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“Although transaction security on the
Internet is a hot topic, it’s only part of the colourful story of
digital cryptography.”
As a kid I was always very excited about opening
a new gift pack sent by the Maggi Fun Club. Not because I enjoyed
the Fun Comic Series (I didn't), but because there was a
prize in each box. And no prize was more sought after than the
Secret Detective’s Handbook.
It contained a Secret
Codebook with which I used to exchange en-coded messages among
my friends and always felt elated to do it.
Now
as a grown up, I am again drawn to secret decoders, but my motive,
now, is not limited to send messages. Now I use to safeguard my
privacy on the Internet. I also like knowing that the data that has
been sent to me hasn't been tampered with.
I use it to provide authentication via digital signatures
or certificates and for preventing users from repudiating (i.e.
rejecting ownership of) their transmitted messages. To do such
things it is apparent that I don’t use that Secret Detective’s
Handbook but use a more profound modus operandi known
as Cryptography.
Most of us think of cryptography (if we actually
ever think of it at all) as something used by the military to
conceal their operations from the enemy during wartime, or by
governments to keep their secrets guarded from other’s eyes. But
today this ancient mathematical science has many more areas
underneath its hood than anyone can envision.
In today's world of Electronic Commerce on the
Internet, the need for secure communications is obviously crucial.
Cryptographic technologies provide enterprises with the best
mechanisms of protecting their information, without putting the
business at risk by exposing it on the Net. Cryptography allows you
to transmit data securely over the Internet. If you are creating any
sort of Web site that will take advantage of e-commerce, you need to
assure your customers that their personal information (including
credit card information) is being sent to you directly, and isn't
being intercepted and used for nefarious purposes.
When downloading controls from a Web site, you have no
doubt run into a prompt asking if you trust the person(s)
responsible for the download. That prompt, known as a Certificate,
ensures that the data has been transmitted directly
Encryption
Encryption is the name given to the
process of applying an algorithm to a message, which scrambles the
data in it – making it very difficult and time consuming, (but not
practically impossible), to deduce the original data, given only the
encoded data. Inputs to the algorithm typically involve additional
secret data called keys, which prevents the message from
being decoded – even if the algorithm is publicly known. The output
is usually garbled text, which is useless unless you decrypt
it.
The safekeeping of keys, in other words, their generation,
storage and exchange, is of paramount importance to ensure the
security of the data. There is no point applying the strongest
levels of cryptographic algorithms, if your keys are stored on a
scrap of paper in your in-tray. The strength of the encryption is
dependent on two basic items: the nature of the mathematical
algorithm and the size of the keys involved. The term
message is used to refer to any piece of data. This message can
consist of ASCII text, a database file, or any data you want to
store or transmit securely. Plaintext is used to refer to
data that has not been encrypted, while cipher text refers to
data that has been.
What are keys?
Keys are additional secret data inputted
along with the plain text, which is used in the algorithm to
encode data in a pattern specific to the key. One of the vital roots
of the strength of the encryption is the size/length of the keys
involved, generally expressed in bits. The key is
generally a long number produced by multiplying two much larger
prime numbers using the algorithm of Factoring.
1. Symmetric
Cryptography – Secret Keys
In symmetric cryptography, the encryption
algorithm requires the same secret key to be used for both
encryption and decryption. Because of the type of key, this is
sometimes called secret key encryption.
The advantage of these algorithms is that they are fast and
efficient. However, the problem is that of key exchange - it is, the
mechanism for safely ensuring both parties, the sender and the
receiver, have the secret key. This is one of the weakest areas of
symmetric cryptography. How do you send the key to your partners?
You cannot just send it in an email message, because it could be
intercepted and, possibly unknowingly, compromise your security.
Furthermore, how can you be sure that your partners will keep your
key secure?
2. Asymmetric
Cryptography – Public/Private Keys
One solution to the problem of key security is
asymmetric cryptography. This uses two keys that are
mathematically related. One key is called the private key
and is never revealed, and the other is called the public
key and is freely given out to all potential correspondents. The
complexity of the relationship between the public key and the
private key means that, provided the keys are long enough, it is
practically impossible to determine one from the other.
The one problem with asymmetric cryptography is that the
processing required is very CPU intensive and this can cause
potential performance problems when many simultaneous sessions are
required.
The almost universal public/private key algorithm is named
RSA after its creators (Ron Rivest, Adi Shamir,
and Len Adleman), and patented by RSA Data Security Inc.
in 1977. A sender uses the receiver's public key to encrypt the
message. Only the receiver has the related private key to decrypt
the message. This is shown here:
So far, we are able to encrypt and decrypt documents. Both of these functions
require our ability to distribute public keys and match them to the
holder of the private key.
If Rahul wants to send Riya some encrypted data, he needs
to know her public key.
If Riya wants to verify the digital signature on a document
as coming from Rahul, she needs to know his public key.
Hash – Its not
just for Breakfast
Like a breakfast hash of eggs, breadcrumbs, and potatoes, a
hash function in computing terms allows you to input data (such as a
document and a key or signature) and then moosh that data into
something more compact (i.e., a really, really big number), called a
digest. In cryptography, a one-way hash is used to
determine whether data has changed. This allows you to ensure that
someone hasn't maliciously tampered with your control.
