Pseudorandom number generation and crytographic authentication

• US RE36,181 E
• Filed: 11/08/1996
• Issued: 04/06/1999
• Est. Priority Date: 06/30/1993
• Status: Expired due to Term

• Current Assignee: Lear Corporation EEDS and Interiors Incorporated (Lear Corporation)
• Original Assignee: United Technologies Automotive, Inc. (Lear Corporation)
• Inventors: Finn, Alan M., Koopman, Philip J. Jr.
• Primary Examiner(s): Gregory, Bernarr E.
• Application Number:
  US08/751,932
• Time in Patent Office: 879 Days
• Field of Search: 380/4, 380/9, 380/23, 380/24, 380/25, 380/46, 380/49, 380/50, 380/21, 380/43, 331/78, 364/717, 364/717.01, 364/717.02, 364/717.03, 364/717.04, 364/717.05, 364/717.06, 364/717.07, 340/825.31, 340/825.34
• US Class Current: 713/168
• CPC Class Codes: G06F 2207/583 Serial finite field implementation, i.e. serial implementation of finite field arithmetic, generating one new bit or trit per step, e.g. using an LFSR or several independent LFSRs; also includes PRNGs with parallel operation between LFSR and outputs
• CPC Class Codes: G06F 7/584 using finite field arithmetic, e.g. using a linear feedback shift register
• CPC Class Codes: G07C 2009/00253 dynamically, e.g. variable code - rolling code
• CPC Class Codes: G07C 2009/00769 with data transmission performed by wireless means
• CPC Class Codes: G07C 2009/00825 remotely by lines or wireless communication
• CPC Class Codes: G07C 2009/00984 fob
• CPC Class Codes: G07C 2209/06 Involving synchronization or resynchronization between transmitter and receiver; reordering of codes
• CPC Class Codes: G07C 9/00182 operated with unidirectional data transmission between data carrier and locks
• CPC Class Codes: H04L 2209/04 Masking or blinding
• CPC Class Codes: H04L 2209/08 Randomization, e.g. dummy operations or using noise
• CPC Class Codes: H04L 2209/12 Details relating to cryptographic hardware or logic circuitry
• CPC Class Codes: H04L 2209/20 Manipulating the length of blocks of bits, e.g. padding or block truncation
• CPC Class Codes: H04L 2209/84 Vehicles
• CPC Class Codes: H04L 9/12 Transmitting and receiving encryption devices synchronised or initially set up in a particular manner
• CPC Class Codes: H04L 9/304 based on error correction codes, e.g. McEliece
• CPC Class Codes: H04L 9/32 including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials

Abstract

An automobile door lock receiver module (30) and a plurality of keychain fob transmitter units (16) contain identification numbers, secret initial values, and secret feedback masks so as to authenticate encrypted messages from any of the assigned fobs, indicative of commands registered by closing switches on the fob. Each fob is synchronized with the receiving module by means of a truly random number concatenated with a secret initial value and encrypted, through a linear feedback shift register or other operations. A second secret initial value is encrypted and command bits are exclusive ORed into the low order bit positions; the two encrypted numbers are concatenated and encrypted to form a key word which is transmitted with the fob ID. Synchronization includes decrypting to recover the truly random number and the secret initial value concatenated therewith; the truly random number is compared with previously received random numbers in order to avoid copying of recently transmitted synchronization commands. Successive lock-related commands utilize the number encrypted from the truly random number and the second secret initial value as starting values, employing a pseudorandom number of encryption iterations. A half-second delay between responses mitigates gaining access through numerical trials. An authenticated panic alarm command operates the headlights and horn of the vehicle but does not alter the synchronization.

Claims

1. A method of cryptographic authentication of transmissions from a transmitting unit to a receiving module, comprising, in said transmitting unit:

separately generating a plurality of pseudorandom numbers;

concatenating said numbers to form a combined word;

performing an encryption operation on said combined word; and

transmitting a command word including a key portion derived from the result of said encryption operation; and

comprising, in said receiving module;

receiving said command word;

performing a decryption operation on the key portion of said command word to recover said combined word;

providing at least one number; and

providing an authentication signal only if at least a portion of said at least one number is identical to a corresponding portion of said recovered combined word.

2. A method according to claim 1 wherein:

said step of providing at least one number comprises separately generating a second plurality of pseudorandom numbers; and

said step of providing an authentication signal comprises providing said authentication signal only if at least a portion of each of said second plurality of pseudorandom numbers is identical to a corresponding portion of said recovered combined word.

3. A method according to claim 2 wherein said generating steps each comprise generating a pair of numbers.

4. A method according to claim 1 wherein said generating step comprises generating a pair of numbers.

5. A method according to claim 1 wherein said step of performing an encryption operation comprises performing a linear encryption operation.

