| Abstract [eng] |
This submission called “Efficient encryption and digital signature schemes” consists of three parts. I. In Part I theoretical analysis of popular public key cryptosystems RSA (Rivest, Shamir, Adleman) with security based on the large integer factorization problem and ElGamal with security based on the discrete logarithm problem, along with new cryptographic primitive termed as "signcryption" proposed by Y. Zheng which simultaneously fulfills both the functions of digital signature and public key encryption in a logically single step, and with a cost significantly smaller than that required by "signature followed by encryption" using popular public key cryptosystem composition is done. For the completeness of analysis description of supplemental algorithms and functions such as AES block cipher, SHA hash functions, HMAC keyed hash function is present. II. In Part II the results of the practical implementation done in Python programming language are analyzed. Effectiveness is described by two factors: 1. Total computation time of signing – encryption – decryption – verification operations; 2. Communication overhead – signed and encrypted message length increase compared to the original plaintext. III. In Part III two effective Signcryption implementation algorithms are proposed: secret sharing without threshold and (k, n) threshold schemes. Results of analysis prove Signcryption being secure and extremely effective signature and encryption cryptosystem. It has very low requirements for the computational power as well as provides almost no data expansion. These properties make it perfect solution for battery-powered small devices such as smart cards, mobile phones and personal digital assistants (PDAs) and applications operating in resource-constrained environment such as contactless wireless identification tokens. |