A one-way function is a mathematical function that
is significantly easier to perform in one direction (the forward
direction) than in the inverse direction. One might, for example,
compute the function in minutes but only be able to compute the
inverse in months or years. A trapdoor one-way function is a one-way
function where the inverse direction is easy if you know a certain
piece of information (the trapdoor), but is difficult otherwise.
Public-key cryptosystems are based on (presumed) trapdoor
one-way functions. The public key gives information about the
particular instance of the function; the private key gives
information about the trapdoor. Whoever knows the trapdoor can
perform the function easily in both directions, but anyone not
knowing the trapdoor can perform the function only in the forward
direction. The forward direction is used for encryption and
signature verification; the inverse direction is used for decryption
and signature generation.
Digital
Signature
A digital signature is not much different from
the handwritten signatures that are used to authenticate a document.
But its much more secure and is not vulnerable to the
handwriting-forgers, whose mere mention may fright some men to
death.
Digital signatures can be used when you have a
message that you plan to distribute in plaintext form, and you want
the recipients to be able to verify that the message comes from you
and that it hasn't been tampered with since it left your hands.
Signing a message does not alter the message, it simply generates a
digital signature string you can bundle with the message or transmit
separately.
Digital signatures are generated using public-key signature
algorithms. A private key is used to generate the signature, and the
corresponding public key is used to validate the signature. This
process is shown in the following illustration:
A digital signature is hash encrypted with a private
signature key. Verifying a digital signature is done by decrypting
the signature using the public signature key, and matching the
result against a hash of the original document.
The strength of a signature is dependent on the
quality of the one-way hash function, and the strength of the
encryption of that hash. If the one-way hash function can be
subverted, than the original document might be changed. If the
encryption isn't sufficiently strong, then the document might have
come from someone other than the holder of the private key.
Nowadays digital signatures are intermittently
used to sign documents over the net. And you can easily visualize a
day when only celebrities will use their hands to sign autographs
for their fans.
But this raises the question – “How does someone know
that an arbitrary public key belongs to someone?” If you
received a public key and were told that this was the public key for
your bank, would you believe it? One very appropriate answer to this
question might be "Who told me?" The answer to this question lies
in Certificates.
Certificates
In essence, they are signed documents, which
match public keys to other information, such as a name or e-mail
address. Certificates are signed by certificate authorities (CAs),
which issue certificates. In essence, a certificate authority is a
commonly trusted third-party, who is relied upon to verify the
matching of public keys to identity, e-mail name, or other such
information (e.g. issuance of credit, access privileges).
Certificate authorities are similar to notaries public.
The benefit of certificates and CAs is that if two people
both trust the same CA, then by exchanging certificates signed by
the CA, they can learn each others public keys, and use them to
encrypt data and send it to one another or to verify the signatures
on document.
To verify a certificate, all that is necessary is the
public key of the CA (plus a possible check against a revocation
list). Certificates and CA's reduce the public-key distribution
problem from verifying and trusting one (or more) public keys per
individual to verifying and trusting the CA's public key and relying
on that to allow verification of others
Certificates have a limited life. They are requested,
created, and then either are revoked (if compromised) or expire.
Expiration is important, as advances in computing power, and the
potential for the discovery of holes in algorithms or protocols may
make certificates unreliable.
Cracking the
Code
As now it’s quite clear that the strength of the
encryption predominantly depends on the key, which should be
sufficiently large to secure the encryption. For e.g. when a
128-digit number is used as a key, it amounts to an encryption of
425-bits. Now guessing such a large number is impracticable and
someone would be really nuts to think of a Brute-Force method
(i.e. trying all the possible combinations).
Factoring, which is the underlying, presumably difficult-to-solve
problem, is something that’s the crux of several public-key
cryptosystems, including RSA. Factoring, in essence, is the act of
splitting an integer into a set of factors. For example, the factors
of 15 are 3 and 5; the factoring problem is to find 3 and 5 when
given 15. That's easy, but what about a really big number such as
‘94,877,863,212,576’? Or how about a 254-digit number? Prime
factorisation requires splitting an integer into factors that are
prime numbers; every integer has a unique prime factorisation.
Multiplying two prime integers together is easy, but as far as we
know, factoring the product is much more difficult. Factoring a key
or "modulus" would allow an attacker to figure out the private key;
thus, anyone who can factor the modulus can decrypt messages and
forge signatures. The security of a key, therefore, depends on
making factoring difficult.
But if a thing is difficult, it doesn’t means that it’s
impossible. Factorising a really-really big number is a very CPU
intensive task and a 512-bit encryption is sufficient to boggle a
Super Computer. By the way, the standard degree of encryption used
by the military forces, now days, is 1024-bit. And as it’s said,
cracking it is not theoretically impossible but even with the latest
state-of-the-art machines, the time it’ll take would be much beyond
our lifetimes.
Significant advances in the mathematics of factoring have
emerged in recent decades, which make the task somewhat
easier. Therefore, factoring researchers still consider the
possibility that a quick-and-easy factoring method might be
discovered quite likely.
Written By:
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Môhit Nanda
Mail me:
katty@rediffmail.com
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