6. A method according to claim 1 wherein said step of performing an encryption operation comprises performing a feedback shift register operation.

7. A method according to claim 6 wherein said step of performing an encryption operation comprises performing a linear feedback shift register operation employing a secret feedback mask and said step of performing a decryption operation comprises performing a reverse linear feedback shift register operation employing the same secret feedback mask as in said encryption operation.

8. A method according to claim 7 wherein said linear feedback shift register operation comprises a number of iterations on the order of the degree of said combined word or more.

9. A method of cryptographically authenticating a transmission from a transmitting unit to a receiving module, comprising:

providing a starting number in said transmitting unit and providing said starting number in said receiving module;

in said transmitting unit;

providing . .an.!. .Iadd.a first .Iaddend.iteration control signal which changes in a pseudorandom manner in response to successive transmissions from said transmitting unit;

performing a variable number of iterations of an iterative encryption operation on said starting number, said variable number determined by said iteration control signal;

transmitting a command word derived at least in part from the result of said encryption operation; and

in said receiving module

receiving said command word;

recovering the result of said encryption operation from said received command word;

providing a second iteration control signal which changes, in the same pseudorandom manner as said first iteration control signal, in response to successive receptions of command words by said receiving module;

performing a variable number of iterations of said iterative encryption operation on said starting number, said variable number determined by said second iteration control signal;

comparing at least a portion of the result of said encryption operation performed in said receiving module with a corresponding portion of said recovered result; and

providing an authentication signal only if said portion of said encryption operation performed in said receiving module is identical to said corresponding portion of said recovered result.

10. A method according to claim 9 wherein said step of performing an iterative encryption operation comprises performing a linear iterative encryption operation.

11. A method according to claim 9 wherein said step of performing an iterative encryption operation comprises performing a feedback shift register operation.

12. A method according to claim 9 wherein said step of performing an iterative encryption operation comprises performing a linear feedback shift register operation employing the same secret feedback mask in said transmitting unit as in said receiving module.

13. A method according to claim 9 wherein:

the same . .secret initial value.!. .Iadd.starting number .Iaddend.is provided in said transmitting unit and in said receiving module; and

said starting number is provided by performing said iterative encryption operation on a word derived at least in part from said secret initial value a number of iterations on the order of the degree of said word, or more.

14. A method according to claim 9 wherein said variable number of iterations is a fraction of the degree of said starting number.

15. A method according to claim 9, comprising:

providing a second starting number in said transmitting unit and providing said second starting number in said receiving module;

in said transmitting unit;

providing a third iteration control signal which changes in a pseudorandom fashion in response to successive transmissions from said transmitting unit;

performing a changeable number of iterations of an iterative encryption process on said . .third.!. .Iadd.second .Iaddend.starting number, said changeable number determined by said third iteration control signal;

transmitting said command word derived at least in part from the result of said encryption process; and

in said receiving module;

recovering the result of said encryption process from said received command word;

providing a fourth iteration control signal which changes, in the same pseudorandom fashion as said third iteration control signal, in response to successive receptions of command words by said receiving module;

performing a changeable number of iterations of said iterative encryption process on said starting number, said changeable number determined by said fourth iteration control signal;

comparing at least a portion of the result of said encryption process performed in said receiving module with a corresponding portion of said recovered result of said encryption process; and

providing an authentication signal only if said portion of said encryption process performed in said receiving module is identical to said corresponding portion of said recovered result of said encryption process.

16. A method according to claim 15 wherein said variable number is different from said changeable number.

17. A method according to claim 15 wherein said pseudorandom manner is different from said pseudorandom fashion.

18. A method according to claim 15 wherein said iterative encryption operation is the same as said iterative encryption process.

19. A method according to claim 9 wherein, in response to the presence of said first and second equal signals, the command portion of said recovered new altered word is exclusive ORed with the corresponding portion of said second new pseudorandom number and said steps (a) and (b), are performed in response to the result of said exclusive OR operation indicating said command is a synchronization command.

20. A method according to claim 9 wherein said iteration control signal changes in response to the value of a bit position of a changing number.

21. A method according to claim 9 wherein said iteration control signal changes in response to the value of a plurality of bit positions of a changing number.

22. A method according to claim 9 wherein said iteration control signal changes in response to the value of a bit position of said starting number.

23. A method of cryptographically authenticating transmissions from any of a plurality of remote command transmitting units to a command performing receiving module, comprising:

providing a set of numbers in each of said transmitting units, each set corresponding to one of said transmitting units, each set including at least one secret initial value, each set essentially unique to the corresponding unit;

providing in said receiving module, said set of numbers for each of said transmitters to which said receiving module is to respond;

transmitting a command word from one of said transmitting units including a key portion derived at least in part from an encryption operation performed on said secret initial value; and

authenticating said command word received at said receiving module utilizing the numbers in a corresponding set.

