Fast XMSS signature verification and nonce sampling process without signature expansion

1. An apparatus, comprising:

a hardware processor to:

pre-compute at least a portion of a message representative;

generate a first random nonce; and

generate an extended Merkel signature scheme (XMSS) parameter, r, by providing the first random nonce concatenated with an input to a first secure hash algorithm (SHA) hash function, wherein a padding buffer of the parameter r is reduced to comprise the random nonce;

compute the message representative of the input message using a Winternitz One Time Signature (WOTS) scheme that invokes a secure hash algorithm (SHA) hash function based on an input message concatenated with the XMSS parameter, r;

generate a signature to be transmitted in association with the message representative, the signature logic to apply a hash-based signature scheme to a private key to generate the signature comprising a public key; and

determine whether the message representative satisfies a target threshold allocation of computational costs between a cost to generate the signature and a cost to verify the signature.

2. The apparatus of claim 1 , the hardware processor to:

precompute a first intermediate hash value based on a predetermined input sequence, a buffer input, and an index input; and

store the first intermediate hash value in a computer-readable memory.

3. The apparatus of claim 2 , the hardware processor to:

precompute a second intermediate hash value based on the predetermined input sequence input and the buffer input; and

store the second intermediate hash value in the computer-readable memory.

4. The apparatus of claim 3 , the hardware processor to:

use at least one of the first intermediate value or the second intermediate hash value to generate the signature.

5. A computer-implemented method, comprising:

pre-computing at least a portion of a message representative;

generating a first random nonce; and

generating an extended Merkel signature scheme (XMSS) parameter, r, by providing the first random nonce concatenated with an input to a first secure hash algorithm (SHA) hash function, wherein a padding buffer of the parameter r is reduced to comprise the random nonce;

computing the message representative of the input message using a Winternitz One Time Signature (WOTS) scheme that invokes a secure hash algorithm (SHA) hash function based on an input message concatenated with the XMSS parameter, r;

generating a signature to be transmitted in association with the message representative, the signature logic to apply a hash-based signature scheme to a private key to generate the signature comprising a public key; and

determining whether the message representative satisfies a target threshold allocation of computational costs between a cost to generate the signature and a cost to verify the signature.

6. The method of claim 5 , further comprising:

precomputing a first intermediate hash value based on a predetermined input sequence, a buffer input, and an index input; and

storing the first intermediate hash value in a computer-readable memory.

7. The method of claim 6 , further comprising: precomputing a second intermediate hash value based on the predetermined input sequence and the buffer input; and storing the second intermediate hash value in the computer-readable memory.

8. The method of claim 6 , further comprising:

using at least one of the first intermediate value or the second intermediate hash value to generate the signature.

9. A non-transitory computer-readable medium comprising instructions which, when executed by a processor, configure the processor to perform operations, comprising: generating a first random nonce; and

generating an extended Merkel signature scheme (XMSS) parameter, r, by providing the first random nonce concatenated with an input to a first secure hash algorithm (SHA) hash function, wherein a padding buffer of the parameter r is reduced to comprise the random nonce; generating the message representative based on an input message;

computing the message representative of the input message using a Winternitz One Time Signature (WOTS) scheme that invokes a secure hash algorithm (SHA) hash function based on an input message concatenated with the XMSS parameter, r;

generating a signature to be transmitted in association with the message representative, the signature logic to apply a hash-based signature scheme to a private key to generate the signature comprising a public key; and

determining whether the message representative satisfies a target threshold allocation of computational costs between a cost to generate the signature and a cost to verify the signature.

10. The non-transitory computer-readable medium of claim 9 , further comprising instructions which, when executed by the processor, configure the processor to perform operations, comprising: precomputing a first intermediate hash value based on a predetermined input sequence, a buffer input, and an index input; and storing the first intermediate hash value in a computer-readable memory.

11. The non-transitory computer-readable medium of claim 10 , further comprising instructions which, when executed by the processor, configure the processor to perform operations, comprising:

precomputing a second intermediate hash value based on the predetermined input sequence and the buffer input; and

storing the second intermediate hash value in the computer-readable memory.

12. The non-transitory computer-readable medium of claim 11 , further comprising instructions which, when executed by the processor, configure the processor to perform operations, comprising:

using at least one of the first intermediate value or the second intermediate hash value to generate the signature.