An RSA-Type OTP Generator

An RSA-Type OTP GeneratorAn RSA-Type OTP GeneratorAiswarya Vinayachandran,Sivasankar MAbstract elemental and secure authentication protocols argon in great demand overdue to the ever expanding use of internet for financial and meat confabulations. Multi incidentor authentication, in fussy 2Factor h everymark (2FA) is preferred to unchanging passwords- further authentication. One Time Passwords (OTPs) play a vital role in the construction of 2FA protocols. In this paper, an economical OTP extension algorithm, based on RSA scheme is discussed. capital punishment and computational issues related to the algorithm atomic number 18 also discussed.Keywords Authentication, RSA, One Time Password, LFSR, Primitive Element1. showationThese days, almost all our day to day activities, starting from buying vegetables to conflict a movie ticket depend on internet. As passing private data is being communicated between the server and the client, secure protocols are required for protect ing these transactions from attackers. Over the years, we realized that encryption methods unsocial are non qualified to secure online transactions. Hence evolved the idea of displace many(prenominal) message each conviction personally to the user and make him to send back the message along with his/her password to complete the transaction. This provides a certify layer of security measure and strength to the existing belief of static passwords.In this paper, we present a substance to retrovert OTPs, based on RSA type exp single(a)ntiation. This research paper is organised as Section 2 explains authentication help Section 3 presently discusses the conventional way of OTP genesis Section 4 is the proposed algorithm Section 5 discusses near the haphazardness in the generation of the OTPs Section 6 analyses the operational complexness and security of the proposed algorithm Section 7 gives some concluding remarks.2. AuthenticationAuthentication is the process of iden tifying the legitimate user 1. The identity is proven by sundry(a) cryptographic methods w here the user has to enter some input to the system. This toilette range from simply entering a password to more complicate security mechanisms like biometrics, strings displayed by tokens, key encryptions. Based on this input, the system volition identify and authenticate the person. After authentication, comes authorization, where the system identifies the various privileges available to the user. Only authorized users hind end get access to the data as not all the users will see the said(prenominal) privileges. near users will be allowed to only read the data while some users will be allowed to read as well as transform it.2.1. Message AuthenticationMessage authentication is utilise to check if the true message has been tampered in the middle of the communication melodic phrase. Message authentication is used to protect the integrity of the message wherein the receiver should be notified if any ph angiotensin converting enzyme numbers in the message are modified, removed or extra bits are added during the communication. This is achieved by sending a message digest usually hash of the message will be the digest together with the message. If the receiver also is obtaining the same digest over the received message then he/she stick out be sure of the integrity of the message.2.2. Entity AuthenticationEntity authentication is the process in which an entity (machine/human) in a distri simplyed ne 2rk will get belief on another entity (machine/human) based on a key already launch between them. The idea is that the key is kept secret and only the twain genuine communicating entities know the secret key.Machine authentication is achieved finished the verification of material bodyal credentials or buildal certificates. Digital security are like a machine provided ID and password or a digital certificated issued by a Certifying Authority (CA). It is like a digital passport that provides trusted identification. Digital Signature is a numerical technique used to validate the authenticity of a digital document, software package or a message. It is used to identify whether a communication is impersonalized. mankind based authentication relies on at least one of the triad key factors something the user knows (a password or an answer to a security question), something the user possesses (an object for authentication, say smart card), and something the user is (behavioural or physiological characteristics of the individual say, finger print and retina s bottomning).3. effected OTP GeneratorsOTP is an authentication technique, which comes in the second layer of authentication protocols after static passwords. An OTP is valid only for a single transaction. Even if an attacker succeeds in decrypting the password of a user, he/she has to get the OTP generated to validate the transaction. Since OTP is based on randomness/collision resistanc e, it is genuinely difficult to gibe an OTP. Even if the attacker succeeds in acquiring an OTP, he may not be able to predict the next OTP.OTP generation is based on hashing algorithms. Hashing is an irreversible process, i.e. for an input we can get the output, but with the obtained output we cannot get back the input. Even if an attacker obtains many OTPs, it is of no use as he/she cannot find a pattern to jeopardize the seed used to generate the OTPs. An OTP is valid for a limited time, for the most part dickens to fifteen minutes based on the web identifys restrictions. Also in online transactions, while entering an OTP, a user is allowed to make errors only a limited number of times, say doubly or thrice, which again adds to its security.A most common way of generating a sequence of OTPs2 is described in algorithm 1.Algorithm 1 Conventional OTP multiplication AlgorithmNote that the weakness of the OTP mechanism lies on the channel used to send the OTP and the security of the device to which the OTP is send. It will be advisable to secure the device with some biometric credentials making it totally safe.4 Proposed RSA type OTP Generating AlgorithmAfter the invention of public key cryptography, encrypted communication reached the next level. In general, public key cryptography relies on some hard mathematical problems like Integer Factorisation Problem (IFP), discrete Logarithm Problem (DLP) 3.As our proposed OTP generation is based on RSA crypto-system, we briefly do a recap of RSA encryption 4.4.1 The RSA AlgorithmThe Rivest-Shamir-Adleman (RSA) algorithm is one of the popular and secure publickey encryption methods. The security of the algorithm relies on the fact that there is no efficient