Weak Keys Remain Widespread in Network Devices

Total Page:16

File Type:pdf, Size:1020Kb

Weak Keys Remain Widespread in Network Devices Weak Keys Remain Widespread in Network Devices Marcella Hastings Joshua Fried Nadia Heninger University of Pennsylvania University of Pennsylvania University of Pennsylvania [email protected] [email protected] [email protected] ABSTRACT Wustrow, and Halderman [21] announced that they had In 2012, two academic groups reported having com- factored tens of thousands of public RSA keys from TLS puted the RSA private keys for 0.5% of HTTPS hosts on certificates. The latter group traced the vulnerability the internet, and traced the underlying issue to widespread to widespread failures in random number generators on random number generation failures on networked de- headless, embedded, and low-resource network devices. vices. The vulnerability was reported to dozens of ven- While this vulnerability revealed the private keys for dors, several of whom responded with security advi- 0.5% of HTTPS hosts on the internet at the time, the sories, and the Linux kernel was patched to fix a boot- immediate security impact on those particular hosts time entropy hole that contributed to the failures. was likely limited by the fact that the vast majority of In this paper, we measure the actions taken by ven- compromised TLS certificates were not browser trusted, dors and end users over time in response to the origi- and were automatically-generated certificates protect- nal disclosure. We analyzed public internet-wide TLS ing web login interfaces on consumer and small-business scans performed between July 2010 and May 2016 and grade routers and firewalls, remote server administra- extracted 81 million distinct RSA keys. We then com- tion interfaces, and embedded device such as cooling puted the pairwise common divisors for the entire set systems, building monitors, cameras, projectors, and in order to factor over 313,000 keys vulnerable to the printers. Rather, the presence of weak keys was an ex- flaw, and fingerprinted implementations to study patch- ternally visible signal that the random number genera- ing behavior over time across vendors. We find that tion subsystems on entire classes of devices and across many vendors appear to have never produced a patch, multiple implementations had failed, likely impacting and observed little to no patching behavior by end users these systems and many other hosts in a variety of ways. of affected devices. The number of vulnerable hosts in- In this paper, we study the disclosure process under- creased in the years after notification and public dis- taken by the authors of [21] and the aftermath of this closure, and several newly vulnerable implementations family of random number generation failures. We ag- have appeared since 2012. Vendor notification, positive gregated publicly available internet-wide TLS scan data vendor responses, and even vendor-produced public se- dating back almost six years, including monthly scans curity advisories appear to have little correlation with during the past four years from multiple sources. We end-user security. give more details on our data sources in Section 3.1. In order to measure the incidence of vulnerable keys, we Keywords extracted the 81 million distinct RSA moduli found in these scans and ran a batch GCD algorithm to factor Security vulnerabilities; networked devices improperly generated RSA keys. We were able to factor over 313,000 moduli. (See Table 1.) To carry out such 1. INTRODUCTION a large computation efficiently for such a large number In February of 2012, Lenstra, Hughes, Augier, Bos, of keys, we modified the algorithm to run in parallel Kleinjung, and Wachter [26] and Heninger, Durumeric, across a distributed cluster. We describe our computa- Permission to make digital or hard copies of all or part of this work for personal tion in detail in Section 3.2. We then manually finger- or classroom use is granted without fee provided that copies are not made or printed vulnerable implementations based on available distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work metadata, including certificate subjects, certificate sub- owned by others than the author(s) must be honored. Abstracting with credit is ject alternative names, port scans, and known private permitted. To copy otherwise, or republish, to post on servers or to redistribute to key behavior, as described in Section 3.3, and examine lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. vulnerability rates over time for user populations asso- IMC ’16, November 14–16, Santa Monica, CA, USA. ciated with identified vendors in Section 4. c 2016 Copyright held by the owner/author(s). Publication rights licensed to Previous studies of vulnerability patching have fo- ACM. ISBN 978-1-4503-4526-2/16/11. $15.00 cused on patching behavior from system administra- DOI: