CRYPTOGRAPHIC DEVICES AND METHODS FOR ENCODING-FREE ENCRYPTION ON ELLIPTIC CURVES

摘要

Encoding-free encryption on elliptic curves is obtained by a device having a processor choosing an integer r∈/q; computing in E(p) the a first point C1=[r]P and a second point C2=[r]Y, wherein E is an elliptic curve defined over p, P∈E(p) is a point of prime order q, Y=[s]P∈E(p) is an encryption key for an integer s∈/q; computing the class β of Ψ(C2); computing a first value c2 by performing an elementary arithmetic operation modulo p between the message m∈/p and the class β; combining the first point C1 and the first value c2 to obtain the ciphertext (C1, c2); and outputting the ciphertext (C1, c2). Decryption of a ciphertext (C1, c2) comprising a first point C1 and a first value c2 to obtain a message m∈/p, is performed by multiplying a decryption key s and the first point C1 to obtain a second point P=(x,y)∈E(p); calculating Ψ(P)∈E(/p2) to obtain a third point; performing an elementary arithmetic operation modulo p between the first value c2 and the class of the third point to obtain the message m; and outputting the message m.

主权项

1. A device for encryption of a message m∈/p to obtain a ciphertext, the device comprising a processor configured to:
compute in E(p) a first point C1=[r1]P and a second point C2=[r2]Y, wherein r1 and r2 are integers derived from an integer r∈/q, E is an elliptic curve defined over p, P∈E (p) is a point of finite order q, Y=[s]P∈E(p) is an encryption key for an integer s∈/q; compute the class β of Ψ(C2), where IP is a mapping function that maps points of E(p) onto points of E(/p2); compute a first value c2 by performing an elementary arithmetic operation modulo p between the message m and the class β; combine the first point C1 and the first value c2 to obtain the ciphertext (C1, c2); and output the ciphertext (C1, c2).