SpaceFlip plus: ordinal cryptography

Patent metadata

Field	Value
Publication number	US-11159317-B2
Application number	US-202117216274-A
Country	US
Kind code	B2
Filing date	Mar 29, 2021
Priority date	Jun 18, 2019
Publication date	Oct 26, 2021
Grant date	Oct 26, 2021

Abstract

Extending the “SpaceFlip” cipher defined in the continued application (Ser. No. 16/855,517) to increase the lifespan of the shared secret key, and avoid the need for key replacement; applicable to Internet of Things devices where re-access is prohibitive, adding convenience to normal secure communication; extending the use of the SpaceFlip quantum safe cryptography. Applying key equivocation cryptography where several keys are interchangeable.

First claim

What is claimed is:

1. A method of extending the useful life of a cryptographic key, the method comprising:
by a processing device:
a cryptographic procedure f, where a cryptographic input, I, yields a cryptographic output, O, by applying a cryptographic key, K 1 : O=f(I,K 1 ), with an infinite number, t, of other keys K 2 , K 3 , . . . K t with K t ≠K j , for all i,j=1, 2, . . . t, and with each of these t keys generating the same cryptographic output from the same cryptographic input: O=f(I, K i ), for i=1, 2, . . . t;
sharing, by two or more communication partners, a secret master key K 0 ;
performing by the two or more communication partners, the following steps, (i), (ii), (iii), and (iiii), in sequence:
(i) selecting, by the communication partners, a derivation algorithm D i ,
(ii) deriving, by the communication partners utilizing the derivation algorithm D i , a key K i , for i=1 from K 0 : K i =D i (K 0 ),
(iii)) utilizing, by the communication partners, K i for an arbitrary measure of usage where an arbitrary amount of cryptographic input, I is processed into a cryptographic output, O, using K i , and
(iiii) incrementing, by the communication partners, the value of i: i→(i+1), and repeating steps (i), (ii), (iii), and (iiii) in sequence for as long as cryptographic input is available to be processed; and
preventing cryptanalytic gains extracted from cryptanalysis of the output generated from keys K 1 , K 2 , . . . K i , of providing assistance in the effort to cryptanalyze K i+1 , due to each K i for i=1, 2, . . . p, where p is arbitrarily large, being accompanied by an infinite number of keys K i 1 , K i 2 . . . K i t , all of which operate on the same cryptographic input, I, in generating the same cryptographic output: O=f(I,K i j ) for j=1, 2, . . . t, which keeps K 0 indefinitely valid.

2. The method of claim 1 , further comprising:
basing the cryptographic procedure, f, on only ordinal properties of the keys, K 1 , K 2 , . . . K p , wherein ordinal properties are defined as follows:
letting key K i be comprised of an ordered series of q real numbers N 1 , N 2 , . . . N q ,
letting an ordinal function, o, be defined over two real numbers, a, and b, where if a<b then o(a,b)=−1, if a=b then o(a,b)=0, and if a>b then o(a,b)=1, and
letting the “ordinal image” of a key, K i , ORD(K i ) be defined as the 0.5q(q−1) ordinal values o(N u , N v ) for u,v=1, 2, . . . q; and
an ordinal property of key K i having the same value for any other key K′ i ≠K i , of which the ordinal images are the same: ORD(K i )=ORD(K′ i ), with infinite keys sharing an ordinal image of K i .

3. The method of claim 2 , further comprising:
basing the cryptographic procedure, f, on an operation NEXT mapping a letter L i of a given alphabet A, to another letter L j ≠L i j=1, 2, . . . (i−1),(i+1) . . . n of the alphabet A on the basis of a geometric structure, “space”, serving as a cryptographic key, defined over n letters in the alphabet A through a set of 0.5n (n−1) distance measures d uv =[u,v] between each letter L u and L v in the alphabet A, where u,v=1, 2, . . . n, and where the distance between L i and L j , d(L i , L j )=[i,j] is the smallest among all the distances from L i to all other letters L w , for w≠i, and where if two or more letters have the same smallest distance with respect to L i , then a Next Equivocation Resolution procedure settles the resulting equivocation by selecting and performing one of procedures (a), (aa), or (aaa), or selecting and performing an ordered sequence of procedure (aa), then procedure (aaa):
(a) two or more equal smallest candidates for the NEXT mapped letter are recursively dismissed, and the NEXT mapped letter is selected from among the remaining letters in the alphabet A,
(aa) a candidate letter that becomes the output of the NEXT operation is recursively selected based on which of the candidate letters has itself a NEXT mapped letter of the smallest distance, and
(aaa) the candidate letter that becomes the output of the NEXT operation is the NEXT mapped letter with the smallest centrality index, if there is only one candidate with the smallest centrality index, where the centrality index of the NEXT mapped letter X is the sum total of distances of NEXT mapped letter X towards all other (n−1) letters; and
if the selected and performed NEXT Equivocation Resolution procedure or sequenced procedure results in no resolution, then the NEXT Equivocation Resolution procedure or sequenced procedure returns ‘Next Letter Undefined’.