http://dx:doi:org/10:1145/2987443:2987486 tors in response to highly publicized vulnerabilities in HTTPS host records 1,526,222,329 OpenSSL [39, 15] or in response to targeted vulnera- Distinct HTTPS certificates 65,285,795 bility notifications [27, 33]. In contrast, the vulnerabil- Distinct HTTPS moduli 50,677,278 ity disclosures undertaken by the authors of [21] were targeted mainly at vendors of embedded and headless Total distinct RSA moduli 81,228,736 devices, which are rarely updated by end users. Vulnerable RSA moduli 313,330 The widespread nature of the flaw provides us with Vulnerable HTTPS host records 2,964,447 an accidental historical experiment allowing us to study Vulnerable HTTPS certificates 1,441,437 the industry's response to disclosure by comparing re- sponses across many vendors. We describe in detail for Table 1: We analyzed six years of internet-wide HTTPS the first time the results from the industry-wide dis- scans in order to study server behavior over time. Each closure process undertaken by the authors of [21]. In host record represents a HTTPS handshake on a given particular, fewer than half of the organizations con- date with a server at some IP address. We augmented tacted about the vulnerabilities responded at all to a our batch GCD computation with RSA public keys ex- best-effort attempt at vulnerability notification. tracted from IMAPS, POP3S, SMTPS, and SSH scans, We also give data on the post-notification internet- but excluded these other protocols from further study. wide vulnerability rates for different vendors in response to the same vulnerability. Many vendors apparently continued to ship vulnerable products for years after client and server negotiate a cipher suite that includes receiving notification of and even acknowledging the se- RSA key exchange, the client uses the server's public curity vulnerability, and in some cases after putting out key to encrypt session key information; when they ne- security advisories for their products. Since the targets gotiate a Diffie-Hellman or elliptic-curve Diffie-Hellman of our study are primarily devices, rather than software cipher suite, the server uses its RSA public key to sign packages, end users must rely on vendors to distribute its key exchange message to prove authenticity. RSA updates in order to patch their own devices. We ob- digital signatures are used to authenticate TLS certifi- serve that for this vulnerability, end-user patching did cates; a certificate may be signed by a trusted certificate not appear to occur at all. authority's public key or by a certificate chaining up to The single largest drop in the number of vulnera- a trusted root key, or self-signed by its own public key. ble keys occurred shortly after the disclosure of the A compromised public key from a TLS certificate Heartbleed vulnerability in April 2014. The decrease could be used to passively decrypt TLS sessions that in vulnerable keys is confined to a handful of devices, had negotiated RSA key exchange. An active attacker for which there was an even larger concurrent drop in could use a compromised certificate key to impersonate the total population of fingerprinted devices, suggest- a trusted server whose certificate used that key, or to ing that while in some cases the publicity may have perform a man-in-the-middle attack to decrypt or mod- prompted device users to regenerate certificates or ap- ify traffic using Diffie-Hellman or RSA cipher suites. ply a patch that also fixed the weak key vulnerability, 74% of the 61,240 vulnerable devices present in our most many device HTTPS interfaces may instead have simply recent scan data from April 2016 only support RSA key been taken offline. In the case of at least one device fam- exchange, making them vulnerable to passive decryp- ily, Heartbleed vulnerability scans were reported to ren- tion by an attacker who is able to observe network traf- der the device non-responsive. This suggests that end- fic. In order for an attacker to intercept network traffic, user device security can improve when vendors patch they would need to be on the network path between the vulnerabilities and end users are encouraged to apply victim client and the true server, or use a network at- patches or change configuration by widespread media tack like DNS or BGP hijacking [8] to force the victim attention and targeted vulnerability notifications, but to connect to the server via the client. that this process did not occur in response to the vul- Among the vulnerable devices that we examined, HTTPS nerabilities we study in this paper. is used primarily to serve remote management inter- faces. Many of the vulnerable firewalls also use TLS to encrypt SSL VPN connections. An attacker who is 2. BACKGROUND able to decrypt connections to one of these devices may obtain administrative credentials for the device or view 2.1 TLS security remote user traffic to internal network resources.
