面向代理重加密算法的程序设计语言研究

doi:10.11959/j.issn.1000-436x.2018106

Abstract

Abstract:

The programming language for proxy re-encryption(PLPRE) based on domain specific language(DSL) was proposed,which was similar to the matical description and was adopt to describe the proxy re-encryption directly.The algorithm designer could describe the algorithm conveniently and quickly by PLPRE,and obtain the programming code for computer.Firstly,the grammar of PLPRE was presented,including the definitions of the keyword and programming logic,then the ACC-PRE algorithm was described by PLPRE as an example.Secondly,the PLPRE parser was realized by ANTLR.Finally,the comparisons between the PLPRE and the related work were made.By using the PLPRE,user does not need to pay attentions to data structure or memory allocation.It is suitable for the cryptography experts who is not familiar with the programming.Thus,PLPRE will decrease the deviation between the design and implement for PRE.

Key words: proxy re-encryption, domain specific language, ANTLR, description of algorithm, implement of cryptography

CLC Number:

TP302

Mang SU,Yan YU,Bin WU,Anmin FU. Research on the programming language for proxy re-encryption[J]. Journal on Communications, 2018, 39(6): 89-97.

Figures/Tables 7

ACC-PRE数学描述	PLPRE描述
Setup (k)→param，选取长度为k的素数p，群G₁、G₂为q的乘法循环群， g 为 G₁的生成元，散列函数组 H₁、H₂、H₃、H₄，其中，H₁:{0,1}^→G₁, $H_{2} : {0, 1}^{} \to Z_{p}^{}$ ,H₃:G₂→{0,1}^l,H₄:{0,1}^→G₁。公开参数 param={p,G ₁,G₂,g,H_i(i=1,…,4)}。定义双线性映射e:G₁ ×G₁→G₂	/method Setup(k)
	q=\sfun Prime(k); /k长大素数/
	G₁=\sfun Group(q);/q阶循环群/
	G_T=\sfun Group(q);
	Zq=\sfun GroupZ(q);
	g=\sfun Generator(G₁);
	/loop(s=1;step=1;until=2)
	{H₁[s]=\sfun Hash(str_b,G₁);}
	H₂=\sfun Hash(str_b,Zq);
	H₃=\sfun Hash(G_T,str_l);
	/构造散列映射关系，str_b表示随意比特串，str_l表示l长比特串，在定义中通过str_l(bits=l)，进行说明/
	\sfun e(G₁,G_T);/构造双线性对/
	\method

ACC-PRE数学描述	PLPRE描述
$R e - E n c (C_{i}, r k_{i \to j}^{c o n d i t i o n}) \to C_{j}$ ，加密代理对密文 C_i进行重加密，生成可以被 sk_j 所解密的密文C_j =(c₁′,c₂′,c₃′,c₄′,c₅′) 。若e(c₁,H₄(c₁\|\|c₂\|\|c ₃\|\|c₄))= e(g,c₅)，则进行以下计算：	/method Re-Enc(rk,C₁,para)
	/rk为重加密密钥，有reKeyGen函数产生，一个包含pk₂及相关参数的一个枚举类型/
${c^{'}}_{1} = c_{1};$	\if (e(C₁[1],H₄(C₁[1]\|\|C₁[2]\|\|C₁[3]\|\|C₁[4]))=e(g,C₁[5]))
${c^{'}}_{2} = c_{2} (p k_{j}^{r} g^{- r}, H_{1} (p k_{i})^{- s k_{i}}) e (p k_{j}^{r}, H_{1} (p k_{j} \| \| c o n d i t i o n) H_{1} (p k_{i})^{- s k_{i}})$	then
$= k e (p k_{j}^{r}, H_{1} (p k_{j} \| \| c o n d i t i o n));$ ${c^{'}}_{3} = c_{3};$	{C₂[1]=C₁[1]；
${c^{'}}_{4} = H_{1} (p k_{j});$	C₂[2]=k*e(pk₂^r,H₁[1](pk₂\|\|para))；
${c^{'}}_{5} = H_{4} ({c^{'}}_{1}, {c^{'}}_{2}, {c^{'}}_{3}, {c^{'}}_{4})^{r}$	/para对应元算法描述中的condition，不同的算法针对的环境不同，因此会出现用户定义的参与，PLPRE中统一约束为比特串/
	C₂[3]=C₁[3]；
	C₂[4]=H₁[1](pk₂)；
	C₂[5]=H₁[2](C₂[1]\|\|C₂[2]\|\|C₂[3]\|\|C₂[4]);
	\method

