(Pseudo) Random Number Generation for Cryptography
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Sensor-Seeded Cryptographically Secure Random Number Generation
International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8 Issue-3, September 2019 Sensor-Seeded Cryptographically Secure Random Number Generation K.Sathya, J.Premalatha, Vani Rajasekar Abstract: Random numbers are essential to generate secret keys, AES can be executed in various modes like Cipher initialization vector, one-time pads, sequence number for packets Block Chaining (CBC), Cipher Feedback (CFB), Output in network and many other applications. Though there are many Feedback (OFB), and Counter (CTR). Pseudo Random Number Generators available they are not suitable for highly secure applications that require high quality randomness. This paper proposes a cryptographically secure II. PRNG IMPLEMENTATIONS pseudorandom number generator with its entropy source from PRNG requires the seed value to be fed to a sensor housed on mobile devices. The sensor data are processed deterministic algorithm. Many deterministic algorithms are in 3-step approach to generate random sequence which in turn proposed, some of widely used algorithms are fed to Advanced Encryption Standard algorithm as random key to generate cryptographically secure random numbers. Blum-Blum-Shub algorithm uses where X0 is seed value and M =pq, p and q are prime. Keywords: Sensor-based random number, cryptographically Linear congruential Generator uses secure, AES, 3-step approach, random key where is the seed value. Mersenne Prime Twister uses range of , I. INTRODUCTION where that outputs sequence of 32-bit random Information security algorithms aim to ensure the numbers. confidentiality, integrity and availability of data that is transmitted along the path from sender to receiver. All the III. SENSOR-SEEDED PRNG security mechanisms like encryption, hashing, signature rely Some of PRNGs uses clock pulse of computer system on random numbers in generating secret keys, one time as seeds. -
A Secure Authentication System- Using Enhanced One Time Pad Technique
IJCSNS International Journal of Computer Science and Network Security, VOL.11 No.2, February 2011 11 A Secure Authentication System- Using Enhanced One Time Pad Technique Raman Kumar1, Roma Jindal 2, Abhinav Gupta3, Sagar Bhalla4 and Harshit Arora 5 1,2,3,4,5 Department of Computer Science and Engineering, 1,2,3,4,5 D A V Institute of Engineering and Technology, Jalandhar, Punjab, India. Summary the various weaknesses associated with a password have With the upcoming technologies available for hacking, there is a come to surface. It is always possible for people other than need to provide users with a secure environment that protect their the authenticated user to posses its knowledge at the same resources against unauthorized access by enforcing control time. Password thefts can and do happen on a regular basis, mechanisms. To counteract the increasing threat, enhanced one so there is a need to protect them. Rather than using some time pad technique has been introduced. It generally random set of alphabets and special characters as the encapsulates the enhanced one time pad based protocol and provides client a completely unique and secured authentication passwords we need something new and something tool to work on. This paper however proposes a hypothesis unconventional to ensure safety. At the same time we need regarding the use of enhanced one time pad based protocol and is to make sure that it is easy to be remembered by you as a comprehensive study on the subject of using enhanced one time well as difficult enough to be hacked by someone else. -
A Note on Random Number Generation
A note on random number generation Christophe Dutang and Diethelm Wuertz September 2009 1 1 INTRODUCTION 2 \Nothing in Nature is random. number generation. By \random numbers", we a thing appears random only through mean random variates of the uniform U(0; 1) the incompleteness of our knowledge." distribution. More complex distributions can Spinoza, Ethics I1. be generated with uniform variates and rejection or inversion methods. Pseudo random number generation aims to seem random whereas quasi random number generation aims to be determin- istic but well equidistributed. 1 Introduction Those familiars with algorithms such as linear congruential generation, Mersenne-Twister type algorithms, and low discrepancy sequences should Random simulation has long been a very popular go directly to the next section. and well studied field of mathematics. There exists a wide range of applications in biology, finance, insurance, physics and many others. So 2.1 Pseudo random generation simulations of random numbers are crucial. In this note, we describe the most random number algorithms At the beginning of the nineties, there was no state-of-the-art algorithms to generate pseudo Let us recall the only things, that are truly ran- random numbers. And the article of Park & dom, are the measurement of physical phenomena Miller (1988) entitled Random generators: good such as thermal noises of semiconductor chips or ones are hard to find is a clear proof. radioactive sources2. Despite this fact, most users thought the rand The only way to simulate some randomness function they used was good, because of a short on computers are carried out by deterministic period and a term to term dependence. -
A Low-Latency Block Cipher for Pervasive Computing Applications Extended Abstract?