Recommended publications
  • Hardness Evaluation of Solving MQ Problems
    MQ Challenge: Hardness Evaluation of Solving MQ Problems Takanori Yasuda (ISIT), Xavier Dahan (ISIT), Yun-Ju Huang (Kyushu Univ.), Tsuyoshi Takagi (Kyushu Univ.), Kouichi Sakurai (Kyushu Univ., ISIT) This work was supported by “Strategic Information and Communications R&D Promotion Programme (SCOPE), no. 0159-0091”, Ministry of Internal Affairs and Communications, Japan. The first author is supported by Grant-in-Aid for Young Scientists (B), Grant number 24740078. Fukuoka MQ challenge MQ challenge started on April 1st. https://www.mqchallenge.org/ ETSI Quantum Safe Workshop 2015/4/3 2 Why we need MQ challenge? • Several public key cryptosystems held contests which solve the associated basic mathematical problems. o RSA challenge(RSA Laboratories), ECC challenge(Certicom), Lattice challenge(TU Darmstadt) • Lattice challenge (http://www.latticechallenge.org/) o Target: Short vector problem o 2008 – now continued • Multivariate public-key cryptsystem (MPKC) also need to evaluate the current state-of-the-art in practical MQ problem solvers. We planed to hold MQ challenge. ETSI Quantum Safe Workshop 2015/4/3 3 Multivariate Public Key Cryptosystem (MPKC) • Advantage o Candidate for post-quantum cryptography o Used for both encryption and signature schemes • Encryption: Simple Matrix scheme (ABC scheme), ZHFE scheme • Signature: UOV, Rainbow o Efficient encryption and decryption and signature generation and verification. • Problems o Exact estimate of security of MPKC schemes o Huge length of secret and public keys in comparison with RSA o New application and function ETSI Quantum Safe Workshop 2015/4/3 4 MQ problem MPKC are public key cryptosystems whose security depends on the difficulty in solving a system of multivariate quadratic polynomials with coefficients in a finite field .
    [Show full text]
  • Side Channel Analysis Attacks on Stream Ciphers
    Side Channel Analysis Attacks on Stream Ciphers Daehyun Strobel 23.03.2009 Masterarbeit Ruhr-Universität Bochum Lehrstuhl Embedded Security Prof. Dr.-Ing. Christof Paar Betreuer: Dipl.-Ing. Markus Kasper Erklärung Ich versichere, dass ich die Arbeit ohne fremde Hilfe und ohne Benutzung anderer als der angegebenen Quellen angefertigt habe und dass die Arbeit in gleicher oder ähnlicher Form noch keiner anderen Prüfungsbehörde vorgelegen hat und von dieser als Teil einer Prüfungsleistung angenommen wurde. Alle Ausführungen, die wörtlich oder sinngemäß übernommen wurden, sind als solche gekennzeichnet. Bochum, 23.März 2009 Daehyun Strobel ii Abstract In this thesis, we present results from practical differential power analysis attacks on the stream ciphers Grain and Trivium. While most published works on practical side channel analysis describe attacks on block ciphers, this work is among the first ones giving report on practical results of power analysis attacks on stream ciphers. Power analyses of stream ciphers require different methods than the ones used in todays most popular attacks. While for the majority of block ciphers it is sufficient to attack the first or last round only, to analyze a stream cipher typically the information leakages of many rounds have to be considered. Furthermore the analysis of hardware implementations of stream ciphers based on feedback shift registers inevitably leads to methods combining algebraic attacks with methods from the field of side channel analysis. Instead of a direct recovery of key bits, only terms composed of several key bits and bits from the initialization vector can be recovered. An attacker first has to identify a sufficient set of accessible terms to finally solve for the key bits.
