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At Crypto '07, Fouque, Leurent and Nguyen presented full key-recovery attacks on HMAC/NMAC-MD4 and NMAC-MD5, by extending the partial key-recovery attacks of Contini and Yin from Asiacrypt '06. Such attacks are based on collision attacks on the underlying hash function, and the most expensive stage is the recovery of the socalled outer key. In this paper, we show that the outer key can be recovered with near-collisions instead of collisions: near-collisions can be easier to find and can disclose more information. This improves the complexity of the FLN attack on HMAC/NMAC-MD4: the number of MAC queries decreases from 288 to 272, and the number of MD4 computations decreases from 295 to 277. We also improved the total complexity of the related-key attack on NMAC-MD5. Moreover, our attack on NMAC- MD5 can partially recover the outer key without the knowledge of the inner key, which might be of independent interest.

New Key-Recovery Attacks on HMAC/NMAC-MD4 and NMAC-MD5