PRINCE { A Low-latency Block Cipher for Pervasive Computing Applications Extended Abstract? Julia Borghoff1??, Anne Canteaut1;2???, Tim G¨uneysu3, Elif Bilge Kavun3, Miroslav Knezevic4, Lars R. Knudsen1, Gregor Leander1y, Ventzislav Nikov4, Christof Paar3, Christian Rechberger1, Peter Rombouts4, Søren S. Thomsen1, and Tolga Yal¸cın3 1 Technical University of Denmark 2 INRIA, Paris-Rocquencourt, France 3 Ruhr-University Bochum, Germany 4 NXP Semiconductors, Leuven, Belgium Abstract. This paper presents a block cipher that is optimized with respect to latency when implemented in hardware. Such ciphers are de- sirable for many future pervasive applications with real-time security needs. Our cipher, named PRINCE, allows encryption of data within one clock cycle with a very competitive chip area compared to known solutions. The fully unrolled fashion in which such algorithms need to be implemented calls for innovative design choices. The number of rounds must be moderate and rounds must have short delays in hardware. At the same time, the traditional need that a cipher has to be iterative with very similar round functions disappears, an observation that increases the design space for the algorithm. An important further requirement is that realizing decryption and encryption results in minimum additional costs. PRINCE is designed in such a way that the overhead for decryp- tion on top of encryption is negligible. More precisely for our cipher it holds that decryption for one key corresponds to encryption with a re- lated key. This property we refer to as α-reflection is of independent interest and we prove its soundness against generic attacks. 1 Introduction The area of lightweight cryptography, i.e., ciphers with particularly low imple- mentation costs, has drawn considerable attention over the last years. -
Lecture Notes on Error-Correcting Codes and Their Applications to Symmetric Cryptography
Lecture Notes on Error-Correcting Codes and their Applications to Symmetric Cryptography Anne Canteaut Inria [email protected] https://www.rocq.inria.fr/secret/Anne.Canteaut/ version: December 4, 2017 Contents 10 Reed-Muller Codes and Boolean Functions 5 10.1 Boolean functions and their representations . .5 10.1.1 Truth table and Algebraic normal form . .5 10.1.2 Computing the Algebraic Normal Form . .8 10.2 Reed-Muller codes . 11 10.2.1 Definition . 11 10.2.2 The (uju + v) construction . 12 10.3 Weight distributions of Reed-Muller codes . 13 10.3.1 Minimum distance of R(r; m) ........................ 13 10.3.2 Weight distribution of R(1; m) ....................... 14 10.3.3 Weight distribution of R(m − 1; m) ..................... 15 10.3.4 Weight distribution of R(2; m) ....................... 15 10.3.5 Duality . 15 10.3.6 Other properties of the weights of R(r; m) ................. 17 11 Stream Cipher Basics 19 11.1 Basic principle . 19 11.1.1 Synchronous additive stream ciphers . 19 11.1.2 Pseudo-random generators . 21 11.1.3 General functionalities of stream ciphers and usage . 22 11.2 Models of attacks . 23 11.3 Generic attacks on stream ciphers . 24 11.3.1 Period of the sequence of internal states . 24 11.3.2 Time-Memory-Data Trade-off attacks . 27 11.3.3 Statistical tests . 36 11.4 The main families of stream ciphers . 37 11.4.1 Information-theoretically generators . 37 11.4.2 Generators based on a difficult mathematical problem . 38 11.4.3 Generators based on block ciphers . -
Cryptanalysis of the Random Number Generator of the Windows Operating System
Cryptanalysis of the Random Number Generator of the Windows Operating System Leo Dorrendorf School of Engineering and Computer Science The Hebrew University of Jerusalem 91904 Jerusalem, Israel [email protected] Zvi Gutterman Benny Pinkas¤ School of Engineering and Computer Science Department of Computer Science The Hebrew University of Jerusalem University of Haifa 91904 Jerusalem, Israel 31905 Haifa, Israel [email protected] [email protected] November 4, 2007 Abstract The pseudo-random number generator (PRNG) used by the Windows operating system is the most commonly used PRNG. The pseudo-randomness of the output of this generator is crucial for the security of almost any application running in Windows. Nevertheless, its exact algorithm was never published. We examined the binary code of a distribution of Windows 2000, which is still the second most popular operating system after Windows XP. (This investigation was done without any help from Microsoft.) We reconstructed, for the ¯rst time, the algorithm used by the pseudo- random number generator (namely, the function CryptGenRandom). We analyzed the security of the algorithm and found a non-trivial attack: given the internal state of the generator, the previous state can be computed in O(223) work (this is an attack on the forward-security of the generator, an O(1) attack on backward security is trivial). The attack on forward-security demonstrates that the design of the generator is flawed, since it is well known how to prevent such attacks. We also analyzed the way in which the generator is run by the operating system, and found that it ampli¯es the e®ect of the attacks: The generator is run in user mode rather than in kernel mode, and therefore it is easy to access its state even without administrator privileges. -