    [Show full text]
  • Petawatt and Exawatt Class Lasers Worldwide
    Petawatt and exawatt class lasers worldwide Colin Danson, Constantin Haefner, Jake Bromage, Thomas Butcher, Jean-Christophe Chanteloup, Enam Chowdhury, Almantas Galvanauskas, Leonida Gizzi, Joachim Hein, David Hillier, et al. To cite this version: Colin Danson, Constantin Haefner, Jake Bromage, Thomas Butcher, Jean-Christophe Chanteloup, et al.. Petawatt and exawatt class lasers worldwide. High Power Laser Science and Engineering, Cambridge University Press, 2019, 7, 10.1017/hpl.2019.36. hal-03037682 HAL Id: hal-03037682 https://hal.archives-ouvertes.fr/hal-03037682 Submitted on 3 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. High Power Laser Science and Engineering, (2019), Vol. 7, e54, 54 pages. © The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/hpl.2019.36 Petawatt and exawatt class lasers worldwide Colin N. Danson1;2;3, Constantin Haefner4;5;6, Jake Bromage7, Thomas Butcher8, Jean-Christophe F. Chanteloup9, Enam A. Chowdhury10, Almantas Galvanauskas11, Leonida A.
    [Show full text]
  • Hardware Implementation of Four Byte Per Clock RC4 Algorithm Rourab Paul, Amlan Chakrabarti, Senior Member, IEEE, and Ranjan Ghosh
    JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 1 Hardware Implementation of four byte per clock RC4 algorithm Rourab Paul, Amlan Chakrabarti, Senior Member, IEEE, and Ranjan Ghosh, Abstract—In the field of cryptography till date the 2-byte in 1-clock is the best known RC4 hardware design [1], while 1-byte in 1-clock [2], and the 1-byte in 3 clocks [3][4] are the best known implementation. The design algorithm in[2] considers two consecutive bytes together and processes them in 2 clocks. The design [1] is a pipelining architecture of [2]. The design of 1-byte in 3-clocks is too much modular and clock hungry. In this paper considering the RC4 algorithm, as it is, a simpler RC4 hardware design providing higher throughput is proposed in which 6 different architecture has been proposed. In design 1, 1-byte is processed in 1-clock, design 2 is a dynamic KSA-PRGA architecture of Design 1. Design 3 can process 2 byte in a single clock, where as Design 4 is Dynamic KSA-PRGA architecture of Design 3. Design 5 and Design 6 are parallelization architecture design 2 and design 4 which can compute 4 byte in a single clock. The maturity in terms of throughput, power consumption and resource usage, has been achieved from design 1 to design 6. The RC4 encryption and decryption designs are respectively embedded on two FPGA boards as co-processor hardware, the communication between the two boards performed using Ethernet. Keywords—Computer Society, IEEEtran, journal, LATEX, paper, template.
    [Show full text]
  • *UPDATED Canadian Values 07-04 201 7/26/2016 4:42:21 PM *UPDATED Canadian Values 07-04 202 COIN VALUES: CANADA 02 .0 .0 12
    CANADIAN VALUES By Michael Findlay Large Cents VG-8 F-12 VF-20 EF-40 MS-60 MS-63R 1917 1.00 1.25 1.50 2.50 13. 45. CANADA COIN VALUES: 1918 1.00 1.25 1.50 2.50 13. 45. 1919 1.00 1.25 1.50 2.50 13. 45. 1920 1.00 1.25 1.50 3.00 18. 70. CANADIAN COIN VALUES Small Cents PRICE GUIDE VG-8 F-12 VF-20 EF-40 MS-60 MS-63R GEORGE V All prices are in U.S. dollars LargeL Cents C t 1920 0.20 0.35 0.75 1.50 12. 45. Canadian Coin Values is a comprehensive retail value VG-8 F-12 VF-20 EF-40 MS-60 MS-63R 1921 0.50 0.75 1.50 4.00 30. 250. guide of Canadian coins published online regularly at Coin VICTORIA 1922 20. 23. 28. 40. 200. 1200. World’s website. Canadian Coin Values is provided as a 1858 70. 90. 120. 200. 475. 1800. 1923 30. 33. 42. 55. 250. 2000. reader service to collectors desiring independent informa- 1858 Coin Turn NI NI 2500. 5000. BNE BNE 1924 6.00 8.00 11. 16. 120. 800. tion about a coin’s potential retail value. 1859 4.00 5.00 6.00 10. 50. 200. 1925 25. 28. 35. 45. 200. 900. Sources for pricing include actual transactions, public auc- 1859 Brass 16000. 22000. 30000. BNE BNE BNE 1926 3.50 4.50 7.00 12. 90. 650. tions, fi xed-price lists and any additional information acquired 1859 Dbl P 9 #1 225.