24. A method according to claim 23 wherein each of said sets includes an identification number;

said transmitting step comprises transmitting said command word including said identification number; and

said authenticating step comprises performing a process to authenticate said received command word only in response to said command word containing an identification number which matches an identification number in one of the sets provided in said receiving module.

25. A method according to claim 24 wherein, in response to receipt of said command word, said receiving module performs an authentication process using successive ones of said sets which have an identification number that matches the identification number included in said received command word until either authentication occurs or all of said sets have been used.

26. A method according to claim 23 wherein, in response to receipt of said command word, said receiving module performs an authentication process on said key portion using successive ones of said sets until either authentication occurs or all of said sets have been used.

27. A method according to claim 23 wherein each set includes at least one corresponding secret feedback mask, and said encryption operation comprises a feedback register pseudorandom number generation operation utilizing said secret feedback mask.

28. A method according to claim 27 wherein said shift register operation is linear.

29. A method of synchronized cryptographic authentication of transmissions from a remote command transmitting unit to a command performing receiving module selectively responsive thereto comprising:

transmitting a command word including a key portion derived from at least one encrypted number generated in said transmitting unit and indicative of a command;

receiving said command word and, in response thereto, comparing a number in said receiving module with a number decrypted from the key portion recovered from said command word, providing an authentication signal based at least in part on identity between said number in said receiving module and said number decrypted from the key portion recovered from said command word, selectively performing the command indicated thereby in response to said authentication signal; and

rendering said receiving module unresponsive, following receipt of one command word, to receipt of an additional command word for a period of time on the order of one-half second, or more.

30. The method according to claim 29 wherein said rendering step comprises providing a waiting period between the conclusion of any operation responsive to receipt of one of said command words and the enabling of said receiving module to be responsive to a subsequently received command word.

31. A method of selectively cryptographically authenticating transmissions, indicative of commands initiated by operating switches, from each of a plurality of transmitting units to a receiving module, comprising:

providing a set of numbers in each one of said transmitting units, each set corresponding to one of said transmitting units and identified by an identification number, each set including at least a pair of secret initial values;

providing in said receiving module the one of said sets corresponding to each of said transmitting units to which said receiving module is to respond.Iadd., the one of said sets having a first and second receiver secret initial value.Iaddend.;

in response to operation of said switches indicating a command other than a lock-related command in one of said transmitting units;

providing a command bit;

generating a random number;

concatenating said random number with a first one of said secret initial values so as to provide a combined word;

performing a first encryption operation on said combined word to provide a first number;

performing a second encryption operation on a second one of said secret initial values to provide a second number;

exclusive ORing a plurality of command bits indicative of said command with the corresponding bits of said second number to provide an altered word;

performing a third encryption operation on the concatenation of said first number with said altered word to provide an encrypted key word;

storing said first and second numbers as first and second pseudorandom numbers for future use in subsequent authentication;

transmitting a command word including said encrypted key word, said command bit, and said identification number;

in response to operation of said switches indicating a lock-related command in one of said transmitting units;

performing a fourth encryption operation on said first number to provide a new first pseudorandom number;

performing a fifth encryption operation on said second number to provide a new second pseudorandom number;

exclusive ORing a plurality of command bits indicative of said lock-related command with the corresponding bits of said new second pseudorandom number to provide a new altered word;

performing a sixth encryption operation on the concatenation of said new first pseudorandom number and said new altered word to provide a new encrypted key word;

storing said new first and second pseudorandom numbers for future use in subsequent authentication in place of said first and second pseudorandom numbers;

transmitting a command word including said new encrypted key word and said identification number;

in said receiver, selectively, in response to receipt of said command word including said command bit;

determining if said receiver has secret initial values related to the received identification number, and if not, terminating all response to said received word, but if so;

performing a first decryption operation on said key word portion of said received command word so as to recover said first number and said altered word;

performing, on said recovered first number, a second decryption operation so as to recover said combined word, comparing said first .Iadd.receiver .Iaddend.secret initial value to a corresponding portion of said recovered combined word and providing a first equal signal only in the event of identity therebetween;

performing a seventh encryption operation on said second .Iadd.receiver .Iaddend.secret initial value to provide said second number, comparing the non-command portion of said recovered altered word with the corresponding portion of said second number and providing a second equal signal only in response to identity therebetween;

then, in response to the absence of either of said first and second equal signals, terminating all further response to said command word;

or otherwise, in response to the presence of said first and second equal signals, comparing the random number portion of said recovered combined word to a random number portion derived from a command word previously received from said transmitter and, in response to identity therebetween, terminating all further response to said command word, but otherwise, (a) storing said random number portion for future use in subsequent synchronization operations and (b) storing said second number and said recovered first number, as first and second pseudorandom numbers for future use in subsequent authentication operations;

