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How to try to predict the output of Micali-Schnorr Generator (MS-DRBG) knowing the factorization. Part II

tl;dr In the previous article of the same series we tried to predict the output of Micali-Schnorr Generator (MS-DRBG) knowing the factorization. In this blog post we continue the effort started in part I showing different strategies.  If you want to skip all my failures and go directly to the (in my humble opinion) most promising approach you can read directly the Solinas Prime and Generalized Mersenne Numbers section below.

If you actually wonder what is MS-DRBG and why I am trying to do it I'd suggest to go back and read the first article.
What I am NOT claiming in this post though is that there is a NSA's backdoor in the ANSI and ISO standards. Introduction and Failure #1 So let's start from were we actually finished the last post. We focused on an easier version of the problem directly extracted from the original Micali Schnorr paper


where the known output is up to 3/4 of the RSA computation and secret state is only 1/4 of the RSA computation.

Assuming we know the fac…
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Slack SAML authentication bypass

tl;dr  I found a severe issue in the Slack's SAML implementation that allowed me to bypass the authentication. This has now been solved by Slack.
Introduction IMHO the rule #1 of any bug hunter (note I do not consider myself one of them since I do this really sporadically) is to have a good RSS feed list.  In the course of the last years I built a pretty decent one and I try to follow other security experts trying to "steal" some useful tricks. There are many experts in different fields of the security panorama and too many to quote them here (maybe another post). But one of the leading expert (that I follow) on SAML is by far Ioannis Kakavas. Indeed he was able in the last years to find serious vulnerability in the SAML implementation of Microsoft and Github. Usually I am more an "OAuth guy" but since both, SAML and OAuth, are nothing else that grandchildren of Kerberos learning SAML has been in my todo list for long time. The Github incident gave me the final…

How to try to predict the output of Micali-Schnorr Generator (MS-DRBG) knowing the factorization

The article was modified since its publication. Last update was 09/10/2017 

tl;dr in this post we are going to describe how to try predict the output of Micali-Schnorr Generator (MS-DRBG)  knowing the factorization of the n value. If this sounds like, "why the hell should I care?", you might want to give a look at this great post from Matthew Green about the backdoor in Dual_EC_DRBG. But In a nutshell, quoting Matthew Green : Dual_EC_DRBG is not the only asymmetric random number generator in the ANSI and ISO standards (see at the bottom).   it’s not obvious from the public literature how one would attack the generator even if one knew the factorization of the n values above. What I am NOT claiming in this post though is that there is a backdoor in one of this standard.

Introduction
The first time I heard about this problem is about couple of weeks ago via this Matthew's tweet: As a curiosity, the NSA didn’t just standardize Dual EC, they also standardized a second sketchy …

CVE-2017-7781/CVE-2017-10176: Issue with elliptic curve addition in mixed Jacobian-affine coordinates in Firefox/Java

tl;dr Firefox and Java suffered from a moderate vulnerability affecting the elliptic curve point addition algorithm that uses mixed Jacobian-affine coordinates where it can yield a result POINT_AT_INFINITY when it should not.

Introduction
Few months ago I was working on a vulnerability affecting the internet standard JWE (slides here) and I got a stroke of luck. Yuppieeee  Basically I was constructing the malicious JWEs needed for the Demo Attack. When something weird happened :S
You can try and share with me the surprise I had, the gist is here

If you try to execute this class with Java 1.7 you basically have

Exception in thread "main" java.lang.IllegalStateException
    at sun.security.ec.ECDHKeyAgreement.deriveKey(Native Method)
    at sun.security.ec.ECDHKeyAgreement.engineGenerateSecret(ECDHKeyAgreement.java:130)
    at javax.crypto.KeyAgreement.generateSecret(KeyAgreement.java:586)
    at orig.EccJava.getAgreedKey(EccJava.java:53)
    at orig.EccJava.main(EccJava.java:44)

😲…

Analisi dei dump di Rousseau (Movimento Cinque Stelle) - Parte I: password

Disclaimer Questo blog post e' scritto da evariste.gal0is ed Antonio Sanso. Entrambi gli autori non hanno nessuna affiliazione politica ed il post ha l'unico scopo di fornire un'analisi tecnica di parte dei dump relativa alle password.
Riassunto delle puntate precedenti
In data 2 agosto 2017 uno dei coautori di questo blog post  (evariste.gal0is) ha segnalato
Il sito Rousseau del M5S è vulnerabile, voti e dati personali degli iscritti sono tutti a rischio #Hack5Stellehttps://t.co/7KPcFsXFhe — evariste.gal0is (@evaristegal0is) August 2, 2017 una severa vulnerabilita' (del tipo SQL injection) che affligeva la piattaforma del Movimento Cinque Stelle chiamata Rousseau: https://rousseau.movimento5stelle.it/ . La sua segnalazione riceve una notevole copertura mediatica e minacce di querela da parte del  Movimento Cinque Stelle* (cosa che spinge  evariste.gal0is a prendere temporaneamente una pausa). Nel frattempo un black hat hacker che si fa chiamare rogue0 viola nuovament…

Historical courses and resorts in Elliptic Curves Cryptography - Is Curve25519 dead?

tl;dr This short blog post serves to me to recollect some of the thing I have been learning (climbing) about Elliptic Curves Cryptography (ECC from now on) during the last months/years, so please take it with a grain of salt since it might contains some erroneous beliefs.

'80 - Introduction Giambattista Vico  was an Italian political philosopher and rhetorician, historian and jurist, of the Age of Enlightenment famous (also) for the concept of historical courses and resorts. This can be resumed with: "some events are repeated in the same way even after a long time;and this is not by chance". Well it seems that this might also applies to ECC so he maybe he was right :)
Elliptic Curve made its first appearance in cryptography with Lenstra in 1984 (eventually published in 1987). Curiously enough he introduced them not while trying to come up with a new crypto system but he employed EC in order to factor integers (a side note, there is a really beautiful survey about…