    [Show full text]
  • 9/11 Report”), July 2, 2004, Pp
    Final FM.1pp 7/17/04 5:25 PM Page i THE 9/11 COMMISSION REPORT Final FM.1pp 7/17/04 5:25 PM Page v CONTENTS List of Illustrations and Tables ix Member List xi Staff List xiii–xiv Preface xv 1. “WE HAVE SOME PLANES” 1 1.1 Inside the Four Flights 1 1.2 Improvising a Homeland Defense 14 1.3 National Crisis Management 35 2. THE FOUNDATION OF THE NEW TERRORISM 47 2.1 A Declaration of War 47 2.2 Bin Ladin’s Appeal in the Islamic World 48 2.3 The Rise of Bin Ladin and al Qaeda (1988–1992) 55 2.4 Building an Organization, Declaring War on the United States (1992–1996) 59 2.5 Al Qaeda’s Renewal in Afghanistan (1996–1998) 63 3. COUNTERTERRORISM EVOLVES 71 3.1 From the Old Terrorism to the New: The First World Trade Center Bombing 71 3.2 Adaptation—and Nonadaptation— ...in the Law Enforcement Community 73 3.3 . and in the Federal Aviation Administration 82 3.4 . and in the Intelligence Community 86 v Final FM.1pp 7/17/04 5:25 PM Page vi 3.5 . and in the State Department and the Defense Department 93 3.6 . and in the White House 98 3.7 . and in the Congress 102 4. RESPONSES TO AL QAEDA’S INITIAL ASSAULTS 108 4.1 Before the Bombings in Kenya and Tanzania 108 4.2 Crisis:August 1998 115 4.3 Diplomacy 121 4.4 Covert Action 126 4.5 Searching for Fresh Options 134 5.
    [Show full text]
  • How to Find Short RC4 Colliding Key Pairs
    How to Find Short RC4 Colliding Key Pairs Jiageng Chen ? and Atsuko Miyaji?? School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan jg-chen, miyaji @jaist.ac.jp { } Abstract. The property that the stream cipher RC4 can generate the same keystream outputs under two di↵erent secret keys has been discov- ered recently. The principle that how the two di↵erent keys can achieve a collision is well known by investigating the key scheduling algorithm of RC4. However, how to find those colliding key pairs is a di↵erent story, which has been largely remained unexploited. Previous researches have demonstrated that finding colliding key pairs becomes more difficult as the key size decreases. The main contribution of this paper is propos- ing an efficient searching algorithm which can successfully find 22-byte colliding key pairs, which are by far the shortest colliding key pairs ever found. 1 Introduction The stream cipher RC4 is one of the oldest and most wildly used stream ciphers in the world. It has been deployed to innumerable real world applications including Microsoft Office, Secure Socket Layer (SSL), Wired Equivalent Privacy (WEP), etc. Since its debut in 1994 [1], many cryptanalysis works have been done on it, and many weaknesses have been exploited, such as [5] [6] and [7]. However, if RC4 is used in a proper way, it is still considered to be secure. Thus it is still considered to be a high valuable cryptanalysis target both in the industrial and academic world. In this paper, we focus on exploiting the weakness that RC4 can generate colliding key pairs, namely, two di↵erent keys will result in the same keystream output.
