Cryptographic operations employing non-linear share encoding for protecting from external monitoring attacks
Systems and methods for performing cryptographic data processing operations employing non-linear share encoding for protecting from external monitoring attacks. An example method includes: receiving a plurality of shares representing a secret value employed in a cryptographic operation, such that the plurality of shares includes a first share represented by an un-encoded form and a second share represented by an encoded form; producing a transformed form of the second share; and performing the cryptographic operation using the transformed form of the second share.
1. A method, comprising:
generating, by a processor, a plurality of shares, wherein a linear combination of the plurality of shares represents a secret value to be employed in a cryptographic operation, wherein the plurality of shares comprises an un-encoded form of a first share and an encoded form of a second share, wherein the encoded form of the second share is produced by applying a non-linear encoding function to the second share;
producing a transformed form of the second share by applying, to the encoded form of the second share, a non-linear decoding function and a masking operation, wherein the non-linear decoding function reverses the non-linear encoding function;
determining an S-box input value by combining the first share, the transformed form of the second share, and a round key by a linear operation;
feeding the S-box input value to an S-box; and
re-masking a masked output value produced by the S-box.
2. The method of claim 1 , wherein the cryptographic operation is represented by one of an encryption operation based on Advanced Encryption Standard (AES) or a decryption operation based on AES.
3. The method of claim 1 , wherein re-masking the masked output value comprises combining the masked output value, the transformed form of the second share, and an output mask by a linear operation.
4. The method of claim 1 , wherein producing the transformed form of the second share prevents the plurality of shares from simultaneously appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
5. The method of claim 1 , wherein producing the transformed form of the second share prevents the plurality of shares from sequentially appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
6. The method of claim 1 , wherein the non-linear encoding function is implemented by a look-up table.
7. The method of claim 1 , wherein the non-linear decoding function is implemented by a look-up table.
8. A computer-readable non-transitory storage medium comprising executable instructions that, when executed by a computing device, cause the computing device to:
generate a plurality of shares, wherein a linear combination of the plurality of shares represents a secret value to be employed in a cryptographic operation, wherein the plurality of shares comprises an un-encoded form of a first share and an encoded form of a second share, wherein the encoded form of the second share is produced by applying a non-linear encoding function to the second share;
produce a transformed form of the second share by applying, to the encoded form of the second share, a non-linear decoding function and a masking operation, wherein the non-linear decoding function reverses the non-linear encoding function;
determining an S-box input value by combining the first share, the transformed form of the second share, and a round key by a linear operation;
feeding the S-box input value to an S-box; and
re-masking a masked output value produced by the S-box.
9. The computer-readable non-transitory storage medium of claim 8 , wherein the transformed form of the second share is represented by a masked decoded form of the second share.
10. The computer-readable non-transitory storage medium of claim 8 , wherein re-masking the masked output value comprises combining the masked output value, a masked form of the second share, and an output mask by a linear operation.
11. The computer-readable non-transitory storage medium of claim 8 , wherein the cryptographic operation is represented by one of an encryption operation based on Advanced Encryption Standard (AES) or a decryption operation based on AES.
12. The computer-readable non-transitory storage medium of claim 8 , wherein producing the transformed form of the second share prevents the plurality of shares from simultaneously appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
13. The computer-readable non-transitory storage medium of claim 8 , wherein producing the transformed form of the second share prevents the plurality of shares from sequentially appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
14. A system, comprising:
a memory; and
a processor, coupled to the memory, the processor configured to:
generate a plurality of shares, wherein a linear combination of the plurality of shares represents a secret value to be employed in a cryptographic operation, wherein the plurality of shares comprises an un-encoded form of a first share and an encoded form of a second share, wherein the encoded form of the second share is produced by applying a non-linear encoding function to the second share;
produce a transformed form of the second share by applying, to the encoded form of the second share, a non-linear decoding function and a masking operation, wherein the non-linear decoding function reverses the non-linear encoding function;
determine an S-box input value by combining the first share, the transformed form of the second share, and a round key by a linear operation;
feed the S-box input value to an S-box; and
re-mask a masked output value produced by the S-box.
15. The system of claim 14 , wherein re-masking the masked output value comprises combining the masked output value, a masked form of the second share, and an output mask by a linear operation.
16. The system of claim 14 , wherein the transformed form of the second share is represented by a masked decoded form of the second share.
17. The system of claim 14 , wherein the cryptographic operation is represented by one of an encryption operation based on Advanced Encryption Standard (AES) or a decryption operation based on AES.
18. The system of claim 14 , wherein producing the transformed form of the second share prevents the plurality of shares from simultaneously appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
19. The system of claim 14 , wherein producing the transformed form of the second share prevents the plurality of shares from sequentially appearing in an un-encoded form in at least one of: a memory, a register bank, or a communication bus.
20. The system of claim 14 , wherein the non-linear encoding function is implemented by a look-up table.