2. INTRODUCTION TO RSA
RSA Algorithm was discovered by a group of three scientists
namely Ron Rivest,Adi Shamir and Len Adleman and was first
published in 1978.
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.
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3. 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.
Where 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. 3
4. EXAMPLE:
Let , e=3, d=7, n=33.
Suppose the message is ‘SUN’ and we use the
numeric values of the characters according to their
serial in alphabets.
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Plaintext Ciphertext(C) after decryption
Sym num M^3 M^3 mod33 C^7 C^7mod33 sym
S 19 6859 28 13492928512 19 S
U 21 9261 21 1801088541 21 U
N 14 2744 5 78125 14 N
5. KEY GENERATION
Each user generates a public/private key pair by:
selecting two large primes at random - p, q
computing their system modulus N=p.q
note ø(N)=(p-1)(q-1)
selecting at random the encryption key e
where 1<e<ø(N), gcd(e,ø(N))=1
solve following equation to find decryption key d
e.d=1 mod ø(N) and 0≤d≤N
publish their public encryption key: KU={e,N}
keep secret private decryption key: KR={d,p,q} 5
6. To encrypt a message M the sender:
obtains public key of recipient KU={e,N}
computes: C=Me mod N, where 0≤M<N
to decrypt the ciphertext C the owner:
uses their private key KR={d,p,q}
computes: M=Cd mod N
note that the message M must be smaller than the
modulus N (block if needed)
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7. ap-1 mod p = 1
where p is prime and gcd(a,p)=1
also known as Fermat’s Little Theorem
useful in public key and primality testing
when doing arithmetic modulo n
complete set of residues is: 0..n-1
reduced set of residues is those numbers
(residues) which are relatively prime to n
eg for n=10,
complete set of residues is {0,1,2,3,4,5,6,7,8,9}
reduced set of residues is {1,3,7,9}
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8. to compute ø(n) need to count number of elements
to be excluded
in general need prime factorization, but for
p (p prime) ø(p) = p-1
for p.q (p,q prime) ø(p.q) = (p-1)(q-1)
Eg:
ø(37) = 36
ø(21) = (3–1)×(7–1) = 2×6 = 12
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9. a generalisation of Fermat's Theorem
aø(n)mod N = 1
where gcd(a,N)=1
Eg:
a=3;n=10; ø(10)=4;
hence 34 = 81 = 1 mod 10
a=2;n=11; ø(11)=10;
hence 210 = 1024 = 1 mod 11
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10. aø(n)mod N = 1 where gcd(a,N)=1
in RSA have:N=p.q
N)=(p-1)(q-1)
carefully chosen e & d to be inverses mod ø(N)
hence e.d=1+k.ø(N) for some k
hence :
Cd = (Me)d = M1+k.ø(N) = M1.(Mø(N))q = M1.(1)q
= M1 = M mod N
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11. Select primes: p=17 & q=11
Compute n = pq =17×11=187
Compute ø(n)=(p–1)(q-1)=16×10=160
Select e : gcd(e,160)=1; choose e=7
Determine d: de=1 mod 160 and d < 160 Value is
d=23 since 23×7=161= 10×160+1
Publish public key KU={7,187}
Keep secret private key KR={23,17,11}
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RSA EXAMPLE
12. sample RSA encryption/decryption is:
given message M = 88 (nb. 88<187)
encryption:
C = 887 mod 187 = 11
decryption:
M = 1123 mod 187 = 88
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13. APPLICATIONS
RSA is widely used for encryption and decryption in
message communication for making the
communication secure.
It is used for digital signature.
It is used for key distribution.
RSA is used in e-commerce and remote banking.
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14. CONCLUSION
After the study, I find that RSA is a powerful and
most widely used scheme for encryption /
decryption and digital signature. It is more secure
than that of DES and others. But as we know that
the key length for secure RSA use has increased
over recent years, and this has put a heavier
processing load on applications using RSA. This
burden has ramifications, especially for electronic
commerce sites that conduct large numbers of
transactions.
Recently, a competing system has begun to
challenge RSA: elliptic curve cryptography (ECC).
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15. The principal attraction of ECC, compared to RSA,
is that it appears to offer equal security for a far
smaller key size; thereby reducing processing
overhead but the confidence level in ECC is not yet
as high as that is in RSA. Also RSA is
fundamentally easier to explain than that of ECC.
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16. INTRODUCTION TO MD5
MD5 Message Digest is a widely used hash
technique, such that it will produce 128-bit hash
value we need to convert the input data into bytes
in order to convert it to hash value. This is useful in
many security applications and it ensures data
integrity.
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17. ALGORITHM CHARACTERISTICS:-
Message-Digest (Fingerprint) algorithms are special
functions which transform input of (usually) arbitrary
length into output (so-called "message digest") of
constant length. These transformation functions
must fulfill these requirements:
no one should be able to produce two different
inputs for which the transformation function returns
the same output
no one should be able to produce input for given
pre-specified output
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18. Message-Digest algorithms serve in digital signature
applications for guaranteeing consistency (integrity) of data.
Commonly used model is as follows (message-digest in
cooperation with asymmetric cryptography):
Sender creates input message (M) and computes its message
digest . Then he uses his private key and encrypts message
digest.
Encrypted message digest is attached to the input message
and the whole message is sent to receiver.
Receiver gets the message and extracts the encrypted
message digest. Then he computes his own message digest
of the received message. He also decodes received message
digest with sender's public key and gets decoded message
digest. Then he compares both message digests. When both
message digests are equal, the message was not modified
during the data transmission. 18
19. MD5 ALGORITHM DESCRIPTION
MD5 algorithm takes input message of arbitrary length
and generates 128-bit long output hash. MD5 hash
algorithm consist of 5 steps.
Step 1. Append Padding Bits
Step 2. Append Length
Step 3. Initialize MD Buffer
Step 4. Process Message in 16-Word Blocks
Step 5. Output
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20. MD5 ALGORITHM USES
MD5 is commonly used hash algorithm. It can be
found in many implementations (available on some
Unix-based system as utility md5; class
MD5CryptoServiceProvider in Microsoft's .NET
Framework (namespace
System.Security.Cryptography).example
implementation in Visual C++ or JavaScript, etc.). It
is used sometimes as file CRC function (Napster...)
or one-way cipher in authentication operations (for
storing user password hash).
MD5 is also used in conjunction with other
cryptographic methods in digital signature
applications or in protocols like SSL and others. 20
21. CONCLUSION:-
Both produce the MD5 hash value. The difference
between the two samples is the leading bit in each
nibble has been flipped. Hash value is not
encrypted one exactly, so you can’t retrieve the
actual value.
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