TY - GEN

T1 - Improving the security of MACs via randomized message preprocessing

AU - Dodis, Yevgeniy

AU - Pietrzak, Krzysztof

PY - 2007

Y1 - 2007

N2 - "Hash then encrypt" is an approach to message authentication, where first the message is hashed down using an ε-universal hash function, and then the resulting k-bit value is encrypted, say with a block-cipher. The security of this scheme is proportional to εq2, where q is the number of MACs the adversary can request. As ε is at least 2-k, the best one can hope for is O(q2 /2k) security. Unfortunately, such small ε is not achieved by simple hash functions used in practice, such as the polynomial evaluation or the Merkle-Damgård construction, where ε grows with the message length L. The main insight of this work comes from the fact that, by using randomized message preprocessing via a short random salt p (which must then be sent as part of the authentication tag), we can use the "hash then encrypt" paradigm with suboptimal "practical" ε-universal hash functions, and still improve its exact security to optimal O(q2/2k). Specifically, by using at most an 0(logL)-bit salt p, one can always regain the optimal exact security O(q2/2k), even in situations where ε grows polynomially with L. We also give very simple preprocessing maps for popular "suboptimal" hash functions, namely polynomial evaluation and the Merkle-Damgård construction. Our results come from a general extension of the classical Carter-Wegman paradigm, which we believe is of independent interest. On a high level, it shows that public randomization allows one to use the potentially much smaller "average-case" collision probability in place of the "worst-case" collision probability ε.

AB - "Hash then encrypt" is an approach to message authentication, where first the message is hashed down using an ε-universal hash function, and then the resulting k-bit value is encrypted, say with a block-cipher. The security of this scheme is proportional to εq2, where q is the number of MACs the adversary can request. As ε is at least 2-k, the best one can hope for is O(q2 /2k) security. Unfortunately, such small ε is not achieved by simple hash functions used in practice, such as the polynomial evaluation or the Merkle-Damgård construction, where ε grows with the message length L. The main insight of this work comes from the fact that, by using randomized message preprocessing via a short random salt p (which must then be sent as part of the authentication tag), we can use the "hash then encrypt" paradigm with suboptimal "practical" ε-universal hash functions, and still improve its exact security to optimal O(q2/2k). Specifically, by using at most an 0(logL)-bit salt p, one can always regain the optimal exact security O(q2/2k), even in situations where ε grows polynomially with L. We also give very simple preprocessing maps for popular "suboptimal" hash functions, namely polynomial evaluation and the Merkle-Damgård construction. Our results come from a general extension of the classical Carter-Wegman paradigm, which we believe is of independent interest. On a high level, it shows that public randomization allows one to use the potentially much smaller "average-case" collision probability in place of the "worst-case" collision probability ε.

UR - http://www.scopus.com/inward/record.url?scp=38349029412&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349029412&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74619-5_26

DO - 10.1007/978-3-540-74619-5_26

M3 - Conference contribution

AN - SCOPUS:38349029412

SN - 354074617X

SN - 9783540746171

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 414

EP - 433

BT - Fast Software Encryption - 14th International Workshop, FSE 2007

PB - Springer Verlag

T2 - 14th International Workshop on Fast Software Encryption, FSE 2007

Y2 - 26 March 2007 through 28 March 2007

ER -