Device for encrypting/decrypting information comprising hardware processing means for computation of a Montgomery product on the basis of the high-radix Montgomery method in order to perform the encryption/decryption based on this Montgomery product, wherein said hardware processing means (150; 200) are adapted to reiterate a loop of operations comprising: - means for performing a first operation of arithmetic addition (24, 76) of a value of one of several first products, denoted a ι. b and a value of a variable, denoted u; - means for performing a second operation of arithmetic addition (28; 80) of a value of one of several second products, denoted m.n, and a value of said variable u, - means for performing a third operation of division of the variable u by a power of 2, denoted 2 ω where ω is the radix, according to a third relationship u: = u 2 ω, wherein the hardware processing means (150; 200) include: - a Carry-Save adder adapted to receive at the input the variable u in the form of a Carry-Save ordered pair and said value of one of several products, denoted a ι. b, respectively m.n, and to provide at the output the result of the first, respectively the second, arithmetic addition operation in the form of a Carry- Save ordered pair, and - means for allocating to the variable u the value obtained at the output of said at least one Carry-Save adder, and wherein the device comprises means for storing the variable u in the form of a Carry-Save ordered pair formed by two variables, denoted C and S and means for performing the third operation of division of the variable u in the form of a Carry-Save ordered pair comprising: • means for calculating and storing a carry digit, denoted R e, which is at risk of being lost by the division of each variable C and S by the power of 2; • means for dividing each variable C and S by the power of 2; wherein the means for performing the first and second operations of addition comprise at least a first Carry-Save adder (157; 230) adapted to perform the first addition operation and a second Carry-Save adder (158; 232) adapted to perform the second addition operation; wherein the means for calculating and storing the carry digit R e comprise means for conventionally adding the ω least significant bits of the variable C, denoted C 0, to the ω least significant bits of the variable S, denoted S 0, according to a fourth relationship R e:= C 0 +S 0; wherein the device comprises: - means (162: 236) for recombining the variable u at least on the basis of values of variables C and S of the Carry-Save ordered pair, - means (166; 238) for reducing the variable u, wherein said means for recombining the variable u and said means for reducing are connected together so as to overlap their operation under control of control means (156; 214); wherein the radix ω is equal to 4 bits in order to optimize the time required for performing the calculation of a Montgomery product on input variables of the Montgomery product encoded on 512 or 1024 bits; wherein the device comprises means (164, 160; 216, 214, 218, 222) for pre-calculating the first products a ι. b and/or the second products m.n. - means for performing a first operation of arithmetic addition (24, 76) of a value of one of several first products, denoted a ι. b and a value of a variable, denoted u; - means for performing a second operation of arithmetic addition (28; 80) of a value of one of several second products, denoted m.n, and a value of said variable u, - means for performing a third operation of division of the variable u by a power of 2, denoted 2 ω where ω is the radix, according to a third relationship u: = u 2 ω, - a Carry-Save adder adapted to receive at the input the variable u in the form of a Carry-Save ordered pair and said value of one of several products, denoted a ι. b, respectively m.n, and to provide at the output the result of the first, respectively the second, arithmetic addition operation in the form of a Carry- Save ordered pair, and - means for allocating to the variable u the value obtained at the output of said at least one Carry-Save adder, and • means for calculating and storing a carry digit, denoted R e, which is at risk of being lost by the division of each variable C and S by the power of 2; • means for dividing each variable C and S by the power of 2; - means (162: 236) for recombining the variable u at least on the basis of values of variables C and S of the Carry-Save ordered pair, - means (166; 238) for reducing the variable u, wherein said means for recombining the variable u and said means for reducing are connected together so as to overlap their operation under control of control means (156; 214);