By Christophe De Cannière, Christian Rechberger (auth.), Xuejia Lai, Kefei Chen (eds.)
This publication constitutes the refereed court cases of the twelfth foreign convention at the idea and alertness of Cryptology and data safeguard, ASIACRYPT 2006, held in Shanghai, China in December 2006.
The 30 revised complete papers provided have been conscientiously reviewed and chosen from 314 submissions. The papers are equipped in topical sections on assaults on hash services, circulation ciphers and boolean services, biometrics and ECC computation, id-based schemes, public-key schemes, RSA and factorization, building of hash functionality, protocols, block ciphers, and signatures.
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Extra info for Advances in Cryptology – ASIACRYPT 2006: 12th International Conference on the Theory and Application of Cryptology and Information Security, Shanghai, China, December 3-7, 2006. Proceedings
Since δm5 = 25 , δa6 becomes δa6 = 25 , that is, δe10 = 23 . Therefore, δe10 = 23 is canceled by δm10 = −23 , and δa11 becomes 0. In the case of m5,6 = 1 and m10,4 = 0, a similar analysis shows that δa11 becomes 0. From Step 17. Because of input diﬀerentials and message expansion, the following message diﬀerentials appear from step 19: δm18 = ±23 , δm19 = ±25 and δm20 = ±210 . δm18 = ±23 is transferred as shown below, and a21,4 = a20,4 (or a21,4 = a20,4 ) is satisﬁed by δa21 = ±23 . δm18 = ±23 → δa19 = ±23 → δb20 = ±23 → δa21 = ±23 Remark.
Discussed above, can be applied to submarine modiﬁcation, submarine modiﬁcation can more eﬃciently satisfy the suﬃcient conditions than random search. Since the structure of the MD-family or SHA-1 is very similar to that of SHA-0, submarine modiﬁcation may also be applicable to those hash functions. 2nd Result: We show that the suﬃcient conditions given by Wang et al. are missing two conditions, and then describe the missing suﬃcient conditions. From the second result, even if a message satisfying all suﬃcient conditions given by Wang et al.
Since the proof of Theorem 3 is almost same as that of Theorem 1 and due to lack of space, we omit the explanation of this proof. Remark. We experimentally conﬁrmed that the probability that this message modiﬁcation can satisfy the target condition without aﬀecting the other suﬃcient conditions is almost 100%. The complexity of this message modiﬁcation is less than the operations of 3 steps. Theorem 4. Suppose we set following conditions as Extra Conditions: a11,16 = m10,16 , m11,21 = m10,16 , m12,16 = m10,16 , a12,14 = 0, a13,14 = 1, m15,14 = m10,16 , m19,21 = m18,16 .