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名称	描述	示例
Setup	初始化函数，实现代理重加密算法参数的初始化，如产生循环群、双线性对、大素数等	/method Setup(k){…}\method，k 为参数初始化参数，通常为大素数位数或循环群阶等，初始化函数的参数可为多个
KeyGen	密钥对生成函数，产生代理重加密参与双方的公私钥对	/method KeyGen(g,Zq){…}\method，g、Zq为初始化过程中已经产生循环群生成元和 q 阶整数群，产生的公私钥对的定义则在定义部分进行描述
ReKeyGen	重加密密钥生成函数，产生代理重加密密钥	/method ReKeyGen (sk₂,sk₁,pk₁){…}\method，其中，sk₂、pk₁、sk₁为用户2的私钥及用户1的公私钥，该函数产生用户1为用户2共享数据的重加密密钥rk_1→2
Enc	加密函数，用于代理重加密的第一次加密	/method Enc(pk₁,m){…}\method，参数pk₁为用户1的公钥，该函数将描述实现将明文m使用pk₁进行第一次加密，产生密文C₁
ReEnc	重加密函数，对第一次的密文进行重加密	/method ReEnc(C₁,rk_1→2){…}\method，参数C₁为第一次加密产生的密文，rk_1→2为代理重加密密钥
Dec	解密函数，分为Dec₁和Dec₂，分别用于第一次加密密文和重加密密文的解密	/method Dec₁(C₁,sk₁){…}\method 和/method Dec₂(C₂,sk₂){…}\method，C₁、C₂表示第一次加密密文和重加密密文，sk₁和sk₂表示用户1和用户2的私钥
main	主函数，用于用户的测试运行	/method main(){…}\method

名称	示例	功能描述
Prime	\sfun Prime(k)	产生长度为k bit的大素数
Group	\sfun Group(q)	产生q阶循环群
Group	\sfun GroupZ(q)	产生Zq
Generator	\sfun Generator(G)	获取群G的生成元
e	\sfun e(G₁,G_T)	产生群G₁到群G_T的双线性对
random	\sfun random(Zq)	选取群Zq中的任意元素
Hash	\sfun Hash(A,B)	构造集合A到B的散列映射关系
@	a@b	实现a和b的连接运算
xor	a xorb	实现a和b的异或运算
^	g ^x	进行g的x次幂运算
*	a*b	群元素a与b进行域内乘运算

ACC-PRE数学描述	PLPRE描述
Enc (m,pk_i)→C_i，用户 i 使用自身公钥 pk_i加密明文信息 m，选取k∈G₂，计算r=H₂(m\|\|k)，则C_i =(c₁,c₂,c₃,c₄,c₅)。	/method Enc(Zq,g,g₁,pk₁,m,C₁) k=\sfun random(GT)；
c ₁=g^r;	/在q阶整数循环群GT上随机选取k/
c₂ =ke(pk_i,H₁(pk_i))^r;	r= H₂(m\|\|k)
c₃=m⊕H₃(k);	C₁[1]=g^r；//密文第一部分，计算g^r mod q
c₄ =H₁(pk_i);
c ₅=H₄(c₁\|\|c₂\|\|c₃\|\|c₄)^r	C₁[2]=k*e(pk₁,H₁[1](pk₁))^r//密文第二部分，m 与 e(pk,H₁[1](pk))r mod q连接
	C₁[3]=m@H₃(k)；//密文第三部分
	C₁[4]=H₁[1](pk₁)；
	C₁[5]=H₁[2](C₁[1]\|\|C₁[2]\|\|C₁[3]\|\|C₁[4]])^r；
	\method

技术	知识背景			适用范围			跨平台
技术	需要关注数据类型	需要关注数据结构	需要计算机编程基础	支持pairing	支持no-pairing	支持重加密算法描述	跨平台
PRL	Yes	Yes	Yes	Yes	No	Part	No
PBC	Yes	Yes	Yes	Yes	No	Part	Part
Cryptol	No	No	No	No	No	No	Yes
PLPRE	No	No	No	Yes	Yes	Yes	Yes

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Research on the programming language for proxy re-encryption

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