Cryptographic token with leak-resistant key derivation

Abstract

Methods and apparatuses for increasing the leak-resistance of cryptographic systems are disclosed. A cryptographic token maintains secret key data based on a top-level key. The token can produce updated secret key data using an update process that makes partial information that might have previously leaked to attackers about the secret key data no longer usefully describe the new updated secret key data. By repeatedly applying the update process, information leaking during cryptographic operations that is collected by attackers rapidly becomes obsolete. Thus, such a system can remain secure against attacks involving analysis of measurements of the device's power consumption, electromagnetic characteristics, or other information leaked during transactions. Transactions with a server can be secured with the token.

Claims

1. A portable cryptographic hardware token for deriving cryptographic authentication codes for securing transactions, said token operable to limit the number of times secret keys are used, thereby providing protection against external monitoring attacks, comprising: (a) a memory configured to store a value for each of a plurality of keys, each of said plurality of keys associated with a different one of a plurality of levels, said plurality of keys comprising a top-level key, a plurality of intermediate-level keys, and a lowest-level key, said plurality of intermediate-level keys comprising at least a second-to-lowest level key, a third-to-lowest level key, and a fourth-to-lowest level key; (b) a processor configured to perform a key update operation, wherein said key update operation comprises communicating with said memory, receiving as an input from said memory a stored value of one of said keys at a particular one of said plurality of levels, and operating on said received key value using a block cipher to generate a value for a key one level below said particular level; and (c) a timer; wherein said processor is further configured to use said key update operation and said timer to periodically derive new key values comprising: (i) at least one new value for said lowest-level key, where said stored value of said second-to-lowest level key is an input to said key update operation; (ii) at least one new value for said second-to-lowest level key, where said stored value of said third-to-lowest level key is an input to said key update operation, and where said at least one new value for said second-to-lowest level key is derived after deriving said at least one new value for said lowest-level key; and (iii) at least one new value for said third-to-lowest level key, where said stored value of said fourth-to-lowest level key is an input to said key update operation, and where said at least one new value for said third-to-lowest level key is derived after deriving said at least one new value for said second-to-lowest level key; and wherein said token is operable to secure a transaction with a server based on a value derived from said at least one new value for said lowest-level key.

2. The portable cryptographic hardware token of claim 1 having a key index value produced using said timer.

3. The portable cryptographic hardware token of claim 1, where said value derived from said at least one new value for said lowest-level key is produced by encryption.

4. The portable cryptographic hardware token of claim 1, where said value derived from said at least one new value for said lowest-level key is produced by hashing.

5. A system comprising the portable cryptographic hardware token of claim 1 in combination with said a server, wherein said server is configured to authenticate said token by: (a) obtaining a candidate key index value for said token; (b) obtaining said token's top-level key value; (c) deriving a server-side second-to-top level key value, corresponding to said candidate key index value, by performing a server-side key update operation, where said token's top-level key value is an input to said server-side key update operation; (d) deriving a succession of server-side key values, including a server-side lowest-level key value, by performing a succession of server-side key update operations, where each of said succession of server-side key values is associated with a different one of a plurality of server-side levels, and where each server-side key value for a particular server-side level above said lowest-level is an input to a corresponding one of said succession of server-side key update operations for deriving a server-side key value one level below said particular server-side level; (e) using a value derived from said server-side lowest-level key value during an attempt to authenticate said token; and (f) if said attempt to authenticate said token fails, repeating (c) through (e) with another candidate key index value.

6. The system of claim 5, wherein said server is further configured to obtain said candidate key index value directly from said token.

7. The system of claim 5, wherein said server is further configured to obtain said candidate key index value indirectly.

8. A method for deriving cryptographic authentication codes in a portable cryptographic hardware token for securing transactions, where said method limits the number of times secret keys are used, thereby providing protection against external monitoring attacks, comprising: (a) storing in a memory a value for each of a plurality of keys, each of said plurality of keys associated with a different one of a plurality of levels, said plurality of keys comprising a top-level key, a plurality of intermediate-level keys, and a lowest-level key, said plurality of intermediate-level keys comprising at least a second-to-lowest level key, a third-to-lowest level key, and a fourth-to-lowest level key; (b) performing a key update operation in a processor configured to communicate with said memory, wherein said key update operation comprises receiving as an input from said memory a stored value of one of said keys at a particular one of said plurality of levels, and operating on said received value in said processor using a block cipher to generate a value for a key one level below said particular level; (c) periodically deriving new key values using said key update operation and a timer, said periodically deriving comprising: (i) deriving at least one new value for said lowest-level key where said stored value of said second-to-lowest level key is an input to said key update operation; (ii) deriving at least one new value for said second-to-lowest level key where said stored value of said third-to-lowest level key is an input to said key update operation, and where said at least one new value for said second-to- lowest level key is derived after deriving said at least one new value for said lowest-level key; (iii) deriving at least one new value for said third-to-lowest level key where said value of said fourth-to-lowest level key is an input to said key update operation, and where said at least one new value for said third-to-lowest level key is derived after deriving said at least one new value for said second-to-lowest level key; and (d) deriving a value from said at least one new value for said lowest-level key for securing a transaction with a server.