    [Show full text]
  • Stream Cipher Designs: a Review
    SCIENCE CHINA Information Sciences March 2020, Vol. 63 131101:1–131101:25 . REVIEW . https://doi.org/10.1007/s11432-018-9929-x Stream cipher designs: a review Lin JIAO1*, Yonglin HAO1 & Dengguo FENG1,2* 1 State Key Laboratory of Cryptology, Beijing 100878, China; 2 State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China Received 13 August 2018/Accepted 30 June 2019/Published online 10 February 2020 Abstract Stream cipher is an important branch of symmetric cryptosystems, which takes obvious advan- tages in speed and scale of hardware implementation. It is suitable for using in the cases of massive data transfer or resource constraints, and has always been a hot and central research topic in cryptography. With the rapid development of network and communication technology, cipher algorithms play more and more crucial role in information security. Simultaneously, the application environment of cipher algorithms is in- creasingly complex, which challenges the existing cipher algorithms and calls for novel suitable designs. To accommodate new strict requirements and provide systematic scientific basis for future designs, this paper reviews the development history of stream ciphers, classifies and summarizes the design principles of typical stream ciphers in groups, briefly discusses the advantages and weakness of various stream ciphers in terms of security and implementation. Finally, it tries to foresee the prospective design directions of stream ciphers. Keywords stream cipher, survey, lightweight, authenticated encryption, homomorphic encryption Citation Jiao L, Hao Y L, Feng D G. Stream cipher designs: a review. Sci China Inf Sci, 2020, 63(3): 131101, https://doi.org/10.1007/s11432-018-9929-x 1 Introduction The widely applied e-commerce, e-government, along with the fast developing cloud computing, big data, have triggered high demands in both efficiency and security of information processing.
    [Show full text]
  • Copyright Infringement
    COPYRIGHT INFRINGEMENT Mark Miller Jackson Walker L.L.P. 112 E. Pecan, Suite 2400 San Antonio, Texas 78205 (210) 978-7700 [email protected] This paper was first published in the State Bar of Texas Corporate Counsel Section Corporate Counsel Review, Vol. 30, No. 1 (2011) The author appreciates the State Bar’s permission to update and re-publish it. THE AUTHOR Mark Miller is a shareholder with Jackson Walker L.L.P., a Texas law firm with offices in San Antonio, Dallas, Houston, Austin, Ft. Worth, and San Angelo. He is Chair of the firm’s intellectual property section and concentrates on transactions and litigation concerning intellectual property, franchising, and antitrust. Mr. Miller received his B.A. in Chemistry from Austin College in 1974 and his J.D. from St. Mary’s University in 1978. He was an Associate Editor for St. Mary’s Law Journal; admitted to practice before the United States Patent and Trademark Office in 1978; served on the Admissions Committee for the U.S. District Court, Western District of Texas, and been selected as one of the best intellectual property lawyers in San Antonio. He is admitted to practice before the United States Supreme Court, the Federal Circuit Court of Appeals, the United States Court of Appeals for the Fifth and Tenth Circuits, the District Courts for the Western, Southern, and Northern Districts of Texas, and the Texas Supreme Court. He is a member of the American Bar Association’s Forum Committee on Franchising, and the ABA Antitrust Section’s Committee on Franchising. Mr. Miller is a frequent speaker and writer, including “Neglected Copyright Litigation Issues,” State Bar of Texas, Intellectual Property Section, Annual Meeting, 2009, “Unintentional Franchising,” 36 St.
    [Show full text]
  • MQ Challenge: Hardness Evaluation of Solving MQ Problems
    MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems * * y * z * x Takanori Yasuda Xavier Dahan Yun-Ju Huang Tsuyoshi Takagi * { Kouichi Sakurai Abstract rity of MPKC is thus based on the one-wayness of the multivariate polynomial maps. In the same vein, Multivariate polynomial (MP) problem is the basis of QUAD [3] is a stream cipher (symmetric key cryp­ security for potentially post-quantum cryptosystems. tography) whose security is guaranteed by the one­ The hardness of solving MP problem depends on a wayness of the multivariate polynomial maps. number of parameters, most importantly the number The one-wayness of multivariate polynomial maps of variables and the degree of the polynomials, as resides in the difficulty to find solutions of a system of well as the number of equations, the size of the base multivariate polynomial equations (MP problem). In field etc. When the degree is two, we investigate the particular, if the multivariate polynomials involved in relation among these parameters and the hardness a MP problem consist only of quadratic polynomials, of solving MP problem, in order to construct hard the problem is called MQ problem: instances of MP problem. These instances are X X used to create a challenge, which may be helpful in (1) (1) (1) f1(x1; : : : ; xn) = aij xixj + bi xi + c = d1; determining appropriate parameters for multivariate 1 i j n 1 i n X X (2) (2) public key cryptosystems, and stimulate furthermore (2) f2(x1; : : : ; xn) = aij xixj + bi xi + c = d2; the research in solving MP problem. 1 i j n 1 i n .
