vb.net code 39 reader Pao-Chi combines his temporary private key with Gwen s public key to get a secret point in Software

Creator Code 3 of 9 in Software Pao-Chi combines his temporary private key with Gwen s public key to get a secret point

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Pao-Chi combines his temporary private key with Gwen s public key to get a secret point
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To read the message, Gwen needs the session key. She gets it by combining her private key with Pao-Chi s temporary public key (he sends his temporary public key along with the encrypted message). This sounds just like Diffie-Hellman. In that scheme, two people combine public and private keys in a special way to generate a shared secret. In this scheme, the same thing is happening. The difference is the underlying math, and that explains the name Elliptic Curve Diffie-Hellman. To read Pao-Chi s intercepted message, Satomi needs one of the private keys, knowing both of the public keys will not do the trick. To break Gwen s private key (probably Satomi s first choice), Satomi must figure out d. That would require her to solve the EC discrete log problem, something that would take a few million years, so Satomi might try a brute force attack. The problem is that d is the same size as the underlying field. Gwen probably chose a 160-bit or 170-bit EC, meaning that d is also 160 bits to 170 bits, so brute force won t work either. Remember that RSA and DH were based on related problems, and that s why the key sizes are the same. But with ECC, you use a different
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The Key Distribution Problem and Public-Key Cryptography
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key size because the underlying problems are different. And solving the EC discrete log problem is harder than solving the factoring or discrete log problem. By the way, it s possible to use ECC to do encryption. However, in the real world, it s not used very much for security and performance reasons. Recall that as you increase the key size, you slow down the computations. And for ECES (elliptic curve encryption scheme) or ECRSA to achieve the level of security of regular RSA, you must use bigger keys. The keys need to be so big that you take too big a hit in performance.
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The three algorithms we ve discussed can be used to solve the key distribution problem. Which one is the best There s probably no answer to that question because each has its advantages and disadvantages. A more appropriate question might be, Which algorithm works best in which situation When you re evaluating each approach, it s a good idea to look at five areas: security, key size, performance, transmission size, and interoperability.
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Is one of the algorithms more secure than the others There s no truly objective answer. It depends on what you think is important. ECC is based on the EC discrete log problem, which is harder ; does this mean it s more secure than RSA, which is based on factoring, or DH, which is based on the discrete log problem Not necessarily. Thousands of mathematicians have been studying the factoring problem for many years (most intently since 1978). Some of them think that if a solution could have been found, it would have been found by now. On the other hand, it took about 300 years to come up with a proof of Fermat s Last Theorem, so maybe the ultimate factoring solution simply has not yet been found. Considering the enormous bank of research available to build on, finding a solution may become easier over time. ECC is newer and less well understood. Far fewer researchers have been attacking it, and for a shorter time. Some people think that more time and effort are needed to develop a better sense of security. Furthermore, despite the lag in research, some classes of curves have been found
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to be susceptible to cryptanalysis. Of the many flavors of elliptic curves, not all of them are used in crypto. For some flavors, it was known early that they contained more weaknesses than others and that there were ways to break them faster than security requirements allowed. Such curves have never been proposed for use in crypto. Other flavors that were proposed for such use were later shown to possess weaknesses. All the weaknesses found so far lie in the F2 area. At this point, it s believed that no application has ever been deployed in the real world with a weak EC. But because some curves have fallen, some cryptographers are not confident in F2 ECC, and others do not trust any curve at all Fp or F2. Some people prefer RSA because DH and ECDH are susceptible to the man-in-the-middle attack. In our sales rep example, the potential attacker is a woman in the middle, Satomi. She could intercept all messages between Pao-Chi and Gwen, establishing DH or ECDH keys with each of them. Pao-Chi would think he s computing a shared secret key with Gwen but would really be computing one with Satomi. Similarly, Gwen would compute a shared secret key with Satomi, thinking she was talking with Pao-Chi. Then if Pao-Chi sent a message to Gwen, only Satomi would be able to decrypt it. She would decrypt it, store the message, reencrypt it with the key she established with Gwen, and send it on (see Figure 4-23). The man-in-the-middle attack is easily thwarted by using authentication along with the key exchange ( 5 discusses authentication), and most protocols include authentication anyway. So for some people, this attack is no real disadvantage. Another issue is each correspondent s ability to contribute to the key. With RSA, only the initiator of the contact has any say in what the session key will be. With DH or ECDH, both parties contribute to generating the session key. Each correspondent performs some operations and sends the result to the other; the final secret depends on each individual s contribution. For some people, this arrangement sounds better than trusting someone else entirely to generate a good key. For others, it s not a great feature. After all, they argue, another party who would do a bad job of generating a session key probably wouldn t do any better with the key exchange. So, the choice of algorithm is a matter of your own feeling of security. At this time, no honest cryptographer can make a definitive statement about which algorithm is more secure.
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