9. The method of claim 8, having a key index value produced using said timer.

10. The method of claim 8, where said value derived from said at least one new value for said lowest-level key is produced by encryption.

11. The method of claim 8, where said value derived from said at least one new value for said lowest-level key is produced by hashing.

12. The method of claim 8, further comprising: authenticating said token by said server when securing a transaction with said server by: (a) obtaining a candidate key index value for said token; (b) obtaining said token's top-level key value; (c) deriving a server-side second-to-top level key value corresponding to said candidate key index value, by performing a server-side key update operation, where said token's top-level key value is an input to said server-side key update operation; (d) deriving a succession of server-side key values, including a server-side lowest-level key value, by performing a succession of server-side key update operations, where each of said succession of server-side key values is associated with a different one of a plurality of server-side levels, and where each server-side key value for a particular server-side level above said lowest-level is an input to a corresponding one of said succession of server-side key update operations for deriving a server-side key value one level below said particular server-side key level; (e) attempting to authenticate said token using a value derived from said server-side lowest-level key value; and (f) if said attempt to authenticate said token fails, repeating steps (c) through (e) with another candidate key index value.

13. The method of claim 12, wherein said server obtains said candidate key index value directly from said token.

14. The method of claim 12, where said server obtains said candidate key index value indirectly.

15. A method of deriving cryptographic authentication codes to secure transactions between a user of a hardware token and a server while providing protection against external monitoring attacks in said token, said token including a memory containing a plurality of key values from a top-level to a lowest-level, where said number of levels is at least four, comprising: in said token, (a) using a timer to update a key index value; (b) performing at least one key update operation based on said key index value to update at least a portion of said memory, where: (i) each key update operation in said at least one key update operation includes a block cipher operation; (ii) each key update operation in said at least one key update operation uses a parent key value as an input to derive a child key value at a level below said parent key value, where at least one child key value corresponds to the lowest-level key value; and (iii) only the key values affected by a change in said key index value are updated; and (c) deriving a value from said lowest-level key value to secure a transaction with a server.

16. The method of claim 15 where said server is configured to authenticate said token by: (a) obtaining a candidate key index value for said token; (b) obtaining a top-level key value for said token; (c) deriving a second-to-top-level key value, corresponding to said candidate value, by performing at least one server-side key update operation, where said top-level key value is an input to said server-side key update operation; (d) deriving a succession of child key values by performing a succession of server-side key update operations to derive a lowest-level server key value, where a parent key value is an input to each of said server-side key update operations deriving said succession child key values; (e) using a value derived from said lowest-level server key value during an attempt to authenticate said token; and (f) if said attempt to authenticate said token fails, repeating said steps (c) through (e) with one or more new candidate values.

17. The method of claim 15 where said token's key index value is produced using said timer.

18. The method of claim 15 where said value derived from said lowest-level key value is produced by encrypting.

19. The method of claim 15 where said value derived from said lowest-level key value is produced by hashing.

20. The method of claim 16 where said candidate key index value is obtained directly from said token.

21. The method of claim 16 where said candidate key index value is obtained indirectly.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows an exemplary embodiment of a key update process through a series of transactions.

(2) FIG. 2 shows an exemplary client-side indexed key update process.

(3) FIG. 3 shows an exemplary server process for deriving a transaction key from a key index and base key.

(4) FIG. 4 shows exemplary embodiments of four state transformation operations.

DETAILED DESCRIPTION OF THE INVENTION

(5) Indexed Key Management

(6) The techniques disclosed herein can enable parties to perform cryptographic operations with increased security against external monitoring attacks. Although exemplary embodiments are described involving two parties, a “client” and a “server”, the terms “client” and “server” are chosen for convenience and might not necessarily correspond directly to any particular role in a system design. For example, the client could be a smartcard, and the server could be a mainframe computer, or vice versa. Furthermore, although most cryptographic operations involve two parties (e.g., one at the client and one at the server), the techniques can, of course, be applied in environments involving only one party (such as in secure memory or storage systems in which both client and server are under a single party's control or are combined in a single device) or in environments involving more than two parties and/or devices.