in said receiver, selectively, in response to receipt of said command word not including said command bit;

determining if said receiver has .Iadd.first and second receiver .Iaddend.secret initial values related to the received identification number, and if not, terminating all response to said received word, but if so;

performing a third decryption operation on the key word portion of said received command word, so as to recover said new first pseudorandom number and said new altered word;

performing an eighth encryption operation on said first . .pseudorandom number.!. .Iadd.receiver secret initial value .Iaddend.to provide a first . .new.!. .Iadd.receiver .Iaddend.pseudorandom number, and comparing said first . .new.!. .Iadd.receiver .Iaddend.pseudorandom number to said recovered . .new.!. .Iadd.receiver .Iaddend.first pseudorandom number and providing a third equal signal in response to identity therebetween;

performing a ninth encryption operation on said second . .pseudorandom number.!. .Iadd.receiver secret initial value .Iaddend.to provide a second . .new.!. .Iadd.receiver .Iaddend.pseudorandom number and comparing the non-command portion of said recovered new altered word to a corresponding portion of said second . .new.!. .Iadd.receiver .Iaddend.pseudorandom number and providing a fourth equal signal only in response to identity therebetween;

then, in the absence of either of said third or fourth equal signals, terminating all further response to receipt of said command word, but in the presence of both of said third and fourth equal signals, exclusive ORing the command portion of said recovered new altered word with the corresponding portion of said second . .new.!. .Iadd.receiver .Iaddend.pseudorandom number, performing the command indicated by the result thereof, and storing said first . .new.!. .Iadd.receiver .Iaddend.pseudorandom number and said second . .new.!. .Iadd.receiver .Iaddend.pseudorandom number for future use in subsequent authentication operations.

32. A method according to claim 31 wherein said encryption operations comprise linear feedback shift register operations.

33. A method according to claim 31 wherein said first, second and third encryption operations employ the same algorithm.

34. A method according to claim 31 wherein said first and fourth encryption operations employ the same algorithm.

35. A method according to claim 31 wherein said second and fifth encryption operations employ the same algorithm.

36. A method according to claim 31 wherein said third and sixth encryption operations employ the same algorithm.

37. A cryptographically authenticated remote control system in which a command transmitting unit selectively causes a physical effect in a command receiving module rendered responsive thereto;

said transmitting unit comprising;

a source of signals for providing first and second seed signals indicative of respective secret pseudorandom number generator initial values and first, second and third mask signals indicative of respective secret feedback masks, each mask defining a respective feedback polynomial for linear feedback shift register pseudorandom number generation, said initial values and said polynomials being essentially unique to said transmitting unit;

command switches operable to indicate a physical effect which is to be caused by said receiving module; and

first signal processing means responsive to selected operation of said switches indicative of a synchronization command for providing a random signal indicative of a variable random number, for performing a first linear feedback shift register pseudorandom number generation operation, on a combined number consisting of the initial value defined by said first seed signal concatenated with the random number defined by said random signal, a given number of iterations on the order of the degree of said fist polynomial, or more, using the mask defined by said first mask signal, said first polynomial having a degree on the order of the degree of said combined word, for performing a second linear feedback shift register pseudorandom number generation operation, on a second word consisting of the initial value defined by said second seed signal, a fixed number of iterations on the order of the degree of said second polynomial, or more, using the mask defined by said second mask signal, said second polynomial having a degree on the order of the degree of said second initial value, for exclusive ORing a plurality of command bits indicative of said synchronization command with a corresponding plurality of bits of the result of said second generation operation to form an altered word, for storing, for future use in authenticating subsequent transmissions to said receiving module, first and second pseudorandom numbers respectively indicative of the results of said first and second generation operations, for performing a third linear feedback shift register pseudorandom number generation operation, on a word consisting of said first pseudorandom number concatenated with said altered word, a predetermined number of iterations on the order of the degree of said third polynomial, or more, using the mask defined by said third mask signal said third polynomial having a degree on the order of the summation of the degrees of said first pseudorandom number and said altered word, and for transmitting, to said receiving module, a command word signal having the result of said third generation operation as a key portion and including a command bit indicative of said synchronization operation;

