Digital Certificates Interview Preparation Guide

a fill - 1/20 per minute
b fill - 1/30 per minute
c can empty - 1/40 per minute


Suppose this take x minute

1 x +1x - 1x
--- -- ---- =1
20 30 40

Solve this x=17(approximately)

A digital signature consists of text that is encrypted using
the private key of a public key[md]private key pair. The
public key is used to decrypt the signature to verify its
authenticity.

(1/10)^18 - (1/10)^20
= 1/(10^18) - 1/(10^20)
= (10^2 - 1)/(10^20)
= 99/(10^20)

list of certificates who have been reovoked access.
It is use in X.500

A one-time signature scheme allows the signature of only a single message using a given piece of private (and public) information. One advantage of such a scheme is that it is generally quite fast. However, the scheme tends to be unwieldy when used to authenticate multiple messages because additional data needs to be generated to both sign and verify each new message. By contrast, with conventional signature schemes like RSA

Undeniable signature scheme, devised by Chaum and van Antwerpen [CV90][CV92], are non-self-authenticating signature schemes, where signatures can only be verified with the signer's consent. However, if a signature is only verifiable with the aid of a signer, a dishonest signer may refuse to authenticate a genuine document. Undeniable signatures solve this problem by adding a new component called the disavowal protocol in addition to the normal components of signature and verification.

Factoring is the act of splitting an integer into a set of smaller integers (factors) which, when multiplied together, form the original integer. For example, the factors of 15 are 3 and 5; the factoring problem is to find 3 and 5 when given 15. Prime factorization requires splitting an integer into factors that are prime numbers; every integer has a unique prime factorization. Multiplying two prime integers together is easy, but as far as we know, factoring the product is much more difficult.

Factoring is the underlying, presumably hard problem upon which several public-key cryptosystems are based, including RSA. Factoring an RSA 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 RSA depends on the factoring problem being difficult and the presence of no other types of attack. Unfortunately, it has not been proven that factoring must be difficult, and there remains a possibility that a quick and easy factoring method might be discovered , although factoring researchers consider this possibility remote.

Factoring has become easier over the last 15 years for two reasons: computer hardware has become more powerful, and better factoring algorithms have been developed.

Hardware improvement will continue inexorably, but it is important to realize that hardware improvements make RSA more secure, not less. This is because a hardware improvement that allows an attacker to factor a number two digits longer than before will at the same time allow a legitimate RSA user to use a key dozens of digits longer than before; a user can choose a new key a dozen digits longer than the old one without any performance slowdown, yet a factoring attack will become much more difficult. Therefore, although the hardware improvement does help the attacker, it helps the legitimate user much more. This general rule may fail in the sense that factoring may take place using fast machines of the future, attacking RSA keys of the past; in this scenario, only the attacker gets the advantage of the hardware improvement. This consideration argues for using a larger key size today than one might otherwise consider warranted. It also argues for replacing one's RSA key with a longer key every few years, in order to take advantage of the extra security offered by hardware improvements. This point holds for other public-key systems as well.

Factoring is a very active field of research among mathematicians and computer scientists; the best factoring algorithms are mentioned below with some references and their big-O asymptotic efficiency. O notation measures how fast an algorithm is; it gives an upper bound on the number of operations (to order of magnitude) in terms of n, the number to be factored, and p, a prime factor of n.

Factoring algorithms come in two flavors, special purpose and general purpose; the efficiency of the former depends on the unknown factors, whereas the efficiency of the latter depends on the number to be factored. Special-purpose algorithms are best for factoring numbers with small factors, but the numbers used for the modulus in the RSA system do not have any small factors. Therefore, general-purpose factoring algorithms are the more important ones in the context of cryptographic systems and their security.