(7) In an exemplary embodiment, the client is initialized with a secret key K.sub.0 for a symmetric cryptosystem, where K.sub.0 is also known to (or derivable by) the server. The key K.sub.0 is usually (but not necessarily) specific to a particular client device or party. The client also has a (typically non-secret) index or transaction counter C, which may be initialized to zero. An additional parameter is an index depth D. The value of D may also be non-secret, and (for example) may be client-specific or may be a system-wide global constant. The value of D determines the cycle length of the key update process.

(8) FIG. 1 shows an exemplary sequence of client device secret state values usable to perform a series of transactions, typically (but not necessarily) using one state per transaction. (The client process used to produce the sequence will be described with respect to FIG. 2 and the corresponding server process will be described with respect to FIG. 3.) A state's secret value typically, but not necessarily, includes a secret session key; therefore, as a matter of convenience, the secret value will be denoted by K and the term “secret value” may be used somewhat interchangeably with “key.” Nevertheless, those skilled in the art will appreciate that they may be different in the general case. Also for clarity of exposition, the figure is drawn showing an exemplary key update process with D=5, meaning that five levels of key values are present. However, there is no specific limitation on D, and those skilled in the art will readily understand how the general principles underlying the exemplary embodiment can be used for other such cycle lengths. Indeed, commercially deployed systems would normally use larger values for D.

(9) Each of the boxes in the figure represents a value of the secret value (K.sub.C). Thus, multiple dots in a box represent different states sharing the same secret value K.sub.C. The top row (row 0) of the figure contains one box, which corresponds to the initial state K.sub.0 110 as well as subsequent states K.sub.30 140 and K.sub.60 170, all of which share the same secret value K.sub.C. The next row (row 1) contains two boxes, the left of which corresponds to a trio of states (K.sub.1 111, K.sub.15, and K.sub.29) sharing the same secret value, and the right box in the second row corresponds to a second trio of states (K.sub.31, K.sub.45, and K.sub.59) sharing yet another secret value. Similarly, row 2 contains four boxes, representing a total of twelve states of which 4 trios each share among themselves the same secret value. More generally, in this exemplary embodiment, row N (where N<D−1) contains 2.sup.N boxes (or unique secret values) and 3(2.sup.N) states, and the last row (N=D−1) contains 2.sup.N boxes and 2.sup.N states. The thicker (curved) path diagrams the process by which the states are updated, starting from the initial state 110 and continuing through to the final state 170. As the states are updated, counter C is also updated (by one for each update).

(10) The exemplary state update processes involve two functions (F.sub.A and F.sub.B), and their inverses (F.sub.A.sup.−1 and F.sub.B.sup.−1), for a total of four functions. At step 100, the client is initialized or personalized with a starting counter C=0 and a starting state having a starting secret value K.sub.C=K.sub.0. At step 110, the device performs the first transaction, using K.sub.C (or a key derived from K.sub.C). The key can be used in virtually any symmetric cryptographic transaction. (For example, such a transaction could involve, without limitation, computing or verifying a MAC (Message Authentication Code) on a message, encrypting or decrypting a message, producing a pseudorandom challenge value, deriving a key, etc. Examples of messages include, without limitation, data specifying the amounts of funds transfer operations, e-mail messages, challenge/response authentication data, parameter update authorizations, code updates, audio messages, digitized images, etc.)

(11) After step 110, the client device's secret value K.sub.C is updated by applying the function F.sub.A and the counter C is incremented, i.e. by performing C←C+1 and K.sub.C←F.sub.A(K.sub.C). (Thus, at step 111, C=1 and K.sub.C=F.sub.A(K.sub.0).). The updated value of K.sub.C is used to perform a transaction at step 111. After step 111, C is incremented again and F.sub.A is again applied to K.sub.C, i.e. by performing C←C+1 and K.sub.C=.sub.2←F.sub.A(K.sub.C), yielding the secret key used at step 112. The same pair of operations (C←C+1 and K.sub.C←F.sub.A(K.sub.C) are similarly applied between steps 112 and 113, and between steps 113 and 114.