    [Show full text]
  • LNCS 4593, Pp
    Analysis of QUAD Bo-Yin Yang1,OwenChia-HsinChen2, Daniel J. Bernstein3, and Jiun-Ming Chen4 1 Academia Sinica and Taiwan Information Security Center [email protected] 2 National Taiwan University [email protected] 3 University of Illinois at Chicago [email protected] 4 Nat’l Taiwan University and Nat’l Cheng Kung University [email protected] Abstract. In a Eurocrypt 2006 article entitled “QUAD: A Practical Stream Cipher with Provable Security,” Berbain, Gilbert, and Patarin introduced QUAD, a parametrized family of stream ciphers. The arti- cle stated that “the security of the novel stream cipher is provably reducible to the intractability of the MQ problem”; this reduction de- duces the infeasibility of attacks on QUAD from the hypothesized infeasi- bility (with an extra looseness factor) of attacks on the well-known hard problem of solving systems of multivariate quadratic equations over fi- nite fields. The QUAD talk at Eurocrypt 2006 reported speeds for QUAD instances with 160-bit state and output block over the fields GF(2), GF(16), and GF(256). This paper discusses both theoretical and practical aspects of attack- ing QUAD and of attacking the underlying hard problem. For example, this paper shows how to use XL-Wiedemann to break the GF(256) instance QUAD(256, 20, 20) in approximately 266 Opteron cycles, and to break the underlying hard problem in approximately 245 cycles. For each of the QUAD parameters presented at Eurocrypt 2006, this analysis shows the implications and limitations of the security proofs, pointing out which QUAD instances are not secure, and which ones will never be proven se- cure.
    [Show full text]
  • Voice Encryption Using Twin Stream Cipher Algorithm تشفير الصوت باستخدام خوارزمية التوأم
    Voice Encryption Using Twin Stream Cipher Algorithm تشفير الصوت باستخدام خوارزمية التوأم اﻻنسيابية Prepared by Omar Mejbel Hammad Aljouani ((401320142)) Supervisor Dr. Hebah H. O. Nasereddin Dr. Abdulkareem O. Ibadi Master Thesis Submitted in Partial Fulfillment of the Requirements of the Master Degree in Computer Science Department of Computer Science Faculty of Information Technology Middle East University Amman - Jordan January - 2016 II ((بسم هللا الرحمن الرحيم(( ّ يَ ْر ف عَََللاَهَا ّل ذي نََآ مَ هنواَ م ْن هك ْمََ وَا ّلَ ذي نََ} ه ه ْ ْ {أَوتواَال عل مََ دَ ر جات ))صدق هللا العظيم(( II III IV Acknowledgment I utilize this opportunity to thank everyone helped me reach this stage and everyone who encourage me during performing this thesis. I want to thank Dr. Hebah H. O. Nasereddin for her guidance and supervision during writing this thesis. Extended thanks are also for my family and friends who encourage me during writing this thesis. I also want to thank everyone who believes that the knowledge is right for everyone. The greatest thank ever to assistant prof. Abdulkareem O. Ibadi, the head of software engineering department at Baghdad College for economic sciences. V Dedication اهدي خﻻصة جهدي العلمي المتواضع الى : قرة عيني الرسول محمد عليه افضل الصﻻة واتم التسليم ...... وطني العراق الجريح .................................... اخي الشهيد الحاضر الغائب صهيب ................... والدي ووالدتي واختي رفاق دربي ومسيرتي ............... كل من كان له بصمة بجهدي العلمي هذا............. كل الشهداء الذين استشهدوا برصاص الغدر والخيانة ...... كل من كان يدعي لي ويوجهني ويتمنى لي الخير ......... جامعة بغداد أخص بها كلية التربية ابن الهيثم ....... اﻻعدادية المركزية للبنين .................. VI Table of Contents AUTHORIZATION STATEMENT ..........................................................
    [Show full text]