*12:08*[Event][New] ICMC 2015: The second International Conference on Mathematics and Computing

Submission: 16 July 2014

From January 5 to January 10

Location: Haldia, India

More Information: http://hithaldia.co.in/icmc2015/

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Submission: 16 July 2014

From January 5 to January 10

Location: Haldia, India

More Information: http://hithaldia.co.in/icmc2015/

The security of HMAC (and similar hash-based MACs) against

state-recovery and universal forgery attacks was very recently shown to

be suboptimal, following a series of surprising results by Leurent et

al. and Peyrin et al. These results have shown that such powerful

attacks require much less than $2^{\\ell}$ computations, contradicting

the common belief (where $\\ell$ denotes the internal state size). In

this work, we revisit and extend these results, with a focus on

properties of concrete hash functions such as a limited message length,

and special iteration modes.

We begin by devising the first state-recovery attack on HMAC with a

HAIFA hash function (using a block counter in every compression function

call), with complexity $2^{4\\ell/5}$. Then, we describe improved

trade-offs between the message length and the complexity of a

state-recovery attack on HMAC. Consequently, we obtain improved attacks

on several HMAC constructions used in practice, in which the the hash

functions limit the maximal message length (e.g., SHA-1 and SHA-2).

Finally, we present the first universal forgery attacks, which can be

applied with short message queries to the MAC oracle. In particular, we

devise the first universal forgery attacks applicable to SHA-1 and

SHA-2.

Linear algebra plays an important role in computer science, especially in cryptography.Numerous cryptog-raphic protocols, scientific computations, and numerical computations are based on linear algebra. Many linear algebra tasks can be reduced to some core problems, such as matrix multiplication, determinant of matrix and the characteristic polynomial of matrix. However, it is difficult to execute these tasks independently for client whose computation abilities are weaker than polynomial-time computational ability. Cloud Computing is a novel economical paradigm which provides powerful computational resources that enables resources-constrained client to outsource their mass computing tasks to the cloud.

In this paper, we propose a new verifiable and secure outsourcing protocol for the problem of computing the characteristic polynomial and eigenvalues of matrix. These protocols are not only efficient and secure, but also unnecessary for any cryptographic assumption.

The $r$-round (iterated) \\emph{Even-Mansour cipher} (also known as \\emph{key-alternating cipher}) defines a block cipher from $r$ fixed public $n$-bit permutations $P_1,\\ldots,P_r$ as follows: given a sequence of $n$-bit round keys $k_0,\\ldots,k_r$, an $n$-bit plaintext $x$ is encrypted by xoring round key $k_0$, applying permutation $P_1$, xoring round key $k_1$, etc. The (strong) pseudorandomness of this construction in the random permutation model (i.e., when the permutations $P_1,\\ldots,P_r$ are public random permutation oracles that the adversary can query in a black-box way) was studied in a number of recent papers, culminating with the work of Chen and Steinberger (EUROCRYPT~2014), who proved that the $r$-round Even-Mansour cipher is indistinguishable from a truly random permutation up to $O(2^{\\frac{rn}{r+1}})$ queries of any adaptive adversary (which is an optimal security bound since it matches a simple distinguishing attack). All results in this entire line of work share the common restriction that they only hold under the assumption that \\emph{the round keys $k_0,\\ldots,k_r$ and the permutations $P_1,\\ldots,P_r$ are independent}. In particular, for two rounds, the current state of knowledge is that the block cipher $E(x)=k_2\\oplus P_2(k_1\\oplus P_1(k_0\\oplus x))$ is provably secure up to $O(2^{2n/3})$ queries of the adversary, when $k_0$, $k_1$, and $k_2$ are three independent $n$-bit keys, and $P_1$ and $P_2$ are two independent random $n$-bit permutations. In this paper, we ask whether one can obtain a similar bound for the two-round Even-Mansour cipher \\emph{from just one $n$-bit key and one $n$-bit permutation}. Our answer is positive: when the three $n$-bit round keys $k_0$, $k_1$, and $k_2$ are adequately derived from an $n$-bit master key $k$, and the same permutation $P$ is used in place of $P_1$ and $P_2$, we prove a qualitatively similar $\\tilde{O}(2^{2n/3})$ security bound (in the random permutation model). To the best of our knowledge, this is the first ``beyond the birthday bound\'\' security result for AES-like ciphers that does not assume independent round keys.

2014-06-12

We extend the FLUSH+RELOAD side-channel attack of Benger et al. to extract a significantly larger number of bits of information per observed signature when using OpenSSL. This means that by observing only 25 signatures, we can recover secret keys of the secp256k1 curve, used in the Bitcoin protocol, with a probability greater than 50 percent. This is an order of magnitude improvement over the previously best known result.

The new method of attack exploits two points: Unlike previous partial disclosure attacks we utilize all information obtained and not just that in the least significant or most significant bits, this is enabled by a property of the \"standard\" curves choice of group order which enables extra bits of information to be extracted. Furthermore, whereas previous works require direct information on ephemeral key bits, our attack utilizes the indirect information from the wNAF double and add chain.

In cloud computing, efficiencies are reaped by resource sharing such as co-location of computation and deduplication of data. This work exploits resource sharing in virtualization software to build a powerful cache-based attack on AES. We demonstrate the vulnerability by mounting Cross-VM Flush+Reload cache attacks in VMware VMs to recover the AES keys of OpenSSL 1.0.1 running inside the victim VM. Furthermore, the attack works in a realistic setting where different VMs are located on separate cores. The modified flush+reload attack we present, takes only in the order of seconds to minutes to succeed in a cross-VM setting. Therefore long term co-location, as required by other fine grain attacks in the literature, are not needed. The results of this study show that there is a great security risk to OpenSSL AES implementation running on VMware cloud services when the deduplication is not disabled.