(12) The transaction at step 115 should use the same value of K.sub.C as did the transaction at step 113, since steps 113 and 115 are shown in the same box. Thus, after the transaction at step 114 the update process is performed by computing C←C+1 (yielding C=5) and K.sub.C=5←F.sub.A.sup.−1(K.sub.C). Note that K.sub.C=5=F.sub.A.sup.−1(K.sub.C=4)=F.sub.A.sup.−1(F.sub.A(K.sub.C=3))=K.sub.C=3. Thus, the value of K.sub.C used at step 115 is the same as the value used at step 113. After the transaction at step 115, K.sub.C is updated using function K.sub.B by incrementing C and computing K.sub.C=6←F.sub.B(K.sub.C). After the transaction at step 116, the secret value for transaction 117 is computed by applying the function F.sub.B.sup.−1 to K.sub.C.

(13) The update process operates such that after each transaction, a key state update process is performed. The key update involves incrementing C and applying one of the functions F.sub.A, F.sub.B, F.sub.A.sup.−1, or F.sub.B.sup.−1 to the state K.sub.C. The use of invertable functions allows a first state and a second state to share the same secret value, where the first state precedes entry into a child (lower level) box from a parent (upper level) box, and the second state is created by reentry into the parent box from the child box. Further, the multiplicity of functions (e.g., F.sub.A and F.sub.B in the exemplary embodiment) allows the creation of multiple child boxes from each parent box and, hence, a large number of allowable states before the sequence is exhausted (e.g., at end state 190). In going from one particular state to another particular state, the choice of functions (e.g., in the exemplary embodiment of FIG. 1, whether to use F.sub.A, F.sub.B, F.sub.A.sup.−1, or F.sub.B.sup.−1) depends on the current direction and location of the two particular states. In particular, referring again to the exemplary embodiment shown in FIG. 1, when moving downward from a parent box to the left-hand child, such as between steps 112 and 113, F.sub.A is applied by computing K.sub.C←F.sub.A(K.sub.C). Further, when moving downward from a parent box to the right-hand child, such as between steps 115 and 116, F.sub.B is applied. Still further, when moving from a left-hand child to its parent, such as between steps 114 and 115, F.sub.A−.sup.1 is applied by computing K.sub.C←F.sub.A.sup.−1(K.sub.C). Finally, when moving from a right-hand child to its parent, such as between steps 116 and 117, F.sub.B.sup.−1 is applied. More generally, the choice of which function to apply in any particular state transition can be determined solely as a function of C, so the client need not maintain any information beyond its current state and its current counter value. This will be explained in greater detail in the section “Client Side Indexed Key Update,” below, in the context of the exemplary embodiment of FIG. 1.

(14) Eventually, the client may reach a point at which the entire table has been traversed. For example, the end of the process of FIG. 1 is reached at step 170, where C=60. After this transaction (or at an earlier point if the table length exceeds the maximum number of transactions allowed by the system), the client device could, and might typically, disable itself, such as by deleting its internal secrets. However, other actions may be preferable in some cases (e.g., by repeating back to step 110, entering a state in which rekeying is required, etc.). In the illustrated exemplary embodiment, the number of transactions that can be performed before the end of the process occurs is equal to

(15) $2^{D-1}+\underset{i=0}{\overset{D-2}{.Math.}}3\left(2^i\right)=2^{D-1}+3\left(2^{D-1}-1\right)=2^{D+1}-3.$

(16) (In the example with D=5, there can thus be 2.sup.6−3=61 transactions.) By choosing a sufficiently large value for D, a system designer can make the maximum number of transactions so large that the “end” will never be reached. For example, D=39 will allow more than 1 trillion (10.sup.12) transactions without repeating.

(17) Client-Side Indexed Key Update

(18) For the exemplary embodiment of FIG. 1, the processes of incrementing C and choosing which function to apply (F.sub.A, F.sub.B, F.sub.A.sup.−1, or F.sub.B.sup.−1) can be performed by the client as shown in FIG. 2. At step 210, the client device verifies that C is valid, for example by confirming that C is non-negative and that C is less than 2.sup.D+1−3. (If C is invalid, then the transaction fails or other appropriate action is taken.) Since the client maintains C&P internally, step 210 can be omitted if the client is confident that C is valid. At step 220, the device initializes temporary depth and counter variables, N and V, with the values stored in D and C, respectively.

