Keys
The PKCS #1 standard defines the mathematical definitions and properties that RSA public and private keys must have. The traditional key pair is based on a modulus, which is the product of two distinct large prime numbers, and, such that .
Starting with version 2.1, this definition was generalized to allow for multi-prime keys, where the number of distinct primes may be two or more. When dealing with multi-prime keys, the prime factors are all generally labeled as for some, such that:
- for
As a notational convenience, and .
The RSA public key is represented as the tuple, where the integer is the public exponent.
The RSA private key may have two representations. The first compact form is the tuple, where is the private exponent. The second form has at least five terms, or more for multi-prime keys. Although mathematically redundant to the compact form, the additional terms allow for certain computational optimizations when using the key.
Read more about this topic: PKCS1
Famous quotes containing the word keys:
“Bless all useful objects,
the spoons made of bone,
the mattress I cook my dreams upon,
the typewriter that is my church
with an altar of keys always waiting.”
—Anne Sexton (1928–1974)
“Thou hast the keys of Paradise, O just, subtle, and mighty opium!”
—Thomas De Quincey (1785–1859)
“And yet we constantly reclaim some part of that primal spontaneity through the youngest among us, not only through their sorrow and anger but simply through everyday discoveries, life unwrapped. To see a child touch the piano keys for the first time, to watch a small body slice through the surface of the water in a clean dive, is to experience the shock, not of the new, but of the familiar revisited as though it were strange and wonderful.”
—Anna Quindlen (b. 1952)