said first signal processing means responsive to selected operation of said switches indicative of a lock-related command for performing a fourth linear feedback shift register pseudorandom number generation operation, on said first pseudorandom number, a first determined number of iterations, using the mask defined by said first mask signal, to provide a new first pseudorandom number, for performing a fifth linear feedback shift register pseudorandom number generation operation, an said second pseudorandom number, a second determined number of iterations, using the mask defined by said second mask signal, to provide a new second pseudorandom number, for exclusive ORing a plurality of command bits indicative of said lock-related command with a corresponding plurality of bits of said new second pseudorandom number to form a new altered word, for performing a sixth linear feedback shift register pseudorandom number generation operation, on a word consisting of said new first pseudorandom number concatenated with said new altered word, said predetermined number of iterations, using the mask defined by said third mask signal, for storing said new first and second pseudorandom numbers for future use in authenticating subsequent transmissions to said receiving module, and for transmitting, to said receiving module, a command word signal having the result of said third generation operation as a key portion;

said receiving module comprising

a signal source for providing third and fourth seed signals respectively indicative of said initial values and fourth, fifth and sixth mask signals respectively indicative of said masks; and

second signal processing means for receiving said command word signal and responsive to said command word including said command bit, for performing a first reverse linear feedback shift register pseudorandom number generation operation, on said key portion of said command word signal, said predetermined number of iterations, using the mask defined by said sixth mask signal, for performing a second reverse linear feedback shift register pseudorandom number generation operation, on a portion of the result of said first reverse generation operation corresponding to said combined word, said given number of iterations, using the mask defined by said fourth mask signal, for comparing said initial value defined by said third seed signal with an equivalent portion of the result of said second reverse generation operation and providing a first equal signal only if they are identical, for performing a seventh linear feedback shift register pseudorandom number generation operation on a word consisting of the initial value defined by said fourth seed signal, said fixed number of iterations, using the mask defined by said fifth mask signal, for comparing a portion of the result of said seventh generation operation, corresponding to the unaltered portion of said altered word, with a corresponding portion of the result of said first reverse generation operation and providing a second equal signal only if they are identical, in response to said first and second equal signals, for storing, for subsequent use, the random number portion of the result of said second reverse operation and for comparing said random number portion with a similar random number portion, previously stored for subsequent use in response to prior performances of said second reverse operation, and for selectively storing third and fourth pseudorandom numbers respectively indicative of the result of said second reverse operation and said seventh generation operation, for future use in subsequent authentication of transmissions from said transmitting unit, only if said compared random portions are not equal;

said second signal processing means responsive to said command word signal not including said command bit for performing a third reverse linear feedback shift register pseudorandom number generation operation, on said key portion of said command word signal, said predetermined number of iterations, using the mask defined by said sixth mask signal, to recover said new first pseudorandom number and said new modified word, for performing an eighth linear feedback shift register pseudorandom number generation operation, on said third pseudorandom number, said first determined number of iterations, using the mask defined by said fourth mask signal, to provide a third new pseudorandom number with said third new pseudorandom number and generating a third equal signal only if they are identical, for performing a ninth linear feedback shift register pseudorandom number generation operation, on said fourth pseudorandom number, said second determined number of iterations, using the mask defined by said fifth mask signal, to provide a fourth new pseudorandom number, for comparing the non-command portion of said recovered new altered word with a corresponding portion of said fourth new pseudorandom number and providing a fourth equal signal only if they are identical, and, in response to said first and second equal signals, for storing for future use in subsequent authentication of transmissions from said transmitting unit, said new third and fourth pseudorandom numbers indicative of the results of said eighth and ninth generation operations, for exclusive ORing the command portion of said recovered new altered word with the corresponding portion of said fourth new pseudorandom number to recover said plurality of command bits and for performing said lock-related command.

38. A system according to claim 37 wherein the initial value indicated by said first seed signal is different from the initial value defined by said second seed signal.

39. A system according to claim 37 wherein said polynomials are all different from each other.

40. A system according to claim 37 wherein said fixed number is equal to said given number.

41. A system according to claim 37 wherein said first determined number is different from said second determined number.

42. A system according to claim 37 wherein said feedback polynomials are maximal length feedback polynomials.

43. A system according to claim 37 wherein said first and second determined numbers each vary as a function of a respective pseudorandom event, responsive to each transmission in said transmitting unit and responsive to each reception in said receiving module.

44. A system according to claim 43 wherein said first and second determined numbers are a fraction of said given number and said fixed number, respectively.

45. A method of cryptographically authenticating a transmission from a transmitting unit to a receiving module, comprising:

providing a starting number in said transmitting unit and providing said starting number in said receiving module;

in said transmitting unit;

providing an iteration control signal which changes in a random manner in response to successive transmissions from said transmitting unit;

performing a variable number of iterations of an iterative encryption operation on said starting number, said variable number determined by said iteration control signal;

transmitting a command word derived at least in part from the result of said encryption operation; and

in said receiving module;

receiving said command word;

recovering the result of said encryption operation from said received command word;

providing a second iteration control signal which changes, in the same random manner as said first iteration control signal, in response to successive receptions of command words by said receiving module;

performing a variable number of iterations of said iterative encryption operation on said starting number, said variable number determined by said second iteration control signal;

comparing at least a portion of the result of said encryption operation performed in said receiving module with a corresponding portion of said recovered result; and

providing an authentication signal only if said portion of said encryption operation performed in said receiving module is identical to said corresponding portion of said recovered result.