(19) At step 230, the device tests whether the variable V is equal to the quantity 2.sup.N−3. If equal, function F.sub.A−.sup.1 should be applied, and processing proceeds to step 235 where the device increments C and updates K.sub.C by computing K.sub.C←F.sub.A−.sup.1(K.sub.C). Otherwise, at step 240, the device tests whether the variable V is equal to the quantity 2(2.sup.N−2). If equal, function F.sub.B.sup.−1 should be applied, and processing proceeds to step 245 where the device increments C and updates K.sub.C by computing K.sub.C←F.sub.B.sup.−1(K.sub.C). Otherwise, at step 250, the device tests whether the variable V is equal to zero. If equal, function F.sub.A should be applied, and processing proceeds to step 255 where the device increments C and updates K.sub.C by computing K.sub.C←F.sub.A(K.sub.C). Otherwise, at step 260, the device tests whether the variable V is equal to the quantity 2.sup.N−2. If equal, function F.sub.B should be applied, and processing proceeds to step 265 where the device increments C and updates K.sub.C by computing K.sub.C←F.sub.B(K.sub.C) by

(20) At step 270, the device checks whether the value of V exceeds 2.sup.N−2. If not, processing proceeds directly to step 280. If V is larger than 2.sup.N−2, the value of V is diminished by 2.sup.N−2 and processing proceeds to step 280. At step 280, V and N are each decremented, then processing proceeds to step 230.

(21) After performing a state update function at step 235, step 245, step 255, or step 265, the client process terminates successfully at step 290. After the successful conclusion of the process of FIG. 2, the secret value K.sub.C is used to perform a cryptographic transaction (or derive a key used to perform the transaction, for example by hashing or encrypting K.sub.C, appending a salt or nonce, etc.).

(22) Note that each iteration of the process of FIG. 2 corresponds to moving down one level in the drawing of FIG. 1, until the correct update operation is determined. Thus, the number of iterations of the loop cannot exceed D. Except for the key update functions (in the exemplary embodiment, F.sub.A, F.sub.B, F.sub.A.sup.−1 or F.sub.B.sup.−1), implementations of the function selection process need not be at all leak resistant; the function selection process of FIG. 2, its input value (i.e., C), and the choice of update functions need not be secret. Finally, as mentioned earlier and illustrated above in the case of the exemplary embodiment, the selection of which function to apply in any particular state transition can be characterized solely as a function of C, so the client need not maintain any information beyond its current state and its current counter value.

(23) Server-Side Indexed Key Derivation

(24) FIG. 3 shows an exemplary server-side process compatible with the exemplary client-side process of FIG. 2. Prior to commencing the process of FIG. 3, the server obtains; the client's counter value C (typically by receiving C from the client device via a digital I/O interface), which is used as a key index. (In this exemplary embodiment, a transaction counter is used as a key index, but alternate embodiments can use a different value or representation of the key index.)

(25) The server also obtains the client's base key value K.sub.0 (for example, by retrieving K.sub.0) from the server's memory, by cryptographically deriving K.sub.0 using other secret keys or secret algorithms, by obtaining K.sub.0, from a third party such as a key server, etc.). The server also knows or obtains D. At step 310, the server validates C to reject any possible invalid values of C. At step 320, the temporary variables N, V, and K are initialized with the values of D, C, and K.sub.0, respectively. At step 330, the server checks; whether the value of V is equal to zero. If so, the value of K equals the client's current secret (K.sub.C), and the process concludes at step 390. Otherwise, processing continues to step 340 where the server tests whether V equals the value 2.sup.N−2. If so, the value of K equals the client's current secret (K.sub.C), and the process concludes at step 390. Otherwise, processing continues to step 350 where the server tests whether V equals the value 2(2.sup.N−2). If so, the value of K equals the client's current secret (K.sub.C), and the process concludes at step 390. Otherwise, at step 360, the server checks whether V is larger than 2.sup.N−2. If not, processing continues at step 370 where V is decremented, K is updated by applying F.sub.A (i.e., K←F.sub.A(K)), and N is decremented. If the test at step 360 reveals that V is larger than 2.sup.N−2, processing continues to step 380, where the value 2.sup.N−1 is subtracted from V, K is updated by applying F.sub.B (i.e., K←F.sub.B(K)), and N is decremented. After either step 370 or step 380, processing continues at step 330. Processing continues until step 330, step 340, or step 350 indicates completion. When the process of FIG. 3 completes at step 390, the value contained in the variable K is equal to the value of K.sub.C at the client for counter value C. The client and server can thus use K=K.sub.C to secure a cryptographic transaction. If an error or error-causing attack occurs, K and K.sub.C will differ and the cryptographic transaction should fail.