Fault attacks are active attacks in which an adversary with physical

access to a cryptographic device, for instance a smartcard, tampers

with the execution of an algorithm to retrieve secret material. Since

the seminal Bellcore attack on RSA signatures, there has been

extensive work to discover new fault attacks against cryptographic

schemes, and to develop countermeasures against such

attacks. Originally focused on high-level algorithmic descriptions,

these works increasingly focus on concrete implementations. While

lowering the abstraction level leads to new fault attacks, it also

makes their discovery significantly more challenging. In order to face

this trend, it is therefore desirable to develop principled,

tool-supported approaches that allow a systematic analysis of the

security of cryptographic implementations against fault attacks.

We propose, implement, and evaluate a new approach for finding fault

attacks against cryptographic implementations. Our approach is based

on identifying implementation-independent mathematical properties we

call fault conditions. We choose them so that it is possible to

recover secret data purely by computing on sufficiently many data

points that satisfy a fault condition. Fault conditions capture the

essence of a large number of attacks from the literature, including

lattice-based attacks on RSA. Moreover, they provide a basis for

discovering automatically new attacks: using fault conditions, we

specify the problem of finding faulted implementations as a program

synthesis problem. Using a specialized form of program synthesis, we

discover multiple faulted implementations on RSA and ECDSA that

realize the fault conditions, and hence lead to fault attacks. Several

of the attacks found by our tool are new, and of independent interest.

In a seminal work at EUROCRYPT \'96, Coppersmith showed how to find

all small roots of a univariate polynomial congruence in polynomial

time: this has found many applications in public-key cryptanalysis

and in a few security proofs. However, the running time of the

algorithm is a high-degree polynomial, which limits experiments: the

bottleneck is an LLL reduction of a high-dimensional matrix with

extra-large coefficients. We present in this paper the first

significant speedups over Coppersmith\'s algorithm. The first

speedup is based on a special property of the matrices used by

Coppersmith\'s algorithm, which allows us to provably speed up the

LLL reduction by rounding, and which can also be used to improve

the complexity analysis of Coppersmith\'s original algorithm.

The exact speedup depends on the LLL algorithm used: for instance,

the speedup is asymptotically quadratic in the bit-size of the

small-root bound if one uses the Nguyen-Stehl\\\'e {\\Ltwo}

algorithm. The second speedup is heuristic and applies whenever

one wants to enlarge the root size of Coppersmith\'s algorithm by

exhaustive search. Instead of performing several LLL reductions

independently, we exploit hidden relationships between these

matrices so that the LLL reductions can be somewhat chained to

decrease the global running time. When both speedups are combined,

the new algorithm is in practice hundreds of times faster for

typical parameters.

Motivated by revelations concerning population-wide surveillance of

encrypted communications, we formalize and investigate the resistance

of symmetric encryption schemes to mass surveillance. The focus is on

algorithm-substitution attacks (ASAs), where a subverted encryption

algorithm replaces the real one. We assume that the goal

of ``big~brother\'\' is undetectable subversion, meaning

that ciphertexts produced by the subverted encryption algorithm

should reveal plaintexts to big~brother yet

be indistinguishable to users from those produced

by the real encryption scheme. We formalize security

notions to capture this goal and then offer both attacks and

defenses. In the first category we show that successful (from the

point of view of big brother) ASAs may be mounted on a large class of

common symmetric encryption schemes. In the second category we show

how to design symmetric encryption schemes that avoid such attacks and

meet our notion of security. The lesson that emerges is the danger of

choice: randomized, stateless schemes are subject to attack while

deterministic, stateful ones are not.

Non-interactive verifiable outsourced computation enables a computationally weak client to outsource the computation of a function $f$ on input $x$ to a more powerful but untrusted server, who will return the result of the function evaluation as well as a proof that the computation is performed correctly. A basic requirement of a verifiable outsourced computation scheme is that the client should invest less time in preparing the inputs and verifying the proof than computing the function by himself.

One of the best solutions of such non-interactive schemes are based on

Yao\'s garble circuit and full homomorphic encryption, which leads to invest $poly(T)$ running time in offline stage and $poly(log T)$ time in online stage of the client, where $T$ is the time complexity to compute $f$.

In this paper, we\'ll present a scheme which does not need to use garble circuit, but to use a very simple technique to confuse the function we are going to compute, and only invests $poly(log T)$ running time in the offline stage.

Recently, the Residue Number System and the Cox-Rower architecture

have been used to compute efficiently Elliptic Curve Cryptography over

FPGA. In this paper, we are rewriting the conditions of Kawamura\'s theorem for the base extension without error in order to define the maximal range of the set from which the moduli can be chosen to build a base. At the same time, we give a procedure to compute correctly the truncation function of the Cox module. We also present a modified ALU of the Rower architecture using a second level of Montgomery Representation. Such architecture allows us to select the

moduli with the new upper bound defined with the condition. This modification makes the Cox-Rower architecture suitable to compute 521 bits ECC with radix downto 16 bits compared to 18 with the classical Cox-Rower architecture. We validate our results through FPGA implementation of a scalar multiplication at classical cryptography security levels (NIST curves). Our implementation uses 35% less LUTs compared to the state of the art generic implementation of ECC

using RNS for the same performance [5]. We also slightly improve the computation time (latency) and our implementation shows best ratio throughput/area for RNS computation supporting any curve independently of the chosen base.