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10

I try to provide a brief intro. ABE Attribute-based encryption (ABE) is a relatively recent approach that reconsiders the concept of public-key cryptography. In traditional public-key cryptography, a message is encrypted for a specific receiver using the receiver’s public-key. Identity-based cryptography and in particular identity-based encryption (IBE) ...


5

Public key crypto vs. identity-based crypto made short: In traditional public key cryptography, a user $A$ generates a private/public key pair $(sk_A,pk_A)$ and since this key pair has absolutely no indication to which indentity (user $A$) it belongs, it is necessary to certify the public key, i.e., bind the public key $pk_A$ to the user $A$'s identity. ...


5

PE is a subclass of FE. This (from the other answer) is correct. Also, from my understanding, your analogy is correct. PE returns the plaintext if the predicate evaluates to true. FE, on the other hand, returns a function of the plaintext. We can say that PE is a subclass of FE, since we can use FE to implement PE. Just use the identity function. ...


4

She can generate a key-pair and include the public key in the book. Having the private counterpart she can at any time proove that she wrote the book by signing an arbitrary statament.


4

In real world applications Attribute-based Encryption (ABE) is used in conjunction with a symmetric cipher, because you can only encrypt group elements with ABE. In this case it is the multiplicative group $G_T$. The number of bits is limited when you try to represent text messages (bit strings) with a group element, because the size of the group is derived ...


3

The problem can be simplified to the following problem, since the standard argument doesn't really take into account that you can't generate all the polynomials of the given maximum degree : Assume that we have sampled a random point $\vec{x}\in \mathbb{F}_p^n$. We let an adversary adaptively choose polynomials of degree at most $d$ and after each choice ...


3

Zero-knowledge proofs of knowledge basically allow Alice to convince someone beyond a reasonable doubt that she knows a certain piece of information (i.e., the answer to a certain question), without revealing what exactly that information is. One simple example involves the discrete logarithm problem, which you might be familiar with: given a (large) prime ...


3

The BSW07 CP-ABE scheme is a pairing based construction. Denoting the pairing as $e:G\times G\rightarrow G_T$ (symmetric notation for simplicity), the message space of this scheme is the prime order $q$ group $G_T$, which in practice is a prime order $q$ subgroup of the multiplicative group of some finite field. Consequently, if you have a message $m$ and ...


3

PE is a subclass of FE. A description can be found on page 256 of the book “Theory of Cryptography: 8th Theory of Cryptography Conference, TCC 2011”. The related paper is available in PDF format via eprint.iacr.org: Functional Encryption: Definitions and Challenges Dan Boneh, Amit Sahai, Brent Waters


3

There really isn't a difference. It is just author preference in notation. Some authors prefer to write the pairing operations multiplicatively $e(P^a, Q^b)=e(P,Q)^{ab}$ while others prefer to write it additively $e(aP,bQ)=e(P,Q)^{ab}$. This comes from the fact that in $e : \mathbb{G}_1\times \mathbb{G}_2\to\mathbb{G}_T$, $\mathbb{G}_1$ and $\mathbb{G}_2$ ...


2

You can probably prove the security against your game from the security in the IND-ID-CCA game of Boneh and Franklin (see http://courses.cs.vt.edu/cs6204/Privacy-Security/Papers/Crypto/IBE-Weil-Pairing.pdf). The idea is to create an adversary $\mathcal{B}$ against IND-ID-CCA from your adversary $\mathcal{A}$. Essentially $\mathcal{B}$ will play ...


2

What you are describing is an anonymous credential system. There are two different ways to go about making these and two actual systems that use those techniques: Microsoft's U-prove and IBM's Idemix. If you're interested in smart card usage, you'd probably prefer U-prove as it tends to work better with smart cards. It's described by its original ...


2

If Bob and Charlie will share a secret, then it information-theoretic privacy might be possible, otherwise the best that can be hoped for is computational anonymity. I haven't come up up with any way to achieve information-theoretic privacy when Bob and Charlie share a secret, so I will only be addressing computational privacy. I assume that Bob can ...


2

Alice generates a signature key-pair and puts $\;$ the fact that she's using this identity-proving construction $\;\;\;\;$ and $\;$ the digital signature scheme $\;\;\;\;$ and $\;$ the prefix-free code $\;\;\;\;$ and $\;$ the verification key into the book, and keeps the signing key. (Let "||" denote concatenation.) For interactive verification, the ...


2

With IBE the public key is a public bitstring as your email. A Key-authority issues a secret key that is tied with this public key.The owner of the secret key can only decrypt. ABE entails more complex access control on decryption operation such as:"Only the owner of the secret key that corresponds to: Area:=Italy AND Age:<30 and Business:=Researcher" ...


2

It's been a while since I've read this paper, and I remember having a lot of trouble with this derivation. I'm sure there is an easy way to see it, but I don't see it, so I'll just brute force through with the algabra. First, some context: When the simulator is given a random element as the last term in the tuple the simulator will either abort (and ...


2

Compute $d$ such that $ed\equiv 1\bmod{\varphi(n)}$ using extended euclidean algorithm. Then compute $g = i^d\bmod{n}$. This is basically RSA decryption.


1

Layering your encryption mechanisms like that would not display collusion-resistance between the two schemes. For example, someone with an Org-A key could decrypt the outer encryption over a record designated for Org-A administrators and then pass the inner ciphertext to someone with an Administrator key. Of course, you could use a different key for each ...


1

In these systems, is adversary able to generate semi-functional ciphertexts? Quoting the paper figlesquidge mentioned in a comment: Crypto 2009 Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions Brent Waters Abstract: We present a new methodology for proving security of encryption systems using what we call ...


1

The problem that arises in the security proof is that the adversary who may win the real game with some probability may however cause the simulation to nearly always abort (by issuing a private key query that requires the simulation to abort) and the probability of an abort may be different for different sets of private key queries. So, the problem is that ...


1

Ok, lets look at the operations. Sign: $s = g * r^{f(t,m)} \pmod n$ This is an assignment. You compute $(g * r^{f(t,m)}) \mod n$ and assign the resulting value to $s$. If you have a multiplication $(a \cdot b) \mod n$, this is equal to $((a \mod n)\cdot (b \mod n)) \mod n$. See for instance here. Verification: $s^e = i * t^{f(t, m)} \pmod n$ This is no ...


1

The previous comments skip an important fact. I think that a PE for all circuits and A FE for all circuits are equivalent in the sense that you can build the second from the first one (the opposite direction is trivial). A key for a circuit C with output size of n bits can be implemwnted as n PE keys in which the i-th key is relative to the circuit that ...



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