(26) State Transformation Operations

(27) The above discussion involved the exemplary cryptographic operations F.sub.A and F.sub.B, and their inverses F.sub.A.sup.−1 and F.sub.B.sup.−1, which will now be described in greater detail. A variety of such functions can be used, and the most appropriate form for these functions depends on the requirements and characteristics of the system.

(28) In the exemplary functions shown in FIG. 4, the input and output of each function is 128-bits in size. For the function F.sub.A, input state 400 is divided into a left half 405 and right half 410, which are each 64 bits. The right half is provided as the input to a DES operation 415, which encrypts its input (right half 410) using a fixed key K.sub.A1. The DES operation is only used as a nonlinear transformation that decreases or eliminates the usefulness of partial information an attacker might have about the input. Consequently, the key K.sub.A1 does not need to be secret and can be a published constant. At operation 420, the result of the DES encryption is XORed onto the left half of the input. The result of the XOR becomes both the result left half 435 and the input to a second DES operation 425. The second DES operation uses key K.sub.A2 to produce a result which, at operation 430, is XORed with the input right half 410. The XOR result becomes the result right half 440. The result left half 435 and result right half 440 are combined to produce the final result 445.

(29) The structure of the function F.sub.B can be essentially identical, except that different keys are used. In particular, the first DES operation 455 encrypts the right half of input 450 using key K.sub.B1, and DES operation 460 encrypts the XOR of the left half and the first DES result using key K.sub.B2. As with F.sub.A, the result left half 465 and right half 468 are combined to produce the final result 470.

(30) The function F.sub.A.sup.−1 (the inverse of F.sub.A) is computed using similar functions as F.sub.A but in the opposite order. The input 475 is divided into a left half 476 and right half 477. At DES operation 478, the left half 476 is encrypted using the DES key K.sub.A2, and the result is XORed with the right half 477. The XOR result becomes the result right half 481 and is used as the input to DES operation 479 which encrypts using the key K.sub.A1. The result of the second DES operation 479 is XORed with the input left half 476 to produce the result left half 480. Finally, the result left half 480 and right half 481 are combined to produce the final result 482. The function F.sub.B.sup.−1 is similar to F.sub.A.sup.−1 except that the input 485 is transformed into output 490 using keys K.sub.B2 and K.sub.B1 instead of K.sub.A2 and K.sub.A1.

(31) The primary objective of the functions F.sub.A, F.sub.B, F.sub.A.sup.−1, and F.sub.B.sup.−1 is to destroy the usefulness of partial information about the input that might have been obtained by an attacker. For example, the DES operations used in the exemplary function F.sub.A shown in FIG. 4 make the function extremely nonlinear. An attacker with statistical information about the value of each of the 128 input bits (such as a guess of the bit's value that is correct with probability slightly greater than 0.5) will have statistical information about the input to the first DES operation 415. However, the DES output will be effectively randomized—even though attackers might know the DES key K.sub.A1. The two DES operations in each update process “mix” the entire input state.

(32) Thus partial statistical information about individual DES input bits does not provide useful statistical information about the DES output bits, provided that attackers never gain enough information to be able to guess the transformation operation entire input.

Other Embodiments

(33) FIG. 4 shows just one exemplary set of functions for F.sub.A and F.sub.B; many other variant or alternate designs can be used. For example, functions produced using additional rounds can be used (for example, a 3-round Luby-Rack off block cipher). More generally, encryption and decryption using any block cipher can be used for the functions and their inverses. The basic functions used to construct the update function only need to prevent partial information leaked about the input from providing useful information about the output, so the functions do not necessarily need to be cryptographically hard to invert. For example, reduced-round variants of DES can be used. Further, although F.sub.A and F.sub.B in FIG. 4 have similar structure, this is not necessary. F.sub.A and F.sub.B can also be selected or modified depending on the state position (for example by using different functions or modified functions for each of the D levels):

(34) Other types of functions can be used for F.sub.A and F.sub.B. For example, if the input state is an odd value between 0 and 2.sup.B, F.sub.A and F.sub.B could be implemented using multiplication modulo 2.sup.B with odd constants and the inverse functions could be implemented using multiplication with the constants' inverses also mod 2.sup.B. (Of course, other operations such as multiplication with prime moduluses can also be used.) The foregoing are provided as examples only; one of ordinary skill in the art will appreciate that a wide variety of other functions exist that can be used to implement functions F.sub.A, F.sub.B, F.sub.A.sup.−1, and F.sub.B.sup.−1.

(35) For additional leak resistance, larger states can be used, for example a 256-bit state can be implemented by using four 64-bit blocks and using four (or more) DES operations to update the state, or by using two (or more) applications of a 128-bit hash function.

