Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit

Smith, Paul J.; Rae, Donald S.; Manderscheid, Ronald W.; Silbergeld, Sam

doi:10.2307/2287541

Cited by 14 publications

(26 citation statements)

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“…As a result, the chi-squared test essentially gives us a lower bound for success. There are various modifications that can be made to the multinomial test in order to force a better agreement with the chi-squared test [22,24], but we will not explore these avenues in this paper.…”

Section: Convergence Of the Multinomial Testmentioning

confidence: 99%

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Cold Boot Attacks in the Discrete Logarithm Setting

Poettering

Sibborn

2015

Lecture Notes in Computer Science

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Abstract. In a cold boot attack a cryptosystem is compromised by analysing a noisy version of its internal state. For instance, if a computer is rebooted the memory contents are rarely fully reset; instead, after the reboot an adversary might recover a noisy image of the old memory contents and use it as a stepping stone for reconstructing secret keys. While such attacks were known for a long time, they recently experienced a revival in the academic literature. Here, typically either RSA-based schemes or blockciphers are targeted. We observe that essentially no work on cold boot attacks on schemes defined in the discrete logarithm setting (DL) and particularly for elliptic curve cryptography (ECC) has been conducted. In this paper we hence consider cold boot attacks on selected wide-spread implementations of DL-based cryptography. We first introduce a generic framework to analyse cold boot settings and construct corresponding key-recovery algorithms. We then study common in-memory encodings of secret keys (in particular those of the wNAF-based and comb-based ECC implementations used in OpenSSL and PolarSSL, respectively), identify how redundancies can be exploited to make cold boot attacks effective, and develop efficient dedicated key-recovery algorithms. We complete our work by providing theoretical bounds for the success probability of our attacks.

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Section: Convergence Of the Multinomial Testmentioning

confidence: 99%

“…At this point, the algorithm fills in all the missing bits with all possible combinations (cf. lines [21][22][23][24][25][26]. Then the algorithm checks whether any of the strings is a match for the private key (by using the public information Q = aP ).…”

Section: Comb Encodingsmentioning

confidence: 99%

Cold Boot Attacks in the Discrete Logarithm Setting

Poettering

Sibborn

2015

Lecture Notes in Computer Science

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“…It is known that the likelihood ratio chi-squared criterion overestimates significance, in the sense that the null hypothesis H0 is rejected too often in relation to the nominal level of significance when Ho is true for *Present address: Abbott Laboratories, Department 436, Abbott Park, IL 60064, U.S.A. moderate sample sizes (see, e.g., Larntz (1978), Smith et al (1981), Lawal (1984) and Hosmane (1987b)). Williams (1976), Smith et al (1981) and Hosmane (1987b) have suggested downward multiplicative correction to G z for testing goodness-of-fit of multinomial distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Williams (1976), Smith et al (1981) and Hosmane (1987b) have suggested downward multiplicative correction to G z for testing goodness-of-fit of multinomial distributions. Larntz (1978) studied the behavior of G 2, concluding that the aberrant behavior of G 2 is due to very small observed counts in the table.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the usual chi-square approximation to the upper tail of the likelihood ratio statistic G 2, is not satisfactory. Several authors have derived adjustments (e.g., Williams (1976), Smith et aL (1981), Hosmane (1987b)), so that the asymptotic mean of G 2 matches the mean of the asymptotic chi-square distribution in the hope that the distribution of G 2 would improve. In this paper, a new adjustment to G 2 is determined on the basis of the n-l-order term (n being the total number) of the Edgeworth expansion of the distribution of smoothed G 2.…”

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