Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

Table 1

Performance of signcryption scheme 𝑉₃ (𝑛=4).

Platforms	Operations* and complexities†			Parameters and sizes‡
	KeyGen	SignCrypt	UnSignCrypt	pk§	sk	Ciphertext
𝐺	1𝑒+2𝑚+1𝑖	1𝑒+7𝑚+1𝑖	7𝑚+3𝑖	log|𝐺|	log|𝐺|	2log|𝐺|
𝐆𝐋𝑛(𝔽𝑞)	~64𝑘log^2𝑞		~640log^2𝑞	~16log𝑞	~16log𝑞	~32log𝑞
𝐔𝐓𝑛(𝔽𝑞)	~20𝑘log^2𝑞		~200log^2𝑞	~6log𝑞	~6log𝑞	~12log𝑞
𝐵50(10)	~2^15			5730	2822	8466

^∗𝑒/𝑚/𝑖: exponentiation/multiplication/inversion in the nonabelian group 𝐺.
†In the sense of bit operations.
‡In the sense of bit length.
§Including system parameters shared by all users.