• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.63-74
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• 2009

In 2005, Wang et al. discovered devastating collision attacks on the main hash functions from the MD4 family. After the discovery of Wang, many analysis results on the security of existing hash-based cryptographic schemes are presented. At CRYPTO'07, Fouque, Leurent and Nguyen presented full key-recovery attacks on HMAC/NMAC-MD4 and NMAC-MD5[4]. Such attacks are based on collision attacks on the underlying hash function, and the most expensive stage is the recovery of the outer key. At EUROCRYPT'08, Wang, Ohta and Kunihiro presented improved outer key recovery attack on HMAC/NMAC-MD4, by using a new near collision path with a high probability[2]. This improves the complexity of the full key-recovery attack on HMAC/NMAC-MD4 which proposed by Fouque, Leurent and Nguyen at CRYPTO'07: The MAC queries decreases from $2^{88}$ to $2^{72}$, and the number of MD4 computations decreases from $2^{95}$ to $2^{77}$. In this paper, we propose improved outer key-recovery attack on HMAC/NMAC-MD4 with $2^{77.1246}$ MAC queries and $2^{37}$ MD4 computations, by using divide and conquer paradigm.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.5 no.1
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• pp.37-50
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• 1995

The smart card with the cryptography and VLSI technologies makes it possible to implement the electronic cash easily. A number of electronic each schemes have been proposed by many cryptographic researchers. In this paper, we propose a practical electronic cash system, using blind digital signature scheme. Schnorr's authentication scheme based on the discrete logarithm problem, and the hierarchical cash tree based on two one-way hash functions for dividable payment. Thisf electronic cash scheme has such properties as privacy of the payment, off-line payment, non-reuseability of cash, transferability of cash to another customer, and dividable payment of cash. This electronic cash protocol is well suited for implementing in smart card.