A Explication of the RSA Algorithm

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Term Paper



Subject: Information System and Cyber Laws

Bachelor of Technology
Computer Science & Engineering
Session: 2012-13

Submitted to: Submitted by:
Ms. Shruti Saxena Arpit Varshney
Roll No.1012210026
Group: 61



Affiliated to



* RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem.

* RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described the algorithm in 1977. 

* Clifford Cocks, an English mathematician, had developed an equivalent system in 1973, but it was classified until 1997

* The RSA scheme is a block cipher in which the plain text and cipher text are integers between 0 and n-1 for some n.

* A Typical size of n is 1024 bits or 309 decimal digits.

* This is a public key encryption scheme.

* In this scheme two pairs of integers {e, n} and {d, n} are used. First of them i.e. {e.n} is called the RSA public key and the other one i.e. {d, n} is called the RSA secret key.

* The sender uses the public key and encrypts the message say M into cipher text as – C = M^e mod n.
C is the cipher text and M is the message or the plane text * At the receiving end the receiver accept the cipher text C and decrypt the C into M using secret key {d, n}- M = C^d mod n.


History and implementation :-

The RSA algorithm was publicly described in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT; the letters RSA are the initials of their surnames, listed in the same order as on the paper. MIT was granted U.S. Patent 4,405,829 for a "Cryptographic communications system and method" that used the algorithm in 1983. The patent would have expired on September 21, 2000 (the term of patent was 17 years at the time), but the algorithm was released to the public domain by RSA Security on 6 September 2000, two weeks earlier. Since a paper describing the algorithm had been published in August 1977, prior to the December 1977 filing date of the patent application, regulations in much of the rest of the world precluded patents elsewhere and only the US patent was granted. Had Cocks' work been publicly known, a patent in the US might not have been possible, either. From the DWPI's abstract of the patent,

The system includes a communications channel coupled to at least one terminal having an encoding device and to at least one terminal having a decoding device. A message-to-be-transferred is enciphered to cipher text at the encoding terminal by encoding the message as a number M in a predetermined set. That number is then raised to a first predetermined power (associated with the intended receiver) and finally computed. The remainder or residue, C, is... computed when the exponentiated number is divided by the product of two predetermined prime numbers (associated with the intended receiver). Clifford Cocks, an English mathematician working for the UK intelligence agency GCHQ, described an equivalent system in an internal document in 1973, but given the relatively expensive computers needed to implement it at the time, it was mostly considered a curiosity and, as far as is publicly known, was never deployed. His discovery, however, was not revealed until 1998 due to its top-secret classification, and Rivest, Shamir, and Adleman devised RSA independently of Cocks' work.


The RSA algorithm involves three steps:-
1)key Generation

RSA involves a public key and a private key. The public key can be known to everyone and is used for encrypting...
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