Encoding abelian variety-based ciphertext with metadata

#Data may be encrypted for many different reasons, such as, for example, for purposes of securing communications, protecting sensitive data (data representing social security numbers, salaries, account information, and so forth), and so forth. One way to encrypt and decrypt data is through public key cryptography, which uses a pair of keys: a public key, which, as the name implies, is widely disseminated; and a private keys, which is known to the owner(s) of the data. One type of public key cryptography system is Elliptic Curve Cryptography (ECC), which is based on the algebraic structure of elliptic curves over finite fields.

#FIG. 1 is a schematic diagram of a computer system according to an example implementation.

#FIG. 2 is a flow diagram depicting a technique to encode metadata into elliptic curve cryptography-based ciphertext to represent a key version associated with the ciphertext according to an example implementation.

#FIG. 3 is a flow diagram depicting a technique to decode key version metadata from elliptic function-based ciphertext according to an example implementation.

#Elliptic curve cryptography is based on the algebraic structure of elliptic curves over finite fields. In general, an elliptic curve is a plane curve, which consists of the points that satisfy the following equation: y2+xy=x3+ax2+b,  Eq. 1 excluding cusps and self-intersections. In Eq. 1, the Cartesian coordinates (x,y) represent a point of the elliptic curve; and “a” and “b” are coefficients. The elliptic curve has a point at infinity. In this manner, the point at infinity acts like the value zero when performing calculations on the elliptic curve, so that if “O” represents the point at infinity, then P+O=P for all points on the elliptic curve, similar to the relationship of x+0=x for real numbers.

#Elliptic curve calculations may involve modular inversions, which may be relatively expensive (from the standpoint of computing resources). For purposes of incorporating the point at infinity O and avoiding such expensive modular inversions, the points on an elliptic curve may alternatively be represented by projective coordinates. In this representation, instead of representing a point on the elliptic curve as a pair of Cartesian coordinates (x,y), three projective coordinates are instead used, such as, for example, coordinates (X,Y,Z). In this representation, the non-projective coordinates (x,y) coordinates are related to the projective coordinates (X,Y,Z) as follows:

#x = x z , and Eq . ⁢ 2 y = x z . Eq . ⁢ 3