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This includes vetting the hacker to make sure they aren't tied to a U. Monero is considered more of a privacy token and allows cybercriminals greater freedom from some of the tracking tools and mechanisms that the bitcoin blockchain brings. On the question of whether to ban payments to attackers, the group of more than 60 members was split.

Part of the problem is that the threat actors are getting savvier at pricing their ransom demands. Let's just rebuild our systems, take a risk, and not pay for it,'" Grens said. At a certain point, it is more economically viable to just pay the ransom rather than hemorrhaging cash due to paralyzed operations. To protect against token forgery, one relies on the usual authenticity functions of user identification and message integrity.

Note that the "user" being identified from the coin is the issuing Bank, not the anonymous spender. To protect against multiple spending, the Bank maintains a database of spent electronic coins. Coins already in the database are to be rejected for deposit.

If the payments are on-line, this will prevent multiple spending. If off-line, the best we can do is to detect when multiple spending has occurred. To protect the payee, it is then necessary to identify the payer. Thus it is necessary to disable the anonymity mechanism in the case of multiple spending. The features of authenticity, anonymity, and multiple-spender exposure are achieved most conveniently using public-key cryptography.

We will discuss how this is done in the next two chapters. We begin by describing these mechanisms, which are based on public-key cryptography. We then build up the protocol gradually for ease of exposition. We start with a simplified scheme which provides no anonymity. We then incorporate the payment untraceability feature, and finally the payment anonymity property.

The result will be a complete electronic cash protocol. One-Way Functions. A one-way function is a correspondence between two sets which can be computed efficiently in one direction but not the other. The elements are typically numbers, but could also be, e. Key Pairs. If phi is a one-way function, then a key pair is a pair s, t related in some way via phi.

We call s the secret key and t the public key. As the names imply, each user keeps his secret key to himself and makes his public key available to all. The secret key remains secret even when the public key is known, because the one-way property of phi insures that t cannot be computed from s.

All public-key protocols use key pairs. For this reason, public-key cryptography is often called asymmetric cryptography. Conventional cryptography is often called symmetric cryptography, since one can both encrypt and decrypt with the private key but do neither without it.

Signature and Identification. In a public key system, a user identifies herself by proving that she knows her secret key without revealing it. This is done by performing some operation using the secret key which anyone can check or undo using the public key. This is called identification. If one uses a message as well as one's secret key, one is performing a digital signature on the message.

The digital signature plays the same role as a handwritten signature: identifying the author of the message in a way which cannot be repudiated, and confirming the integrity of the message. Secure Hashing. A hash function is a map from all possible strings of bits of any length to a bit string of fixed length. Such functions are often required to be collision-free: that is, it must be computationally difficult to find two inputs that hash to the same value.

If a hash function is both one-way and collision-free, it is said to be a secure hash. The most common use of secure hash functions is in digital signatures. Messages might come in any size, but a given public-key algorithm requires working in a set of fixed size.

Thus one hashes the message and signs the secure hash rather than the message itself. The hash is required to be one-way to prevent signature forgery, i. Forging the Bank's digital signature without knowing its secret key is one way of committing token forgery, but not the only way. A bank employee or hacker, for instance, could "borrow" the Bank's secret key and validly sign a token.

This key compromise scenario is discussed in 5. Withdrawal: Alice sends a withdrawal request to the Bank. Bank prepares an electronic coin and digitally signs it. Bank sends coin to Alice and debits her account. Bob contacts Bank5 and sends coin. Bank verifies the Bank's digital signature. Bank verifies that coin has not already been spent.

Bank consults its withdrawal records to confirm Alice's withdrawal. Bank credits Bob's account and informs Bob. Bob gives Alice the merchandise. For example, the Bank might be a credit card company, or the overall banking system. In the latter case, Alice and Bob might have separate banks. If that is so, then the "deposit" procedure is a little more complicated: Bob's bank contacts Alice's bank, "cashes in" the coin, and puts the money in Bob's account.

Payment: Alice gives Bob the coin. Bob verifies the Bank's digital signature. Deposit: Bob sends coin to the Bank. Bank credits Bob's account. The above protocols use digital signatures to achieve authenticity. The authenticity features could have been achieved in other ways, but we need to use digital signatures to allow for the anonymity mechanisms we are about to add. For this, it is necessary that the Bank not be able to link a specific withdrawal with a specific deposit.

We will give examples of blind signatures in 3. In the withdrawal step, the user changes the message to be signed using a random quantity. This step is called "blinding" the coin, and the random quantity is called the blinding factor. The Bank signs this random-looking text, and the user removes the blinding factor. The user now has a legitimate electronic coin signed by the Bank. The Bank will see this coin when it is submitted for deposit, but will not know who withdrew it since the random blinding factors are unknown to the Bank.

Obviously, it will no longer be possible to do the checking of the withdrawal records that was an optional step in the first two protocols. Note that the Bank does not know what it is signing in the withdrawal step. This introduces the possibility that the Bank might be signing something other than what it is intending to sign. To prevent this, we specify that a Bank's digital signature by a given secret key is valid only as authorizing a withdrawal of a fixed amount.

An example of this is the "randomized blind signature" occurring in the Ferguson scheme discussed in 3. Withdrawal: Alice creates an electronic coin and blinds it. Alice sends the blinded coin to the Bank with a withdrawal request. Bank digitally signs the blinded coin. Bank sends the signed blinded coin to Alice and debits her account. Alice unblinds the signed coin. Bob contacts Bank and sends coin. Bank enters coin in spent-coin database.

The ideal situation from the point of view of privacy advocates is that neither payer nor payee should know the identity of the other. This makes remote transactions using electronic cash totally anonymous: no one knows where Alice spends her money and who pays her.

