Blinding

As Blinding is known in cryptography , a method in which a client a service can be used in a coded form, without knowing either the input or the output. The method finds particular to prevent side channel attacks and the identity-based encryption ( English Identity-Based Encryption , IBE ) application.

Mathematical definition

In the blinding process, there are two bijective functions , one of which is needed to be blinding (encoding) and the other is needed to be deblinding (i.e., unblinding; decoding).

The RSA cryptosystem is usually used as the encryption function . However, other asymmetric encryption functions can also be used. The following definitions are also used:

symbol	Mathematical definition	Explanation
news
${\displaystyle m}$	${\displaystyle \exists m:m\in \mathbb {N} }$	the plaintext
${\displaystyle c}$	${\displaystyle \exists c:c\in \mathbb {N} }$	the ciphertext
RSA cryptosystem
${\displaystyle N}$	${\displaystyle \exists N:N\in \mathbb {N} \land N>m}$	The product of two prime numbers ${\displaystyle p,q}$
${\displaystyle e}$	${\displaystyle \exists e:e\in \mathbb {N} }$	the exponent of the public key
${\displaystyle d}$	${\displaystyle \exists d:d\in \mathbb {N} }$	the exponent of the private key
${\displaystyle (N,e)}$		the public key
${\displaystyle (N,d)}$		the private key
${\displaystyle f}$	${\displaystyle \exists f:(m,(N,e))\mapsto m^{e}(\!{\bmod {N}})=c}$	the RSA encryption function, which accepts the plain text and the public key and outputs the ciphertext
${\displaystyle g}$	${\displaystyle \exists g:(c,(N,d))\mapsto c^{d}=\left(m^{e}\left(\!{\bmod {N}}\right)\right)^{d}=\left(m^{e}\right)^{d}(\!{\bmod {N}})=m(\!{\bmod {N}})=m}$	the RSA decryption function, which accepts the ciphertext and the private key and outputs the plaintext
Blinding functions
${\displaystyle r}$	${\displaystyle \exists r:r\in \mathbb {N} \cap {]1,N[}\land \gcd(r,N)=1}$	Which used only once and transmitted in plain text random number relatively prime to be. ${\displaystyle N}$
${\displaystyle B}$	${\displaystyle \exists B:(m,r)\mapsto (m\,r)^{e}\left(\!{\bmod {N}}\right)=m'}$	the blinding function
${\displaystyle D}$	${\displaystyle \exists D:(f(m'),r)\mapsto f(m')\,r^{-1}\left(\!{\bmod {N}}\right)=f(m)\left(\!{\bmod {N}}\right)=f(m)}$	the deblinding function
↑ a b c d e see RSA key generation

This applies to blinding and deblinding, neglecting the public and private keys, as well as : ${\displaystyle r}$

${\displaystyle m=g(c)=g(f(m))\equiv m=g(c)=g(D(f(B(m))))}$

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1. ^ ^{A b c d} David Gray, Caroline Sheedy: Public Key Infrastructures, Services and Applications . In: EuroPKI 2010, Lecture Notes in Computer Science (LNCS) . tape 6711 . Springer, Berlin, Heidelberg 2011, ISBN 978-3-642-53997-8 , E-Voting: A New Approach Using Double-Blind Identity-Based Encryption, p. 93-108 (English).