4. The method of claim 3 , wherein the cryptographic procedure f utilizes the operation LINE, of which the operation LINE is defined as a sequence of l letters beginning with a starting letter X 1 , followed by letter X 2 =NEXT(X 1 ), followed by letter X 3 =NEXT(X 2 ), . . . X l =NEXT(X l−1 ), with each next letter, Xi, i=2, 3, . . . l selected among all the letters of the alphabet A, except the letters X 1 , X 2 , . . . X i−1 , and where the operation LINE is expressed as L l =LINE(X 1 , l).

5. The method of claim 4 , wherein the cryptographic procedure f utilizes an operation FIGURE, of which the operation FIGURE is defined as a sequence of LINE operations, where an original letter X 0 is mapped with a first LINE operation to a letter X 1 , where letter X 1 is operated on with the LINE operation to map X 1 to letter X 2 , and where letter X i is operated on with the LINE operation to map X j to letter X j+1 , with t LINE operators applied in succession, resulting in an outcome letter X t ; the mapping X 0 →X t based only on ordinal properties of K i .

6. The method of claim 5 , further comprising:
a procedure of mutual identity verification, where the operation FIGURE is used for mutual identity verification by two parties sharing a master key K 0 , where one of the two parties, designated as the “identity prover” or “prover” proves its identity to the other of the two parties designated as the “identity verifier” or “verifier”, wherein the verifier randomly sets a starting letter X, then conveys to the prover the definition of the operation FIGURE; and
the prover further applying the operation FIGURE on X and identifying X′ as the letter which the operation FIGURE points to if it starts with X: X′=FIGURE(X), and the prover then communicating X′ to the verifier, the verifier also applying the operation FIGURE to X to compute X′, if the reply from the prover matches the verifier's own calculation of the result of applying the operation FIGURE on X, then the verifier is indicated that the prover is in possession of a shared key, and where after successful repetition of this procedure of mutual identity verification the verifier accepts the prover as a communication partner.

7. The method of claim 5 , further comprising:
providing for durable secure communication with the shared secret master key K 0 in cases where one communication partner is located where access to replace the shared secret master key is difficult.

8. The method of claim 3 , further comprising:
a communication procedure between communicating partners, for transmitting and receiving any message of any length consisting of the letters of the alphabet A, comprising:
the transmitting communicating partner transmitting a letter X from the alphabet A, X∈A to the receiving communicating partner by transmitting a FIGURE comprised of l successive LINEs, X=FIGURE(Y, t 1 , t 2 , . . . t l )=LINE(LINE( . . . LINE(Y, t 1 ) . . . , t l−1 ), t l );
indicating a starting letter of the next line of size t i (for i=2, 3, . . . l) letters by applying LINE on letter Y at length t i , for i=1, 2, . . . l lines, resulting in letter X; and
selecting randomly, by the transmitting communicating partner, letter Y∈A and se

Assignees

• Samid Gideon

Inventors

• Samid Gideon

Classifications

• H04L9/50

  using hash chains, e.g. blockchains or hash trees · CPC title

• H04L9/0861

  Generation of secret information including derivation or calculation of cryptographic keys or passwords · CPC title

• H04L63/0407

  wherein the identity of one or more communicating identities is hidden (cryptographic mechanisms or cryptographic arrangements for anonymous credentials or for identity based cryptographic systems H04L9/00) · CPC title

• G06F21/602 Primary

  Providing cryptographic facilities or services · CPC title

• H04L63/0471

  applying encryption by an intermediary, e.g. receiving clear information at the intermediary and encrypting the received information at the intermediary before forwarding · CPC title