The talk then went on to describe recent results concerning the case of a dishonest majority of adversaries. Clearly this scenario is very important to focus on if MPC schemes are to be deployed in the real world. Early efforts to obtain this level of security were very inefficient, but some recent innovations have proposed using a homomorphic encryption scheme to improve this. This was first suggested in Eurocrypt 2011 by Bendlin, Damgård, Orlandi and Zakarias (pdf). By dividing the computation into two phases ('offline' and 'online'), they manage to perform a secure multiplication in around 8ms. These results are improved upon in a recent paper by Damgård, Pastro, Smart and Zakarias (pdf), which reduces the complexity and storage requirements of the scheme even further. Multiparty computation is an active area of research in Bristol, and it was nice to see it represented in Oxford with Ivan's excellent talk.

One session that interested me in the afternoon was on cryptanalysis and security analysis. This began with Martin Albrecht presenting joint work with Kenny Paterson on breaking a recent IBE scheme of Chen

Whilst this attack was considered in the original paper, the authors severely underestimated the efficiency with which Gröbner bases can be computed. Apparently this problem is surprisingly common in the literature, and stems from using analysis of the XL algorithm to obtain security estimates, whereas in practice the F4 and F5 algorithms are far more efficient. Although in the original paper security of the scheme was proven to be based on the DHIES scheme, this attack does not allow you to break DHIES. The key flaw is that their proof assumes that a specific function can be modelled by a random oracle, when in fact the output of this function is dependent on the secret key. So the use of a random oracle here is completely inappropriate, and invalidates the security proof.

The third talk in the session, given by Julia Borghoff, followed in a similar vein, attacking the lightweight stream cipher A2U2. The attack also involved creating a system of multivariate quadratic equations and using Gröbner basis computations to solve this. Firstly an efficient chosen plaintext attack was presented, followed by a more complex 'guess and determine' attack requiring only a known plaintext. However, some doubts were raised afterwards as to how feasible this attack would be in practice due to the high number of Gröbner basis applications required.

In between these talks on cryptanalysis, our recent PhD graduate Steve Williams presented his work on the security analysis of the SSH key exchange protocol. Although the underlying application layer of SSH has been thoroughly analysed in the past, no-one had yet performed an analysis of the vital key exchange protocol used to initiate the shared secret. Since the initial messages transmitted in the protocol contain a signature, it is not possible to obtain indistinguishability of the key generated in this stage. So the security of this can only be shown to be one-way, which Steve successfully proves. A transformation is then applied to this shared key, and Steve went on to show that this transformation in fact means that the final keys generated in SSH are indistinguishable.

One session that interested me in the afternoon was on cryptanalysis and security analysis. This began with Martin Albrecht presenting joint work with Kenny Paterson on breaking a recent IBE scheme of Chen

*et al.*(pdf). The basic attack involved exploiting the relationship between the master secret key and the private keys for each identity that are generated from the master key. Specifically, each private key is given by a quadratic function in the master key components. So given enough of these keys, an attacker has a system of multivariate quadratic equations in the master key that can be solved using a Gröbner basis computation.Whilst this attack was considered in the original paper, the authors severely underestimated the efficiency with which Gröbner bases can be computed. Apparently this problem is surprisingly common in the literature, and stems from using analysis of the XL algorithm to obtain security estimates, whereas in practice the F4 and F5 algorithms are far more efficient. Although in the original paper security of the scheme was proven to be based on the DHIES scheme, this attack does not allow you to break DHIES. The key flaw is that their proof assumes that a specific function can be modelled by a random oracle, when in fact the output of this function is dependent on the secret key. So the use of a random oracle here is completely inappropriate, and invalidates the security proof.

The third talk in the session, given by Julia Borghoff, followed in a similar vein, attacking the lightweight stream cipher A2U2. The attack also involved creating a system of multivariate quadratic equations and using Gröbner basis computations to solve this. Firstly an efficient chosen plaintext attack was presented, followed by a more complex 'guess and determine' attack requiring only a known plaintext. However, some doubts were raised afterwards as to how feasible this attack would be in practice due to the high number of Gröbner basis applications required.

In between these talks on cryptanalysis, our recent PhD graduate Steve Williams presented his work on the security analysis of the SSH key exchange protocol. Although the underlying application layer of SSH has been thoroughly analysed in the past, no-one had yet performed an analysis of the vital key exchange protocol used to initiate the shared secret. Since the initial messages transmitted in the protocol contain a signature, it is not possible to obtain indistinguishability of the key generated in this stage. So the security of this can only be shown to be one-way, which Steve successfully proves. A transformation is then applied to this shared key, and Steve went on to show that this transformation in fact means that the final keys generated in SSH are indistinguishable.

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