46. A method according to claim 45 wherein said iteration control signal changes in response to the value of a plurality of bit positions of a random number. .Iadd.

47. A cryptographically authenticated remote control system in which a command transmitting unit selectively causes a physical effect in a command receiving module rendered responsive thereto,

the transmitting unit comprising

a first signal generator for providing a plurality of number signals indicative of respective pseudorandom numbers;

a signal processor for concatenating the plurality of number signals to form a combined word signal indicative of a combined word;

an encrypter for encrypting the combined word signal to form an encrypted combined word signal; and

transmission means for transmitting a command signal including a key portion derived from the encrypted combined word signal; and

the receiving module comprising

reception means for receiving the command signal;

a decrypter for decrypting the key portion of the command signal to recover the combined word signal;

a second signal generator for providing at least one number signal; and

authentication means for providing an authentication signal only if at least a portion of said at least one number signal is identical to a corresponding portion of the recovered combined word signal. .Iaddend..Iadd.48. A system according to claim 47 wherein

said at least one number signal comprises a second plurality of number signals indicative of respective pseudorandom numbers; and

the authentication means comprises means for providing an authentication signal only if at least a portion of each of the second plurality of number signals is identical to a corresponding portion of the recovered combined word signal. .Iaddend..Iadd.49. A system according to claim 47 wherein the encrypter comprises means for performing a linear encryption operation. .Iaddend..Iadd.50. A system according to claim 47 wherein the encrypter comprises means for performing a feedback shift operation. .Iaddend..Iadd.51. A system according to claim 50 wherein the feedback shift operation is linear. .Iaddend..Iadd.52. A system according to claim 51 wherein the linear feedback shift register operation employs a secret feedback mask. .Iaddend..Iadd.53. A system according to claim 50 wherein the linear feedback shift register operation employs a secret feedback mask and the decrypter comprises means for performing a reverse CRC operation employing the same secret feedback mask as the CRC operation. .Iaddend..Iadd.54. A system according to claim 53 wherein the linear feedback shift register operation comprises a number of iterations on the order of the degree of the combined word or more. .Iaddend..Iadd.55. A cryptographically authenticated remote control system in which a command transmitting unit selectively causes a physical effect in a command receiving module rendered responsive thereto, comprising

means for providing a starting number signal in the transmitting unit and for providing the same starting number signal in the receiving module, the starting number signal indicative of a starting number; and

comprising in the transmitting unit

a first signal generator for providing a first iteration control signal which changes in a pseudorandom manner in response to successive transmissions from the transmitting unit;

a first signal processor for iterating a variable number of times an iterative encryption operation on the starting number signal, the variable number determined by the first iteration control signal, and for providing a first resulting signal therefrom;

transmission means for transmitting a command signal derived at least in part from the first resulting signal; and

comprising in the receiving module;

reception means for receiving the command signal;

a signal conditioner for recovering the first resulting signal from the command signal;

a second signal generator for providing a second iteration control signal which changes in the same pseudorandom manner as the first iteration control signal in response to successive receptions of command signals by the receiving module;

a second signal processor for iterating a variable number of times an iterative encryption operation on the starting number signal, the variable number determined by the second iteration control signal, and for providing a second resulting signal therefrom;

comparison means for comparing at least a portion of the first resulting signal with a corresponding portion of the second resulting signal; and

authentication means for providing an authentication signal only if the portion of the first resulting signal is identical to the corresponding

48. portion of the second resulting signal. .Iaddend..Iadd.56. A system according to claim 55 wherein the iterative encryption operation comprises a linear iterative encryption operation. .Iaddend..Iadd.57. A system according to claim 55 wherein the iterative encryption operation comprises a feedback shift register operation. .Iaddend..Iadd.58. A system according to claim 57 wherein the feedback shift register operation is linear. .Iaddend..Iadd.59. A system according to claim 58 wherein the linear feedback shift register operation employs a secret feedback mask. .Iaddend..Iadd.60. A system according to claim 59 wherein the linear feedback shift register operation employs the same secret feedback mask in the transmitting unit as in the receiving module. .Iaddend..Iadd.61. A system according to claim 55 further comprising means for providing a secret initial value signal in the transmitting unit and the same secret initial value signal in the receiving unit;

and further wherein the starting number signal is indicative of a word derived at least in part from the secret initial value signal, and is formed at least in part from a number of iterations of an iterative encryption operation on the order