It turns out that this is too much to ask: there is no way in such a scenario for the consumer to obtain a signed receipt. Thus we are forced to settle for payer anonymity. If the payment is to be on-line, we can use Protocol 3 implemented, of course, to allow for payer anonymity. In the off-line case, however, a new problem arises. If a merchant tries to deposit a previously spent coin, he will be turned down by the Bank, but neither will know who the multiple spender was since she was anonymous.

Thus it is necessary for the Bank to be able to identify a multiple spender. This feature, however, should preserve anonymity for law-abiding users. The solution is for the payment step to require the payer to have, in addition to her electronic coin, some sort of identifying information which she is to share with the payee.

This information is split in such a way that any one piece reveals nothing about Alice's identity, but any two pieces are sufficient to fully identify her. This information is created during the withdrawal step. The withdrawal protocol includes a step in which the Bank verifies that the information is there and corresponds to Alice and to the particular coin being created.

To preserve payer anonymity, the Bank will not actually see the information, only verify that it is there. Alice carries the information along with the coin until she spends it. At the payment step, Alice must reveal one piece of this information to Bob. Thus only Alice can spend the coin, since only she knows the information. This revealing is done using a challenge-response protocol. In such a protocol, Bob sends Alice a random "challenge" quantity and, in response, Alice returns a piece of identifying information.

The challenge quantity determines which piece she sends. At the deposit step, the revealed piece is sent to the Bank along with the coin. If all goes as it should, the identifying information will never point to Alice. However, should she spend the coin twice, the Bank will eventually obtain two copies of the same coin, each with a piece of identifying information.

Because of the randomness in the challenge-response protocol, these two pieces will be different. Thus the Bank will be able to identify her as the multiple spender. Since only she can dispense identifying information, we know that her coin was not copied and re-spent by someone else.

Alice creates an electronic coin, including identifying information. Alice blinds the coin. Bank verifies that the identifying information is present. Bob sends Alice a challenge. Alice sends Bob a response revealing one piece of identifying info. Bob verifies the response. Deposit: Bob sends coin, challenge, and response to the Bank. Bank enters coin, challenge, and response in spent-coin database.

Note that, in this protocol, Bob must verify the Bank's signature before giving Alice the merchandise. In this way, Bob can be sure that either he will be paid or he will learn Alice's identity as a multiple spender. Such implementations are for the off-line case; the on-line protocols are just simplifications of them. The first step is to discuss the various implementations of the public-key cryptographic tools we have described earlier.

There are two ways of doing it: the cut-and-choose method and zero-knowledge proofs. Cut and Choose. When Alice wishes to make a withdrawal, she first constructs and blinds a message consisting of K pairs of numbers, where K is large enough that an event with probability 2-K will never happen in practice.

These numbers have the property that one can identify Alice given both pieces of a pair, but unmatched pieces are useless. She then obtains signature of this blinded message from the Bank. This is done in such a way that the Bank can check that the K pairs of numbers are present and have the required properties, despite the blinding.

When Alice spends her coins with Bob, his challenge to her is a string of K random bits. For each bit, Alice sends the appropriate piece of the corresponding pair. For example, if the bit string starts When Bob deposits the coin at the Bank, he sends on these K pieces. If Alice re-spends her coin, she is challenged a second time.

Since each challenge is a random bit string, the new challenge is bound to disagree with the old one in at least one bit. Thus Alice will have to reveal the other piece of the corresponding pair. When the Bank receives the coin a second time, it takes the two pieces and combines them to reveal Alice's identity. Although conceptually simple, this scheme is not very efficient, since each coin must be accompanied by 2K large numbers.

Zero-Knowledge Proofs. The term zero-knowledge proof refers to any protocol in public-key cryptography that proves knowledge of some quantity without revealing it or making it any easier to find it. In this case, Alice creates a key pair such that the secret key points to her identity. This is done in such a way the Bank can check via the public key that the secret key in fact reveals her identity, despite the blinding.

In the payment protocol, she gives Bob the public key as part of the electronic coin. She then proves to Bob via a zero-knowledge proof that she possesses the corresponding secret key. If she responds to two distinct challenges, the identifying information can be put together to reveal the secret key and so her identity.

There are two kinds of digital signatures, and both kinds appear in electronic cash protocols. Suppose the signer has a key pair and a message M to be signed. Digital Signature with Message Recovery. Thus SSK is said to have a trapdoor, or secret quantity that makes it possible to perform a cryptographic computation which is otherwise infeasible. The function VPK is called a trapdoor one-way function, since it is a one-way function to anyone who does not know the trapdoor.

In this kind of scheme, the verifier receives the signed message SSK M but not the original message text. The verifier then applies the verification function VPK. Digital Signature with Appendix. In this kind of signature, the signer performs an operation on the message using his own secret key. The result is taken to be the signature of the message; it is sent along as an appendix to the message text.

The verifier checks an equation involving the message, the appendix, and the signer's public key. If the equation checks, the verifier knows that the signer's secret key was used in generating the signature. We now give specific algorithms. RSA Signatures. The most well-known signature with message recovery is the RSA signature. Let N be a hard-to-factor integer.

Given v, it is easy to find s if one knows the factors of N but difficult otherwise. Thus the "vth power mod N " map is a trapdoor one-way function. Blind RSA Signatures. The above scheme is easily blinded. Suppose that Alice wants the Bank to produce a blind signature of the message M. She generates a random number r and sends rv. M mod N to the Bank to sign. The Bank does so, returning r. Ms mod N Alice then divides this result by r.

The Schnorr Algorithms. The Schnorr family of algorithms includes an identification procedure and a signature with appendix.

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