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A recently proposed masking method, based on secret sharing and multi-party computation methods, introduces a set of sufficient requirements for implementations to be provably resistant against first-order DPA with minimal assumptions on the hardware.
The original paper doesn\'t describe how to construct the Boolean functions that are to be used in the implementation. In this paper, we derive the functions for all invertible $3 \\times 3$, $4 \\times 4$ S-boxes and the $6 \\times 4$ DES S-boxes. Our methods and observations can also be used to accelerate the search for sharings of larger (e.g. $8 \\times 8$) S-boxes. Finally, we investigate the cost of such protection.
shuffle, called a public shuffle,
in which a shuffler can perform shuffle publicly without needing information kept secret.
Their scheme uses an encrypted permutation matrix to shuffle
This approach significantly reduces the cost of constructing a mix-net
to verifiable joint decryption. Though their method is successful in making
shuffle to be a public operation, their scheme
still requires that some trusted parties should choose a permutation
to be encrypted and construct zero-knowledge proofs on the
well-formedness of this permutation.
In this paper, we propose a method to construct a public shuffle
without relying on permutations and randomizers generated privately: Given an
$n$-tuple of ciphertext $(c_1,\\dots,c_n)$, our shuffle algorithm
computes $f_i(c_1,\\dots,c_n)$ for $i=1,\\dots,\\ell$ where each
$f_i(x_1,\\dots,x_n)$ is a symmetric polynomial in $x_1,\\dots,x_n$.
Depending on the symmetric polynomials we use, we propose two concrete constructions.
One is to use ring homomorphic encryption with constant ciphertext
complexity and the other is to use simple ElGamal encryption with
linear ciphertext complexity in the number of senders. Both
constructions are free of zero-knowledge proofs and publicly
We consider the problem of universal composability in cases, when we cannot assume independence of instances. Next we formalize the interleaving attack and a related security notion. In time-aware protocols time-based separation of instances is one of the standard implementation techniques. We propose an event-driven clock model towards purely symbolic analysis of time-aware protocols.
We disprove the claim that NC-Rainbow is as secure as Rainbow in general and show how to reduce the complexity of MinRank attacks from 2^288 to 2^112 and of HighRank attacks from 2^128 to 2^96 for the proposed instantiation over the ring of Quaternions. We further reveal some facts about Quaternions that increase the complexity of the signing algorithm. We show that NC-Rainbow is just a special case of introducing further structure to the secret key in order to decrease the key size. As the results are comparable with the ones achieved by equivalent keys, which provably do not decrease security, and far worse than just using a PRNG, we recommend not to use NC-Rainbow.