## Three paper Thursday: Shamir x3 at Eurocrypt

April 19th, 2012 at 15:02 UTC by

For the past 4 days Cambridge has been hosting Eurocrypt 2012.

There were many talks, probably interesting, but I will only comment on 3 talks given by Adi Shamir, 1 during the official conference and 2 during the rump session.
Among the other sessions I mention that the best paper was given to this paper by Antoine Joux and Vanessa Vitse for the enhancement of index calculus to break elliptic curves.

Official Talk: Minimalism in cryptography, the Even-Mansour scheme revisited

In this work, Adi et al. presented an analysis on the Even-Mansour scheme:

﻿﻿﻿E(P) = F(P ⊕ K1) ⊕ K2

Such scheme, some times referred to as key whitening, is used in the DESX construction and in the AES-XTS mode of operation (just a few examples).

Adi et al. shown a new slide attack, called SLIDEX, which has been used to prove a tight bound on the security of the Even-Mansour scheme.

Even more, they show that using K1 = K2 you can achieve the same security.

Rump talk 1: security of multiple key encryption

Here Adi considered the case of encrypting data multiple times with multiple keys, as in 3DES:
data -> c1 = E_k1(data) ->  c2 = E_k2(c1) -> c3 = E_k3(c2) -> c4 = E_k3(c3) …. and so on.

The general approach to break a scheme where a key is used 2 times or 3 times (2DES, 3DES for e.g.) is the meet-in-the-middle attack, where you encrypt from one side and then decrypt from the other side, and by storing a table of the size of the key space (say n bits) you can eventually find the keys used in a scheme using only a few pairs of plaintext/ciphertext. For 2 keys such an attack would require 2^{n} time, for 3 keys 2^{2n}. Therefore some people may assume that increasing the number of keys by 1 (i.e. to use 4 keys) may increase the security of this scheme. This is in fact not true.

Adi shown that once we go beyond 3 keys (e.g. 4, 5, 6, etc…) the security only increases once every few keys. If you think of it, using 4 keys you can just apply the meet-in-the-middle attack in 2^{2n} time to the left 2 encryptions and also in 2^{2n} time to the right 2 decryptions. After this, he shown how to use the meet-in-the-middle attack to solve the knapsack problem and proposed the idea of using such an algorithm to solve other problems as well.

Rump talk 2: the cryptography of John Nash

Apparently John Nash, member of MIT during the 1950s, wrote some letters to the NSA in 1955 explaining the implications of computational complexity for security (this wasn’t known at the time).

John Nach also sent a proposal for an encryption scheme that is similar with today’s stream ciphers. However the NSA’s replied saying that the scheme didn’t match the security requirements of the US.
Adi Shamir and Ron Rivest then analysed the scheme and found that in the known plaintext model it would require something like 2^{sqrt(n)} time to break (which John Nach considered not to be a polynomial time, and therefore assumed would be secure).

The letters are now declassified. This blog also comments on the story.

Entry filed under: Academic papers, Cryptology, Three Paper Thursday

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