(36) In alternate embodiments, other key update processes can be used. For example, by using more than two update functions (and their inverses), each parent state can have more than 2 child states. In fact, parents can have any number of child states, although as the number of child states increases, the number of cryptographic operations involving the parent state value, and the number of states sharing the same secret key, also increase; thus potentially increasing attackers' opportunity to attack the system.

(37) The type of state updating process illustratively described with respect to FIG. 1 is advantageous because it uses very little memory and very little processing overhead, while the maximum number of transactions using the same secret value is small. (The more often such secret values are used, the greater the likelihood of successful external monitoring attack.) Therefore, in an alternate embodiment, transactions are performed using only the states at the lowest level of the diagram (which are produced only once), so that secret values are not reused. This reduces the opportunity for information to leak, but increases the processing overhead per transaction to an average of about four updates. (Also, the amount of time per transaction is not exact, since the number of update processes ranges from 2 to 2D−2. However, this is often not a problem, since few applications will ever need values of D larger than about 40 and many devices can perform thousands of cryptographic operations per second.)

(38) In yet another alternate embodiment, the client can cache a value at each vertical level or row. By caching higher-up values, it is not necessary to perform inverse operations, but slightly more memory is required. In such an embodiment, an average of two applications of F.sub.A or F.sub.B (which, in such an embodiment, do not need to have easy inverse functions) are required per operation if only bottom-level (single-use) states are used for transactions. A diagram of the state update processes for such an implementation would resemble a hash tree. For implementations requiring constant-time or more predictable performance, the additional processing time available during operations requiring only a single application of F.sub.A or F.sub.B can be used to precompute values that will be needed in the future, and thereby limit the execution time to two F.sub.A or F.sub.B operations per transaction.

(39) In still other embodiments, the key index used by the server can be a value other than a transaction counter, since all the server requires is information sufficient to derive the current transaction key from the root key.

(40) In some applications, C can be incremented periodically (e.g., if C is driven by a timer) or by some event other than transactions being performed. In such embodiments, if the client (or server) fails to correctly update C and derive the corresponding updated key, the transaction will fail. If the first value of C that is tried by the client (or server) fails, other likely session key values (such as those with close values of C) can be tried. (Of course, if the client and server versions of C diverge too far, the transaction will not proceed.) While the key index (e.g., C) is normally exchanged explicitly, in cases such as this the server might be able to guess or obtain C indirectly.

(41) If both the client and server need to be secured against external monitoring attacks, the transaction can be performed using the larger of the two parties' transaction counters C. In particular, the client and server can exchange counter values, and (if the counters are not equal) each device can set its counter value to equal the larger of its value and the received value. The device with the lower value updates its secret to derive the appropriate transaction key. This update can be implemented by applying a combination of the usual update functions and their inverses. (For example, referring to the technique exemplified in FIG. 1, a client at state 117 could skip to state 136 by applying F.sub.A.sup.−1 twice then applying F.sub.B three times. In general, the total number of update functions required should be less than 2D−1. This “fast-forward” capability maintains the property that no state is used or derived more than a finite number of—here three—times.) In devices implementing this capability, care should be taken to assure that the system will not fail if a large, incorrect value of C is encountered. (For example, devices can reject excessively large jumps in C or can require additional cryptographic authentication, for example of the most significant bits of C.) Such a protocol can be used to agree on a transaction counter for embodiments involving more than two parties in cryptographic transactions.

(42) Finally, the actual value used for the transaction key can be the value produced from the transformation function, or a value derived from the transformation result can be used. For example, the transformation result can be encrypted or hashed to produce the session key. A hashing step can help to limit the number of operations performed with any given key and thus help to limit the amount of information about the key that can leak to attackers. Alternatively or additionally, additional hashing operations can be performed periodically during the use of the session key, or fresh session keys can be required periodically.

(43) To observe the largest possible number of transactions with a given secret key, an attacker might try to reset a target device before the device's memory can be updated with the new value of K.sub.C (e.g., during or immediately after the computation of F.sub.A or F.sub.B). However, such a reset does not necessarily mean an attack is in progress, since resets can occur during the normal operation of many systems. (For example, power can be lost if a smartcard is removed during a transaction.) Therefore, in a preferred embodiment, a failure counter stored in nonvolatile memory is updated prior to each update process. Before the update begins, the counter is tested to determine whether the number of sequential failures exceeds a maximum value and, if not, the transaction proceeds normally. Once the new value of K.sub.C has been computed and safely written to memory and C has been incremented, the failure counter is reset. The probability that the counter threshold will be exceeded during normal operation of the device (i.e., when no attack is in progress) will be small, particularly if the update process is rapid.