Stream Ciphers
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by HAL-CEA Stream ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression Anne Canteaut, Sergiu Carpov, Caroline Fontaine, Tancr`edeLepoint, Mar´ıa Naya-Plasencia, Pascal Paillier, Renaud Sirdey To cite this version: Anne Canteaut, Sergiu Carpov, Caroline Fontaine, Tancr`edeLepoint, Mar´ıaNaya-Plasencia, et al.. Stream ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression. FSE 2016 : 23rd International Conference on Fast Software Encryption, Mar 2016, Bochum, Germany. Springer, 9783 - LNCS (Lecture Notes in Computer Science), pp.313-333, Fast Software Encryption 23rd International Conference, FSE 2016, Bochum, Germany, March 20- 23, 2016, <http://fse.rub.de/>. <10.1007/978-3-662-52993-5 16>. <hal-01280479> HAL Id: hal-01280479 https://hal.archives-ouvertes.fr/hal-01280479 Submitted on 28 Nov 2016 HAL is a multi-disciplinary open access L'archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destin´eeau d´ep^otet `ala diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publi´esou non, lished or not. The documents may come from ´emanant des ´etablissements d'enseignement et de teaching and research institutions in France or recherche fran¸caisou ´etrangers,des laboratoires abroad, or from public or private research centers. publics ou priv´es. Stream ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression? -
Random Number Generation Using MSP430™ Mcus (Rev. A)
Application Report SLAA338A–October 2006–Revised May 2018 Random Number Generation Using MSP430™ MCUs ......................................................................................................................... MSP430Applications ABSTRACT Many applications require the generation of random numbers. These random numbers are useful for applications such as communication protocols, cryptography, and device individualization. Generating random numbers often requires the use of expensive dedicated hardware. Using the two independent clocks available on the MSP430F2xx family of devices, software can generate random numbers without such hardware. Source files for the software described in this application report can be downloaded from http://www.ti.com/lit/zip/slaa338. Contents 1 Introduction ................................................................................................................... 1 2 Setup .......................................................................................................................... 1 3 Adding Randomness ........................................................................................................ 2 4 Usage ......................................................................................................................... 2 5 Overview ...................................................................................................................... 2 6 Testing for Randomness................................................................................................... -
A Bibliography of Papers in Lecture Notes in Computer Science (2002) (Part 2 of 4)
A Bibliography of Papers in Lecture Notes in Computer Science (2002) (Part 2 of 4) Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 02 May 2020 Version 1.11 Title word cross-reference -adic [1754, 1720]. -Center [1691]. -D [1664, 84, 1060, 1019, 1637, 1647, 1364]. -Gram [1705]. -Level [50]. -List [1694]. -nearest [408]. -Partition [434]. -SAT (3; 3) [1732]. 0 [426]. 1 [426, 1647]. 1=f [420]. -Split [1732]. -Stability [164]. -Stage [1260]. 168 [1729]. 2 [1662]. -Tier [1430]. [1740, 943, 1677, 420, 50, 1732]. 3 [146, 154, 18, 1094, 1033, 1664, 196, 992, 1020, .NET [88]. 1065, 84, 29, 1640, 1075, 1093, 1662, 1023, 142, 1011, 1019, 1637, 30, 219, 1364, 1107, 1430]. /Geom/c [659]. 3 × 3 [536]. 4 [1060]. 8 · 168 [1729]. (G) [659]. 2 [1056]. st [208]. TM [596]. [213]. 2 1003.1q [1336]. 128 [1540]. 1980-88 [19]. ax7 + bx + c [1729]. ax8 + bx + c [1729]. ∆ 1989-1997 [20]. [1694]. Dy2 = x3 [1735]. k [1701, 434, 1677, 408, 1691]. kth [1711]. 2 [637]. 21 [208]. 2nd [1247]. MIN ERVA [292]. NEMESIS [358]. p [1754]. n [301]. N = pq [1752]. P [164, 1720]. 3G [649, 102, 640]. 3GPP [673]. 3rd [709]. Ψ [285]. q [1705]. x [1735]. y00 = f(x; y) [164]. 1 2 90 [186]. 95 [1328, 1329]. -
Improved Correlation Attacks on SOSEMANUK and SOBER-128
