In cryptography, blinding is a technique by which an agent can provide a service to (i.e, compute a function for) a client in an encoded form without knowing either the real input or the real output. Blinding techniques also have applications to preventing side-channel attacks on encryption devices. Cryptography has had a long and colourful history. ... In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...

More precisely, Alice has an input x and Oscar has a function f. Alice would like Oscar to compute y = f(x) for her without revealing either x or y to him. The reason for her wanting this might be that she doesn't know the function f or that she does not have the resources to compute it. Alice "blinds" the message by encoding it into some other input E(x); the encoding E must be a bijection on the input space of f, ideally a random permutation. Oscar gives her f(E(x)), to which she applies a decoding D to obtain D(f(E(x))) = y. Alice and Bob are conventional placeholder terms referring to common archetypal characters used in explanations in fields such as cryptography and physics. ... In mathematics, a bijection, bijective function, or one-to-one correspondence is a function that is both injective (one-to-one) and surjective (onto), and therefore bijections are also called one-to-one and onto. ...

Of course, not all functions admit of blind computation.

The most common application of blinding is the blind signature. In a blind signature protocol the signer digitally signs a message without being able to learn its content. In cryptography, a blind signature is a form of digital signature in which the content of a message is disguised (blinded) before it is signed. ...

The one-time pad is an application of blinding to the secure communication problem. Alice would like to send a message to Bob secretly, however all of their communication can be read by Oscar. Therefore Alice sends the message after blinding it with a secret key or pad that she shares with Bob. Bob reverses the blinding after receiving the message. In this example, the function f is the identity and E and D are both typically the XOR operation. Excerpt from a one time pad. ... An identity function f is a function which doesnt have any effect: it always returns the same value that was used as its argument. ... Exclusive disjunction (usual symbol XOR occasionally EOR) is a logical operator that results in true if one of the operands, but not both of them, is true. ...

Blinding can also be used to prevent certain side channel attacks on asymmetric encryption schemes. Side channel attacks allow an adversary to recover information about the input to a cryptographic operation, by measuring something other than the algorithm's result, e.g., power consumption, computation time, or radio-frequency emanations by a device. Typically these attacks depend on the attacker knowing the characteristics of the algorithm, as well as (some) inputs. In this setting, blinding serves to alter the algorithm's input into something unpredictable state. Depending on the characteristics of the blinding function, this can prevent some or all leakage of useful information. Note that security depends also on the resistance of the blinding functions themselves to side-channel attacks. In cryptography, a side channel attack is any attack based on information gained from the physical implementation of a cryptosystem, rather than theoretical weaknesses in the algorithms (compare cryptanalysis). ... In cryptography, an asymmetric key algorithm uses a pair of different, though related, cryptographic keys to encrypt and decrypt. ...

For example in RSA blinding involves computing the blinding operation E(x) = x r^e mod N, where r is random, x is the ciphertext, and e and N have the conventional meaning from RSA. As usual, f(x) = x^d mod N, and finally it is unblinded with D(x) = (x^e)/r mod N. Jump to: navigation, search In cryptography, RSA is an algorithm for public key encryption. ...

External links

• Remote Timing Attacks are Practical