(44) The exemplary key update process described with regard to FIGS. 1, 2, and 3 assures that no secret key value is ever used in more than a relatively small number of (here, three) transactions. Attackers thus have the opportunity to collect information about the secret state during the three transactions themselves, the three key update processes that produce the transaction keys, and the three update processes that transform the transaction keys after the transactions. Implementers should make sure that the total amount of information about the secrets that leaks to attackers during these processes is not enough to compromise the secret state. When characterizing a design, it is often useful to determine or estimate the maximum amount of information that can leak from each transaction without compromising security.

(45) Other Considerations

(46) Cryptographic operations should normally be checked to ensure that incorrect computations do not compromise keys or enable other attacks. Cryptographic implementations of the techniques disclosed herein can be combined with error-detection and/or error-correction logic to ensure that cryptographic operations are performed correctly. For example, a simple and effective technique is to perform cryptographic operations twice, ideally using two independent hardware processors and implementations, with a comparator to verify that both produce identical results. If the results produced by the two units do not match, the comparator will prevent either result from being used. In situations where security is more important than reliability, the comparator can make the device self-destruct if serious errors occur. For example, the comparator can cause a self-destruct if two defective DES operations occur sequentially or if five defective DES operations occur during the lifetime of the device. In some cryptosystems, redundancy is not necessary. For example, with RSA, self-checking functions can be incorporated into the cryptosystem implementation itself or verification can be performed after the operations.

(47) Self-diagnostic functions such as a POST (power-on-self-test) should also be incorporated to verify that cryptographic functions have not been damaged. In some smartcards and other devices, the ATR (answer-to-reset) is provided before a comprehensive self-test can be completed. In such cases, the self-test can be deferred until the first transaction or until a sufficient idle period. For example, a flag indicating successful POST completion can be set upon initialization. While the card is waiting for a command from the host system, it can attempt the POST. Any I/O received during the POST will cause an interrupt, which will cancel the POST (leaving the POST-completed flag at zero). If any cryptographic function is called, the device will check the POST flag and (if it is not set) perform the POST first.

(48) Conclusions

(49) This patent encompasses a family of related techniques that enable the construction of devices that are significantly more resistant to attack than devices of similar cost and complexity that do not use the techniques disclosed herein. In addition, multiple security techniques might be required to make a system secure; and leak resistance can be used in conjunction with other security methods or countermeasures.

(50) As those skilled in the art will appreciate, the techniques described above are not limited to particular host environments or form factors. Rather, they can be used in a wide variety of applications, including without limitation: cryptographic smartcards of all kinds including without limitation smartcards substantially compliant with ISO 7816-1, ISO 7816-2, and ISO 7816-3 (“ISO 7816-compliant smartcards”); contactless and proximity-based smartcards and cryptographic tokens; stored value cards and systems; cryptographically secured credit and debit cards; customer loyalty cards and systems; cryptographically authenticated credit cards; cryptographic accelerators; gambling and wagering systems; secure cryptographic chips; tamper-resistant microprocessors; software programs (including without limitation programs for use on personal computers, servers, etc. and programs that can be loaded onto or embedded within cryptographic devices); key management devices; banking key management systems; secure web servers; electronic payment systems; micropayment systems and meters; prepaid telephone cards; cryptographic identification cards and other identity verification systems; systems for electronic funds transfer; automatic teller machines; point of sale terminals; certificate issuance systems; electronic badges; door entry systems; physical locks of all kinds using cryptographic keys; systems for decrypting television signals (including, without limitation broadcast television, satellite television, and cable television); systems for decrypting enciphered music and other audio content (including music distributed over computer networks); systems for protecting video signals of all kinds; intellectual property protection and copy protection systems (such as those used to prevent unauthorized copying or use of movies, audio content, computer programs, video games, images, text, databases, etc.); cellular telephone scrambling and authentication systems (including telephone authentication smartcards); secure telephones (including key storage devices for such telephones); cryptographic PCMCIA cards; portable cryptographic tokens; and cryptographic data auditing systems.

(51) All of the foregoing illustrates exemplary embodiments and applications from which related variations, enhancements and modifications will be apparent without departing from the spirit and scope of those particular techniques disclosed herein. Therefore, the invention(s) should not be limited to the foregoing disclosure, but rather construed by the claims appended hereto.