Improved Correlation Attacks on SOSEMANUK and SOBER-128 Joo Yeon Cho Helsinki University of Technology Department of Information and Computer Science, Espoo, Finland 24th March 2009 1 / 35 SOSEMANUK Attack Approximations SOBER-128 Outline SOSEMANUK Attack Method Searching Linear Approximations SOBER-128 2 / 35 SOSEMANUK Attack Approximations SOBER-128 SOSEMANUK (from Wiki) • A software-oriented stream cipher designed by Come Berbain, Olivier Billet, Anne Canteaut, Nicolas Courtois, Henri Gilbert, Louis Goubin, Aline Gouget, Louis Granboulan, Cedric` Lauradoux, Marine Minier, Thomas Pornin and Herve` Sibert. • One of the final four Profile 1 (software) ciphers selected for the eSTREAM Portfolio, along with HC-128, Rabbit, and Salsa20/12. • Influenced by the stream cipher SNOW and the block cipher Serpent. • The cipher key length can vary between 128 and 256 bits, but the guaranteed security is only 128 bits. • The name means ”snow snake” in the Cree Indian language because it depends both on SNOW and Serpent. 3 / 35 SOSEMANUK Attack Approximations SOBER-128 Overview 4 / 35 SOSEMANUK Attack Approximations SOBER-128 Structure 1. The states of LFSR : s0,..., s9 (320 bits) −1 st+10 = st+9 ⊕ α st+3 ⊕ αst, t ≥ 1 where α is a root of the primitive polynomial. 2. The Finite State Machine (FSM) : R1 and R2 R1t+1 = R2t ¢ (rtst+9 ⊕ st+2) R2t+1 = Trans(R1t) ft = (st+9 ¢ R1t) ⊕ R2t where rt denotes the least significant bit of R1t. F 3. The trans function Trans on 232 : 32 Trans(R1t) = (R1t × 0x54655307 mod 2 )≪7 4. The output of the FSM : (zt+3, zt+2, zt+1, zt)= Serpent1(ft+3, ft+2, ft+1, ft)⊕(st+3, st+2, st+1, st) 5 / 35 SOSEMANUK Attack Approximations SOBER-128 Previous Attacks • Authors state that ”No linear relation holds after applying Serpent1 and there are too many unknown bits...”. -
Random-Number Functions
Title stata.com Random-number functions Contents Functions Remarks and examples Methods and formulas Acknowledgments References Also see Contents rbeta(a,b) beta(a,b) random variates, where a and b are the beta distribution shape parameters rbinomial(n,p) binomial(n,p) random variates, where n is the number of trials and p is the success probability rcauchy(a,b) Cauchy(a,b) random variates, where a is the location parameter and b is the scale parameter rchi2(df) χ2, with df degrees of freedom, random variates rexponential(b) exponential random variates with scale b rgamma(a,b) gamma(a,b) random variates, where a is the gamma shape parameter and b is the scale parameter rhypergeometric(N,K,n) hypergeometric random variates rigaussian(m,a) inverse Gaussian random variates with mean m and shape param- eter a rlaplace(m,b) Laplace(m,b) random variates with mean m and scale parameter b p rlogistic() logistic variates with mean 0 and standard deviation π= 3 p rlogistic(s) logistic variates with mean 0, scale s, and standard deviation sπ= 3 rlogistic(m,s) logisticp variates with mean m, scale s, and standard deviation sπ= 3 rnbinomial(n,p) negative binomial random variates rnormal() standard normal (Gaussian) random variates, that is, variates from a normal distribution with a mean of 0 and a standard deviation of 1 rnormal(m) normal(m,1) (Gaussian) random variates, where m is the mean and the standard deviation is 1 rnormal(m,s) normal(m,s) (Gaussian) random variates, where m is the mean and s is the standard deviation rpoisson(m) Poisson(m) -
A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications
Special Publication 800-22 Revision 1a A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications AndrewRukhin,JuanSoto,JamesNechvatal,Miles Smid,ElaineBarker,Stefan Leigh,MarkLevenson,Mark Vangel,DavidBanks,AlanHeckert,JamesDray,SanVo Revised:April2010 LawrenceE BasshamIII A Statistical Test Suite for Random and Pseudorandom Number Generators for NIST Special Publication 800-22 Revision 1a Cryptographic Applications 1 2 Andrew Rukhin , Juan Soto , James 2 2 Nechvatal , Miles Smid , Elaine 2 1 Barker , Stefan Leigh , Mark 1 1 Levenson , Mark Vangel , David 1 1 2 Banks , Alan Heckert , James Dray , 2 San Vo Revised: April 2010 2 Lawrence E Bassham III C O M P U T E R S E C U R I T Y 1 Statistical Engineering Division 2 Computer Security Division Information Technology Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899-8930 Revised: April 2010 U.S. Department of Commerce Gary Locke, Secretary National Institute of Standards and Technology Patrick Gallagher, Director A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS Reports on Computer Systems Technology The Information Technology Laboratory (ITL) at the National Institute of Standards and Technology (NIST) promotes the U.S. economy and public welfare by providing technical leadership for the nation’s measurement and standards infrastructure. ITL develops tests, test methods, reference data, proof of concept implementations, and technical analysis to advance the development and productive use of information technology. ITL’s responsibilities include the development of technical, physical, administrative, and management standards and guidelines for the cost-effective security and privacy of sensitive unclassified information in Federal computer systems.