49. of the degree of the word. .Iaddend..Iadd.62. A system according to claim 55 wherein the variable number is a fraction of the degree of the starting number. .Iaddend..Iadd.63. A system according to claim 55 comprising:

means for providing a second starting number signal in the transmitting unit and for providing the same second starting number signal in the receiving module, the starting number signal indicative of a starting number; and

comprising in the transmitting unit

a third signal generator for providing a third iteration control signal which changes in a pseudorandom fashion in response to successive transmissions from the transmitting unit;

a third signal processor for iterating a changeable number of times an iterative encryption process on the second starting number signal, the changeable number determined by the third iteration control signal, and for providing a third resulting signal therefrom;

transmission means for transmitting the command signal derived at least in part from the third resulting signal; and

comprising in the receiving module

fourth signal conditioning means for recovering the third resulting signal from the command signal;

a fourth signal generator for providing a fourth iteration control signal which changes in the same pseudorandom fashion as the third iteration control signal, in response to successive receptions of command signals by the receiving module;

a fourth signal processor for iterating a changeable number of times an iterative encryption operation on the starting number signal, the variable number determined by the fourth iteration control signal, and for providing a fourth resulting signal therefrom;

comparison means for comparing at least a portion of the third resulting signal with a corresponding protion of the fourth resulting signal; and

authentication means for providing an authentication signal only if the portion of the third resulting signal is identical to the corresponding portion of the fourth resulting signal. .Iaddend..Iadd.64. A system according to claim 63 wherein the variable number is different from the changeable number. .Iaddend..Iadd.65. A system according to claim 63 wherein the pseudorandom manner is different from the pseudorandom fashion. .Iaddend..Iadd.66. A system according to claim 65 wherein the iterative encryption operation is the same as the iterative encryption process. .Iaddend..Iadd.67. A system according to claim 55 wherein the iteration control signal changes in response to the value of a bit position of a changing number. .Iaddend..Iadd.68. A system according to claim 67 wherein the changing number is the starting number. .Iaddend..Iadd.69. A system according to claim 55 wherein the iteration control signal changes in response to the value of a plurality of bit positions of a changing number. .Iaddend..Iadd.70. A system according to claim 69 wherein the changing number is the starting number. .Iaddend..Iadd.71. A cryptographically authenticated remote control system in which any of a plurality of command transmitting units selectively causes a physical effect in a command receiving module rendered responsive thereto, comprising;

transmitter memory for storing a set of numbers in each of the transmitting units, each set corresponding to one of the transmitting units, each set including at least one secret initial value, each set essentially unique to the corresponding unit;

receiver memory for storing in the receiving module the set of numbers for each of the transmitters to which the receiving module is to respond;

transmission means for transmitting to the receiving module from one of the transmitting units a command word including a key portion derived at least in part from an encryption operation performed on the secret initial value; and

authentication means for authenticating the command word received at the receiving module utilizing the numbers in a corresponding set. .Iaddend..Iadd.72. A system according to claim 71 wherein each set includes an identification number and the command word includes the identification number; and

comprising authentication means for authenticating the command word received at the receiving modules utilizing the numbers in a corresponding set only in response to the command word containing an identification number which matches an identification number in one of the sets disposed in the receiving module. .Iaddend..Iadd.73. A system according to claim 72 wherein the receiving module further comprises selection means for performing an authentication process using successive ones of the sets which have an identification number that matches the identification number included in the received command word until either authentication occurs or all of the sets have been used. .Iaddend..Iadd.74. A system according to claim 71 wherein the receiving module further comprises selection means for performing an authentication process on the key portion using successive ones of the sets until either authentication occurs or all of the sets have been used. .Iaddend..Iadd.75. A system according to claim 71 wherein each set includes at least one corresponding secret feedback mask, and the encryption operation comprises a feedback shift register pseudorandom number generation operation using the secret feedback mask. .Iaddend..Iadd.76. A system according to claim 75 wherein the feedback shift register operation is linear. .Iaddend..Iadd.77. A synchronized cryptographic authenticated remote control system in which a command transmitting unit selectively causes a physical effect in a command receiving module rendered responsive thereto comprising;

transmission means for transmitting a command word including a key portion derived from at least one encrypted number generated in the transmitting unit and indicative of a command;

reception means for receiving the command word and, in response thereto, for comparing a number in the receiving module with a number decrypted from the key portion recovered from the command word;

authentication means for providing an authentication signal based at least in part on identity between the number in the receiving module and the number decrypted from the key portion recovered from the command word and for selectively performing the command indicated thereby in response to the authentication signal; and

deactivation means for rendering the receiving module unresponsive, following receipt of one command word, to receipt of an additional command word for a period of time on the order of one-half second, or more. .Iaddend..Iadd.78. A system according to claim 77 wherein the period of time commences on the conclusion of receipt of one of the command words. .Iaddend..Iadd.79. An authentication system for generating an authentication signal upon the identity between two signals comprising

