second method is probabilistic , wherein , for example and not limitation , the two communicating parties , alice and bob , both know a probabilistic string p of real numbers and generate keys based on this string , see appendix c . some of the bits may still be different after the initial bit string construction so alice and bob then participate in a second phase called information reconciliation . the second phase results in alice and bob holding exactly the same key . however , eve may have partial knowledge of the reconciled strings , in the form of shannon bits . therefore , a third and final phase called privacy amplification is performed to eliminate any partial information collected by eve . phase i — alice and bob rally packets back and forth to generate a bit string from truncated round - trip timings . this string is then systematically permuted . the procedure is as follows : ( i ) alice sends bob a network packet and logs the time t a0 . ( ii ) bob records the time of reception as t b0 and responds immediately to alice with another network packet . ( iii ) alice records the time of reception as t a1 , and responds immediately with a network packet . ( iv ) bob records the time of reception as t b1 and responds immediately to alice with another network packet . depending on the quality of the network connection , only some bits of δt a and δt b are kept . the higher order bits are dropped . typical experimental data and criteria for the truncation can be found in [ 18 ]. by taking a suitable probability distribution it can be shown that the average of δt a equals the average of δt b . ( vi ) repeat steps ( i ) through ( v ) in order to create enough bits that are then concatenated as a string of bits of a pre - determined length . ( i )-( vi ) alternatively , alice and bob each know a random probabilistic array p . they independently proceed as described in appendix c to generate correlated raw random keys k a and k b . phase ii — once sufficient bits are created , the process is stopped . alice and bob must now use the relative time series to create an unconditionally secure pad or key . one skilled in the art can deduce , from a study of various papers in the list of references that there are many ways to proceed . the present invention uses an approach which , very loosely speaking , is initially related to that of bennett et al . [ 1 ]. however in [ 3 , 4 and 10 ], several changes and improvements have been indicated . these changes , based on fundamental results in algebraic coding theory , information theory , block design and classical statistics together achieve the following results : ( b ) a method for estimating the initial and subsequent bit correlations and key - lengths ; ( c ) a precise procedure on how to proceed optimally at each stage ; ( d ) a formal proof that k a converges to k b ; after phase i , alice and bob have their respective binary arrays k a and k b and both perform the following steps of phase ii : ( vii ) shuffle and partition . alice and bob apply a permutation to k a and k b . they then partition the remnant raw keys into sub - blocks of length l = 4 . ( viii ) parity exchange and bisective search with l = 4 : parities are computed and exchanged for each sub - block of length 4 by alice and bob . simultaneously they discard the bottom bit of each sub - block so that no new information is revealed to eve . if the parities agree alice and - bob retain the three top bits of each sub - block . if the parities disagree alice and bob perform a bisective search discarding the bottom element in each sub - block exactly as described in [ 1 ] and [ 5 ] ( see also [ 4 ]). the procedure in steps ( vii ) and ( viii ) is denoted by kap 4 . ( ix ) estimate correlation from the length of the new key , we can calculate the expected initial bit correlation x 0 between k a and k b [ 4 ]. using x 0 we can calculate the present expected correlation x = φ 4 ( x 0 ). ( x ) shuffle , parity exchange , bisective search with the optimal l : to the remnant keys k a , k b we apply a permutations in order to separate adjacent keys . as a non - restrictive example , one such f can be implemented by shuffling the bit order from ( 1 , 2 , 3 . . . , n ) into the order ( 1 , p + 1 , 2 p + 1 , . . . q 1 p + 1 , 2 , p + 2 , 2 p + 2 , . . . , q 2 p + 2 , . . . , p − 1 , 2 p − 1 , 3 p − 1 , . . . , q p - 1 p + p − 1 , p , 2 p , 3 p , q p p + p ), where q i =( n - i )/ p . given the present correlation x we choose the optimal value for l = l ( x ) by using the tables in [ 4 ]. similar to ( viii ), ( ix ) for the case l = 4 , we carry out the procedure kap l . from x , or from the new common length of the remnant keys , we calculate the expected present correlation after kap l has been applied . we repeat ( xi ) until the stopping condition holds . ( xi ) stopping condition : for key length n and correlation x we have n ( l - x )& lt ; ε , a predetermined small positive number . we then proceed to the verification procedure , an example of which is as follows . ( xii ) verification procedure : let k a , k b both be of length n . let t be the smallest integer for which 2 t ≦ n . construct a binary matrix m = m ij , ( 1 ≦ i ≦ t + 1 , 1 ≦ j ≦ 2 t ) as follows : a . the entries m ij , ( 1 ≦ ij ≦ t ) are the entries of the t × t identity matrix i txt . b . the ( t + 1 ) th row of m is the all - ones vector , that is m t + 1j = 1 ( 1 ≦ j ≦ 2 t ). c . denote the top t entries in the j th column by the binary vector v j ( 1 ≦ j ≦ 2 t ). thus , vj ={ m ij | 1 ≦ i ≦ t }. then we impose the condition that the vectors v j are all distinct . thus , the set { v j } equals the set of all 2 t distinct binary vectors of length t . d . denote the rows of m by r 1 , r 2 , . . . , r t + 1 . let x , y denote the remnant keys k a , k b written as row vectors of length n . let x , y denote the vectors that result when a row of zeros of length 2 t - n is adjoined , on the right of x , y respectively . thus x =( x , 000 . . . 0 ), y =( y , 000 . . . 