BY- ARUSH SAXENA

(HOTBURN)

Review of Cryptography and its terms -oEncryption,

oDecryption,

oAuthentication,

oDigital signature.

What is RSA ? Key Generation Algorithm Encryption Decryption

Usage of RSA RSA Security Implementation Tools

decryption

algorithm

encryption

algorithmmessage

message

Transmission Channel

encryption key

decryption key

Encryption: The transformation of data into a formunreadable by anyone is known as encryption.

Decryption: It is the opposite of encryption. It mayrequire secret decryption key.

Authentication: Authentication in a digital setting is aprocess whereby the receiver of a digital message canbe confident of the identity of the sender and/or theintegrity of the message. Authentication protocols canbe based on either conventional secret-keycryptosystems like DES or on public-key systems likeRSA; authentication in public-key systems uses digitalsignatures.

Digital Signature: It is an unforgeable piece of dataasserting that a named person wrote or otherwiseagreed to the document to which the signature isattached.

Public Key algorithm invented in 1977 by Ron

Rivest, Adi Shamir and Leonard Adleman (RSA).

Supports Encryption and Digital Signature.

Most Widely used public Key Algorithm.

Gets its security from integer factorization

Problem.

Relatively easy to understand and implement.

A public encryption method that relies on a public encryption algorithm, a public decryption algorithm, and a public encryption key.

Using the public key and encryption algorithm, everyone can encrypt a message.

The decryption key is known only to authorized parties.

p and q are two prime numbers. n = pq pi = (p-1)(q-1)Choose e is such that 1 < e < pi and gcd(pi,e) = 1.Compute d is such that d=e-1 mod(pi). The public key is (n, e) and the private key is (n,

d).

Sender ‘A’ does the following:-• Obtains the public key (n, e).

• Represents the plaintext message as a positive

integerm.

• Computes the ciphertext c = me mod n.

• Sends the ciphertext c to ‘B’.

Recipient B does the following:-• Uses his private key (n, d) to compute

m = cd mod n.

• Extracts the plaintext from the message

representativem.

RSA is used in security protocols such as:-IPSEC -- IP Data Security

-TLS/SSL -- transport data security (web)

-PGP -- email security

-SSH -- terminal connection security

-SILC -- conferencing service security

RSA gets its security from factorization problem. Difficulty of factoring large numbers is the basis of security of RSA. Over 1000 bits long numbers are used.

Integer factorization problem (finding number's prime factors):o Positive integer n, find its prime factors: n = p1 p2 ... pi

where, pi is positive distinct prime number. Example: 257603 = 41 * 61 * 103

o Factorization algorithms can be used to factor faster than brute forcing: Trial division, Pollard's rho, Pollard's p-1, Quadratic sieve, elliptic curve factorization, Random square factoring, Number field sieve, etc.

In order to implement RSA one requiresArbitrary Precision Arithmetic

Pseudo Random Number Generator(PRNG)

Prime Number Generator