Reducing leakage of information from cryptographic systems

A computer readable storage memory for storing computer readable instructions, the computer readable instructions providing a key-generating module when executed by one or more processing devices, the computer readable instructions comprising:

• logic configured to modify an original secret key SK using a pairwise independent hash function to produce a modified secret key SK′, the modified secret key SK′ having plural individual components, the pairwise independent hash function being given by HK(r)=ar+b or HK(r)=Ar*B, where a, b, A, B, and r are selected values and HK refers to a hash function that is keyed by a key K;
• logic configured to store a modified secret key collection having members selected from among the modified secret key SK′ and the individual components of the modified secret key SK′ including one or more of selected values a, b, A, B, and r, the modified secret key collection being updated periodically;
• logic configured to receive ciphertext information that includes an encrypted message from a message-sending entity, the encrypted message being created based on a counterpart key;
• and
• logic configured to decrypt the encrypted message by performing plural partial operations using members of the modified secret key collection to generate plural respective partial operation results, the encrypted message being decrypted based on a combination of the plural partial decryption results,
• leakage of meaningful information being reduced by decrypting an encrypted message in plural partial operations using the modified secret key collection.

A computer-implemented decryption system, implemented by computing functionality, for decrypting an encrypted message provided within received ciphertext information, comprising:

• one or more memories operatively coupled to one or more processors providing:
• logic configured to retrieve one or more inputs including ciphertext information that includes the encrypted message from a message-sending entity;
• and
• logic configured to generate plural partial operation results based on modified secure information, the modified secure information being generated using a pairwise independent hash function, the modified secure information having plural members being updated periodically, the pairwise independent hash function being given by HK(r)=ar+b or HK(r)=Ar*B, where a, b, A, B, and r are selected values and HK refers to a hash function that is keyed by a key K,
• the encrypted message being decrypted based on a combination of the plural partial results based on the modified secure information and one or more of selected values a, b, A, B, and r,
• leakage of meaningful information being reduced due to difficulty in assembling meaningful information from separate leakage information leaked from the respective plural partial operation results.