first and second nonvolatile memory;

a starting number stored in each of first and second nonvolatile memory;

a first signal generator for providing a first iteration control signal which changes in a pseudorandom manner in response to successive operations of the authentication system;

a first signal processor coupled to the first nonvolatile memory for iterating a variable number of times an iterative encryption operation on the starting number, the variable number determined by the first iteration control signal, and for providing a first resulting signal therefrom;

reception means for receiving the first resulting signal;

a second signal generator for providing a second iteration control signal which changes in a pseudorandom manner in response to successive receptions of the first resulting signal;

a second signal processor coupled to the second nonvolatile memory for iterating a variable number of times an iterative encryption operation on the starting number, the variable number determined by the second iteration control signal, and for providing a second resulting signal therefrom;

comparison means for comparing at least a portion of the first resulting signal with a portion of the second resulting signal; and

authentication means for providing an authentication signal only if the portion of the first resulting signal is identical to the corresponding portion of the second resulting signal. .Iaddend..Iadd.80. A system according to claim 79 wherein the iterative encryption operation comprises a linear iterative encryption operation. .Iaddend..Iadd.81. A system according to claim 79 wherein the iterative encryption operation comprises a feedback shift register operation. .Iaddend..Iadd.82. A system according to claim 81 wherein the feedback shift register operation is linear. .Iaddend..Iadd.83. A system according to claim 82 wherein the linear feedback shift register operation employs a secret feedback mask. .Iaddend..Iadd.84. A system according to claim 83 wherein the linear feedback shift register operation employs the same secret feedback mask in the transmitting unit as in the receiving module. .Iaddend..Iadd.85. A system according to claim 79 further comprising means for providing a secret initial value signal in the transmitting unit and the same secret initial value signal in the receiving unit; and

further wherein the starting number signal is indicative of a word derived at least in part from the secret initial value signal, and is formed at least in part from a number of iterations of an iterative encryption operation on the order of the degree of the word. .Iaddend..Iadd.86. A system according to claim 79 wherein the variable number is a fraction of the degree of the starting number. .Iaddend..Iadd.87. A remote control lock system comprising

a transmitter having

a first pseudorandom number generator for generating a first pseudorandom number, and a second pseudorandom number generator for generating a second pseudorandom number;

a first signal processor for concatenating the first and second pseudorandom numbers to form a combined word;

a plurality of command switches indicative of respective lock commands;

a second signal processor responsive to the plurality of command switches for generating a combined signal derived at least in part from the combined word and indicative of a lock command; and

transmission means for transmitting the combined signal to a receiver responsive thereto; and

a receiver having

recovery means for recovering the combined word and the lock command from the combined signal;

a third pseudorandom number generator for generating a third pseudorandom number and a fourth pseudorandom number generator for generating a fourth pseudorandom number;

a third signal processor for concatenating the third and fourth pseudorandom numbers to form an authentication word; and

comparison means for comparing the combined word and the authentication word, for generating an authentication signal in response to identity therebetween, and for authorizing the performance of the lock command upon the generation of the authentication signal. .Iaddend..Iadd.88. The system of claim 87 in which the first, second, third, and fourth pseudorandom number generators employ a feedback shift register. .Iaddend..Iadd.89. A remote control lock system comprising a transmitter and a receiver, the transmitter comprising at least one transmitter register having a plurality of bit positions indicative of binary states, wherein the binary state of at least one of the bit positions determines the number of iterations of an iterative encryption algorithm performed on the contents of the transmitter register. .Iaddend..Iadd.90. The system of claim 89 wherein the receiver comprises at least one receiver register having a plurality of bit positions indicative of binary states, wherein the binary state of at least one of the bit positions determines the number of iterations of an iterative encryption algorithm performed on the contents of the receiver register; and

comparison means for comparing the contents of a number derived at least in part from the contents of the transmitter register with a number derived at least in part from the contents of the receiver register to provide an authentication signal upon identity therebetween. .Iaddend..Iadd.91. The system of claim 90 wherein the iterative encryption algorithm is a feedback shift register algorithm. .Iaddend..Iadd.92. The system of claim 91 wherein the feedback shift resister algorithm is linear. .Iaddend..Iadd.93. The system of claim 92 comprising

command switches on the transmitter indicative of a plurality of lock related commands;

a signal processor responsive to the command switches for concatenating any one of the lock related commands with a number derived at least in part from the contents of the transmitter register; and

the comparison means comprising means for communicating a signal representative the lock related command from the transmitter to the receiver, and authorization means for authorizing performance of the lock related command on the condition that at least a portion of the contents of the transmitter register is identical to a corresponding portion of the contents of the receiver register. .Iaddend.