0 ). e . our verification criterion is to check that x . r i = y . r i , ( 1 ≦ i ≦ t + 1 ). if the verification criterion is not satisfied we remove the first t + 1 bits from k a , k b and repeat steps ( x ), ( xi ) and check again if the verification criterion is satisfied . eventually , it will be satisfied . at this stage alice and bob have confirmed that they now share the same key . once confirmed , the final remnant raw key as transformed by phase 2 is modified by removing the first t + 1 bits from k a = k b . our new key is re - named the “ reconciled key ” and phase 3 , privacy amplification is performed . phase iii — at this stage alice and bob now have a common reconciled key . in certain cases it is possible that the key is only partially secret to eavesdropper , eve , in the sense that eve may have some information on the reconciled key in the form of shannon bits . alice and bob now begin the process of privacyamplification that is the extraction of a final secret key from a partially secret one ( see [ 1 ] and [ 2 ]). a well - known result of bennett , brassard and robert ( see [ 18 ]) shows that eve &# 39 ; s average information about the final secret key is less than 2 − s / ln 2 shannon bits as explained below ( see also shannon [ 9 ]). ( xiii ) privacy amplification — let the upper - bound on eve &# 39 ; s number of shannon bits be k and let s & gt ; 0 be some security parameter that alice and bob may adjust as desired . alice and bob now apply a hash function described in “ method for the construction of hash functions based on sylvester matrices , balanced incomplete block designs and error - correcting codes ”, co - pending irish patent application , ( the entire contents of which is hereby included by reference as if fully set forth herein [ 3 ]) which produces a final secret key of length n - k - s from the reconciled key of length n . the system and method of the present invention provide an unconditionally secure key agreement scheme based on network dynamics as follows . in phase i , alice and bob permute the bits of what remains of their respective raw keys , which keys incorporate delay occasioned by network noise . in phase ii , the key from phase i undergoes the treatment of lomonaco [ 5 ]. that is , in phase ii alice and bob partition the remnant raw key into blocks of length l . an upper bound on the length of the final key has been estimated and the sequence of values of i that yield key lengths arbitrarily close to this upper bound has also been estimated [ 4 ]. in phase ii , for each of these blocks , alice and bob publicly compare overall parity checks , making sure each time to discard the last bit of the compared block . each time an overall parity check does not agree , alice and bob initiate a binary search for the error , i . e ., bisecting the mismatched block into two sub - blocks , publicly comparing the parities for each of these sub - blocks , while discarding the bottom bit of each sub - block . they continue their bisective search on the sub - block for which their parities are not in agreement . this bisective search continues until the erroneous bit is located and deleted . they then proceed to the next i - block .. phase i is then repeated , i . e ., a suitable permutation is chosen and applied to obtain the permuted remnant raw key . phase ii is then repeated , i . e ., the remnant raw key is partitioned into blocks of length l , parities are compared , etc . precise expressions for the expected bit correlation ( see below ) following each step have been obtained in [ 4 ], where it is also shown that this correlation converges to 1 . moreover in [ 4 ] the expected number of steps to convergence as well as the expected length of the reconciled key are tabulated . the probability that corresponding bits agree in the arrays k a , k b is known as the bit correlation probability or , simply , as the bit correlation . it can be shown ( see [ 4 ]) that each round can be used to increase the bit - correlation . for example , if we start with a bit - correlation of 0 . 7 then after one round with l = 3 the bit - correlation increases to about 0 . 77 and then to 0 . 87 . for l = 2 the corresponding numbers are 0 . 84 and 0 . 97 . estimates are also available for the key lengths after a round of the protocol of the present invention , for various values of l [ 4 ]. the final secret key can now be used for a one - time pad to create perfect secrecy or can be used as a key for a symmetric key cryptosystem such as rijndael [ 12 ] or triple des [ 18 ]. a simplified version of the algorithm for the values l = 2 and 3 is described in appendix a . the system and method of the present invention provides secure transmission over wireless and wire media and networks as set forth below ; it will be understood by those skilled in the art , that the above - described embodiments are but examples from which it is possible to deviate without departing from the scope of the invention as defined in the appended claims . the following references are hereby incorporated by reference as if fully set forth herein . [ 1 ] charles bennett , frangois bessette , gilles brassard , louis salvail , and john smolin , experimental quantum cryptography , europcrypt &# 39 ; 90 ( arhus , denmark ), 1990 , pp . 253 - 265 . [ 2 ] charles h . bennett , gilles brassard , and jean - marc robert , privacy amplification by public discussion , siam j . of computing , 17 , no . 2 ( 1988 ), pp . 210 - 229 . [ 3 ] aiden bruen and david wehlau , method for the construction of hash functions based on sylvester matrices , balanced incomplete block designs , and error - correcting codes , irish patent co - pending irish patent application . [ 4 ] aiden bruen and david wehlau , a note on bit - reconciliation algorithms , non - elephant encryption systems technical note 01 . xx ne2 , 2001 . [ 5 ] samuel j . lomonaco , a quick glance at quantum cryptography , cryptologia 23 ( 1999 ), no . 1 , pp . 1 - 41 . 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