View computation and transmission for a set of keys refreshed over multiple epochs in a cryptographic device
View Patent ↗A first cryptographic device is configured to store a set of keys that is refreshed in each of a plurality of epochs. The first cryptographic device computes for each of at least a subset of the epochs at least one view based on at least a portion of the set of keys for that epoch, and transmits the views to a second cryptographic device in association with their respective epochs. At least one view computed for a current one of the epochs is configured for utilization in combination with one or more previous views computed for one or more previous ones of the epochs to permit the second cryptographic device to confirm authenticity of the set of keys for the current epoch. The first cryptographic device may include an authentication token and the second cryptographic device may include an authentication server.
1. A method comprising:
storing in a first cryptographic device a set of keys that is refreshed in each of a plurality of epochs;
computing for each of at least a subset of the epochs a plurality of views based on at least a portion of the set of keys for that epoch; and
transmitting, in association with respective ones of the epochs, at least a subset of the plurality of views computed for that epoch to a second cryptographic device;
wherein said subset of views for a current one of the epochs is configured for utilization in combination with one or more previous views computed for one or more previous ones of the epochs to permit the second cryptographic device to confirm authenticity of the set of keys for the current epoch.
2. The method of claim 1 wherein at least one view in said subset of views computed for the current one of the epochs comprises one or more elements of a codeword that is computed by applying a designated encoding function to the set of keys for the current one of the epochs.
3. The method of claim 1 wherein transmitting the views comprises transmitting at least one view in said subset of views computed for the current one of the epochs encoded in a passcode generated by the first cryptographic device and transmitted from the first cryptographic device to the second cryptographic device.
4. The method of claim 1 wherein the first cryptographic device comprises a transmission-aware cryptographic device that maintains information characterizing transmission of said one or more previous views to the second cryptographic device.
5. The method of claim 1 wherein the set of keys in a given epoch t comprises a set of t keys K t = κ 1 . . . κ t .
6. The method of claim 5 wherein at least one view in said subset of views computed for the current one of the epochs is computed by:
determining a pseudorandom vector {right arrow over (ν)} T for a given time T based at least in part on T and state information σ shared by the first and second cryptographic devices; and
generating said at least one view as b T =K t ·{right arrow over (ν)} T .
7. The method of claim 5 wherein computing the plurality of views for the current one of the epochs comprises:
determining m pseudorandom vectors {{right arrow over (ν)} T i }, iε{0, . . . , m−1} for a given time T based at least in part on T and state information a shared by the first and second cryptographic devices; and
generating m views as b T i =K t ·{right arrow over (ν)} T i ;
wherein the m views are encoded in a passcode generated by the first cryptographic device.
8. The method of claim 7 wherein the m views comprise respective ones of m freshest bits of the set of keys K t = κ 1 . . . κ t .
9. The method of claim 7 wherein only a designated number of final bits of {right arrow over (ν)} T i are non-zero.
10. The method of claim 7 wherein determining m pseudorandom vectors {{right arrow over (ν)} T i }, iε{0, . . . , m−1} comprises:
setting {right arrow over (ν)} T i [j] jε[t−m+1, . . . , t] as follows: if j=t−i, setting {right arrow over (ν)} T i [j]=1, and otherwise setting {right arrow over (ν)} T i [j]=0; and
randomly assigning remaining positions of {right arrow over (ν)} T i .
11. The method of claim 7 wherein determining m pseudorandom vectors {{right arrow over (ν)} T i }, iε{0, . . . , m−1} comprises:
setting {right arrow over (ν)} T i [j] jε[t−m+1, . . . , t] as follows: if jε[t−i, . . . , t], setting {right arrow over (ν)} T i [j]=1, and otherwise setting {right arrow over (ν)} T i [j]=0; and
randomly assigning remaining positions of {right arrow over (ν)} T i .
12. The method of claim 1 wherein computing the plurality of views for the current one of the epochs comprises:
determining a plurality of pseudorandom vectors; and
generating a plurality of views as respective view vectors based on respective ones of the pseudorandom vectors;
wherein sub-vectors defined by a designated group of elements of each view vector are substantially linearly independent.
13. The method of claim 1 wherein computing transmitting said subset of views computed for the current one of the epochs comprises:
selecting from a plurality of possible views at a given time;
transmitting the selected view; and
repeating the selecting and the transmitting of the selected view at each of one or more additional times.
14. The method of claim 13 where the selecting at a given time T is based at least in part on a view transmission history H T and further comprises:
computing, for each time t included in H T , corresponding vectors V={{right arrow over (ν)} t i } tεH T iε{0, . . . , m−1} ; and
selecting a time T′=T+δ from δε[a,b] such that the vectors {{right arrow over (ν)} T′ i } iε{0, . . . , m−1} satisfy a specified condition;
wherein the selected view is based on the vectors {{right arrow over (ν)} T′ i } iε{0, . . . , m−1} .
15. The method of claim 14 wherein the specified condition is that the vectors {{right arrow over (ν)} T′ i } iε{0, . . . , m−1} are linearly independent of the vectors in V.
16. The method of claim 14 wherein the specified condition is that a maximum amount of new information is transmitted in the selected view relative to previous views in the view transmission history.
17. A computer program product comprising a non-transitory processor-readable storage medium having embodied therein one or more software programs, wherein the one or more software programs when executed by a processor of the first cryptographic device cause the method of claim 1 to be performed.
18. An apparatus comprising:
a first cryptographic device comprising a processor coupled to a memory;
the first cryptographic device being configured to store in the memory a set of keys that is refreshed in each of a plurality of epochs under control of the processor;
wherein the first cryptographic device is further configured:
to compute for each of at least a subset of the epochs a plurality of views based on at least a portion of the set of keys for that epoch; and
to transmit, in association with respective ones of the epochs, at least a subset of the plurality of views computed for that epoch to a second cryptographic device;
wherein said subset of views for a current one of the epochs is configured for utilization in combination with one or more previous views computed for one or more previous ones of the epochs to permit the second cryptographic device to confirm authenticity of the set of keys for the current epoch.
19. The apparatus of claim 18 wherein the first cryptographic device comprises an authentication token and the second cryptographic device comprises an authentication server.
20. The apparatus of claim 19 wherein the authentication token comprises one of a hardware authentication token and a software authentication token.
21. The method of claim 1 wherein said subset of views for the current one of the epochs is selected from the plurality of views computed for the current one of the epochs based at least in part on information characterizing transmission of one or more previous views computed for one or more previous ones of the epochs.