way to factor very monolithic numbers. Using an encryption key (e, N), the algorithm is as followsChoose two very adult prime numbers, p and q Set N be to p.q.Choose any outsized integer, d, such(prenominal) that gcd(d, (N) ) = 1.Find e such that e.d = 1 (mod (N)) The encryption key (e,n) is made public. The decryption key d is kept private by the user.Represent the message as an integer between 0 and (N-1).Encrypt the message by raising it to the eth causation mod n. The consequence is the cipher schoolbook C.To decrypt the cipher text message C, raise it to the power d mod n4.2 Proposed OTP Generation TechniqueOur proposed algorithm is based on RSA encryption/decryption process and is described in Algorithm 2 below.Algorithm 2 Proposed AlgorithmThe above procedure can be represented by a schematic diagram as in Fig.1.Fig. 1. Architecture of the Proposed Model4.3. A Comment on the Selection of N and the Possible Number of OTPs premise day OTPs are of generally 6 digits in distance. Hence they can range from 000000 to 999999, totalling to 10,00,000. This is so, as we have 10 choices (numbers 0 to 9) for every digit and hence 10.10.10.10.10.10 = 106 = 10,00,000. If we incorporate a module to condition that the first two most si gnificant digits should be non zero, even then 9.9.10.10.10.10 = 8,10,000 OTPs are available. In our proposed algorithm, if we require 6 digit OTPs, we can select N nigh to the integer 999999. For example a choice of 991 . 997 = 988027 will be sufficient for our implementation. As the number of bits used to represent a 6 digit decimal number is approximately 20 bits (log2 999999 =19.93156713), we need to select a 20 bit RSA number for our algorithm. Note that, a 20 bit RSA crypto system can be easily broken by the present day computers when e and N are known outside. But here as the attacker does not know N and a, he/she cannot guess the next OTP, which is some random number that lies between 1 and N-1.The only information that the attacker can get is the current OTP, which is some 6 digit number.5. Randomness in the Generation of the OTPs from ZN*Considering the demand for OTPs and the computational expenses of different exponential algorithms, it is advisable to follow a systemat ic accession for the selection of the random number a 1, 2, ,N1 .We propose two convincing methods for the selection of a.5.1. Linear Feedback Shift Registers (LFSRs)LFSR is a mechanism for generating random numbers based on the initial seed given to it. So if we start with a non-zero 20 bit string, the LFSR can generate all the other 2201 20-bit strings. We refer to 5 for some basic facts about LFSR.An LFSR of length L consists of L stages 0,1 , , L-1, each capable of storing one bit and having one input and output and a clock which controls the movement of data. During each unit of measurement of time the following operations are performed (i) the content of stage 0 is output and forms part of the output sequence (ii) the content of stage i is moved to stage i 1 for each i, 1 i L 1 (iii) the new content of stage L 1 is the feedback bit s which is calculated by adding together modulo 2 the preliminary contents of a fixed subset of stages 0,1, , L 1.We note that for an n- bit LFSR connectionpolynomials are available, where is the Eulers totient function. So, for a six digit OTP, i.e. for a 20 bit string, we have = 24,000 choices. With each connection polynomial, we can generate all the 20-bit strings in different random ways. Since we have 24,000choices, we can assign a single connection polynomial for a single customer, and OTPs generated for each customer will be in entirely different pattern.5.2 Primitive Roots some other mechanism for generating 6 digit random numbers is by utilize the concept of primitive roots.We refer 6 for the concepts related to cyclic groups and generators/primitive elements..Let p be a prime number. Consider Zp*. Let g ZP*. As i vary from 0 to p1, by computing gi mod p, we can generate all elements in Zp*. Here g is called the primitive root/generator of Zp*.As we have selected an RSA number N, which is not a prime number, to follow this kind of random number generation, we can N as a prime number very make full to 9999 99. For example, N = p = 999983 will be sufficient. It is a known result that, if g is a primitive root, then gi is also a primitive root if gcd (i,(p))=1. Hence we are available with ((p)) generators 6. Hence if N = 999983 (a six digit prime), we have ((999983)) =493584 generators which means we have sufficiently large number of primitive roots at our disposal.6. Computational Complexity and protective cover of the Proposed AlgorithmThe proposed algorithm is an RSA-type algorithm which uses standard exponentiation for its computation. The modular exponentiation operation generally consumes a considerable amount of time for large operands as it consists of a series of square-and-multiply operations under a modular value. For a particular user, e will be fixed. Hence the time complexity for ae (mod N) is O(log2e). As RSA is a widely implemented cryptosystem, improvements in modular exponentiation algorithms are evolving very frequently 7. Though the proposed algorithm uses the con cept of RSA with a 20-bit modular (where as the current standard is 256 to 512 bits), since a, e, N are not known publicly we achieve security through obscurity.7. Conclusions and coming(prenominal) WorksIn this paper, we have proposed a new method to generate OTPs and discussed the possible ways of implementing it practically. There may exist other invigorated methods with less time complexity. Incorporating new methods we can design more efficient algorithm for generating OTPs. The possibility of generating alphanumeric OTPs will be also explored, in future.References1Bruce Schneier, Applied Cryptography, Wiley Publications, 2002.2 L. Lamport, Password authentication with insecure communication, communicationsof the ACM,vol.24,no.11, pp.770-772,1981.3 Neal Koblitz, Towards a Quarter Century of Public Key Cryptography, A peculiar(prenominal) Issue ofDesigns, codes and Cryptography, Vol. 19, No. 2/3, Springer, 2000.4 Rivest R. L. ,Shamir A.,Adleman L., A Method for Obtaining Digi tal Signatures andPublic-key Cryptosystems, Communications of the ACM, Vol. 21, No. 2, pp. 120-126, 1978.5 Alfred, J., Van Menezes Paul, C., Oorschot, S., Vanstone, A. Handbook of AppliedCryptography , CRC Press LCC (1996)6 pile K Strayer, Elementary Number Theory ,Waveland Press, 2001.7 Gueron, Shay and Krasnov, Vlad , Software Implementation of Modular Exponentiation, Using Advanced Vector Instructions Architectures , LNCS Vol. 7369, pp.119-135, Springer, 2012.